Question: What subtypes of Magic monsters are there?

Creature type (Dungeons & Dragons)

Creature type (''Dungeons & Dragons'')
In the Dungeons & Dragons fantasy role-playing game, creature types are rough categories of creatures which determine the way game mechanics affect the creature. In the 3rd edition and related games, there are between thirteen and seventeen creature types. Creature type is determined by the designer of a monster, based upon its nature or physical attributes. The choice of type is important, as all creatures which have a given type will share certain characteristics (with some exceptions). In 3rd and 3.5 editions, type determines features such as hit dice, base attack bonus, saving throws, and skill points.
Certain magic items and special abilities, such as the ranger's favored enemy ability (prior to 4th edition) and bane weapons (in 3rd and 3.5 editions) interact with creature type.
3rd and 3.5 editions
Aberration

An aberration can have a bizarre anatomy, strange abilities, alien mindset, or any combination thereof. Examples include the beholder, illithid (mind flayer) and rust monster. The rules state that all aberrations have darkvision out to 60 feet. As a group, they have no other special abilities or immunities.[1]
Animal

The game classifies "Animals" as living, nonhuman vertebrate creatures, with no innate magical abilities or capacity for language or culture. Virtually all animal type monsters are based on real world animals. Creature entries based on mythological, fictional, or nonexistent animals are usually classified as magical beasts (see below). Besides ordinary fish, birds, reptiles and mammals, the animal type is also applied to depictions of dinosaurs, prehistoric animals, and "dire" or specially modified, often larger and scarier, versions of real world animals.
Some real world animals are not given the animal type in the game. Examples include arthropods (insects, spiders, etc.) and worms, which the game classifies as "vermin" (see below) and not animals. Mollusks, such as octopuses, are often classified as animals despite their real-world bases being more closely related to vermin type creatures. Creatures deemed inconsequential by DMs or designers are not given any creature type at all, instead being treated as "set dressing" unless a specific game effect targets such non-creatures. Examples include actual-sized spiders, sparrows, fleas, worms, shellfish, and mice. "Swarm" type creatures are occasionally written to represent such otherwise nonthreatening creatures if they were to group together by some force of magic within the game world.
Under the rules of D&D, animal type creatures do not have an Intelligence score higher than 2. When a designer makes a change to an animal creature that increases its Intelligence or grants it additional abilities, the designer is encouraged to also change the creature's type, usually from animal to magical beast.
When real world animals are rendered as vermin (see below) in D&D, they have no Intelligence scores at all.
Beast
In 3rd edition, the beast type was used for nonhistoric and fantastic, but not necessarily magical vertebrates. The beast type was merged into the animal type in 3.5 edition.
Construct

A construct is either an animated object of some sort, or an artificially crafted creature.
Most construct are mindless automatons, obeying their creator's commands absolutely. This makes them immune to bribery and absolutely trustworthy, although some take their orders literally and fail to consider their intent. A few constructs, however, such as Inevitables, are as intelligent as living creatures.
As they lack a metabolism or internal organs, constructs are immune to many effects, such as poison, fatigue, exhaustion, disease, ability drain, level drain, death effects and critical hits.
Constructs are almost always created by wizards, sorcerers or clerics, though some are created by other character classes or spell-casting monsters. The first step in making a construct, sometimes performed by a non-spellcaster, is building the body; the second is a ritual requiring the casting of specific spells to bind a spirit of some kind (typically an elemental drawn from the Inner Planes) into the body and imbue it motion and special abilities. Most constructs are made of metal, but other materials — including bone and corpses—can be used.
The creation methods for certain constructs are unknown, or might have much more stringent requirements. Warforged, for example, can only be created with the help of specific artifacts, the creation forges.
Golems are the best-known type of construct.
Deathless

Deathless are cadavers animated or empowered by Positive energy (whereas Undead are animated or empowered by Negative energy).
Dragon

A dragon is a reptile-like creature, usually winged, and tends to have magical or unusual abilities.
Elemental

An elemental is composed of one or more of the four classical elementals of air, earth, fire, or water. Elementals almost always have the extraplanar subtype. Most natives of the elemental planes are elementals, however there are some exceptions, for example most types of genies are native to the elemental planes, however genies are outsiders.
Fey

A fey is a creature which usually has supernatural abilities and a human-shaped form. A fey also usually connected to nature, or some other force or place. Many are based on faeries from mythology. Fey share a common native language called Sylvan.
Giant

A giant is a humanoid-shaped creature of great strength and size. All giants have low-light vision. As a group, they have no other special abilities or immunities.
Humanoid

Humanoids are bipeds of Small or Medium size with few or no supernatural or extraordinary abilities. Most humanoids can speak, and usually have well-developed societies. Larger bipeds are giants (see above), and bipeds with more special abilities are fey, monstrous humanoids or outsiders. In 3.0 and 3.5 editions, the Player's Handbook races (humans, dwarves, elves, gnomes, halflings, half-elves, half-orcs) are all humanoids.
Prior to 3rd edition, "humanoid" referred exclusively to orcs, goblinoids and similar creatures, while more advanced creatures such as Elves and Dwarves were referred to as demihumans and humans were outside of both categories.
Magical beast

A magical beast is similar to an animal in many ways, but usually has a higher intelligence, and possesses supernatural or extraordinary abilities. Examples include manticores and pegasi. All magical beasts have darkvision out to 60 feet as well as low-light vision; as a group, they have no other special abilities or immunities.
Monstrous humanoid

A monstrous humanoid is similar to a humanoid (see above), but usually has monstrous or animalistic features. Examples include harpies and minotaurs. All monstrous humanoids have darkvision out to 60 feet; many have supernatural abilities as well.
Ooze
An ooze is an amorphous or mutable creature without a single solid form. Oozes are usually mindless and homogeneous, and reproduce by simply splitting into two. The most famous ooze is the gelatinous cube. Many oozes dwell underground, and most secrete an acid from their skin that dissolves flesh and other materials rapidly. Oozes are essentially blind, but an ability called "blindsight", which allows them to discern nearby objects and creatures without needing to see them, more than compensates for this.
Outsider

An outsider is at least partially composed of the essence (if not the material) of a plane other than the Material Plane. Most outsiders (including angels, demons, devils and most genies) have the extraplanar subtype and are native to another Plane, such one of the Outer Planes or Elemental Planes; the rest (such as aasimars, tieflings and couatls) have the native subtype and are native to the Prime Material Plane. All outsiders have darkvision out to 60 feet. As a group, they have no other special abilities or immunities.
Planetouched

Planetouched are mortal creatures whose ancestors were extraplanar creatures such as celestials, fiends, or elementals. Aasimar (humans with celestial blood), tieflings (humans with fiendish blood) and genasi (humans with elemental blood) are the primary planetouched races. Other examples include tanarukk (orcs descended from demons) and celadrin (elves descended from celestials).
Plant

A plant is a vegetable creature that can perceive and affect the world in some way. Ordinary plants are considered objects rather than creatures.
Shapechanger

Shapechanger was a type in 3rd edition. It was converted to a subtype in 3.5 edition.
Undead

An undead is a once-living creature animated by spiritual or supernatural forces. Some, such as ghosts and vampires, have Intelligence scores; others, such as zombies, do not. All undead have darkvision out to 60 feet and immunity to mind-affecting effects, poison, sleep effects, paralysis, stunning, disease, death effects, critical hits, nonlethal damage, ability drain, or energy drain. In general, cleric spells that heal other creatures damage undead, and vice versa. Most undead can be "turned" (destroyed or driven away) by a Paladin or good Cleric or "rebuked" (controlled or made to cower in awe) by an evil Cleric.
Vermin
A vermin can be an insect, arachnid, arthropod, worm, or other invertebrate. Some have magical abilities, and others are giant versions of real insects. Most vermin are considered mindless individually. Since many vermin are too small to model individually, they are often represented as swarms (clusters that act like single creatures and sometimes have hive minds).
4th edition types, origins and keywords
In 4th edition, type was split into types and origins. Beast, humanoid and monstrous humanoid remained classified as creature types, while many subtypes from earlier editions were converted to keywords, as were some types, such as undead and construct.
Types
Animate
Animates are magically animated creatures, such as golems, zombies and shambling mounds. Animates generally possess the construct, plant or undead keyword. Intelligent undead and plant creatures generally belong to the humanoid or magical beast type rather than the animate type, and the Warforged are humanoids with the living construct keyword rather than animates.
Beast
The beast type encompasses mundane animals, as well as unintelligent monstrous animals, such as basilisks, hydras, owlbears and purple worms, and non-intelligent non-humanoid creatures which do not fit into another category, such as oozes.
Humanoid
Intelligent living or undead creatures which are at least roughly humanoid generally belong to the humanoid type. Examples include humans, driders, giants, vampires and warforged.
Magical Beast
The magical beast type encompasses intelligent non-humanoid living or undead creatures, such as beholders, dragons and treants.
Origins
Aberrant
Aberrant creatures are native to or corrupted by the Far Realm. Examples of aberrants include aboleths, beholders and illithids.
Elemental
Elemental creatures are native to the Elemental Chaos. Many elementals from earlier editions have been converted to elemental humanoids or elemental magical beasts, as have many demons and yugoloths, as well as the slaadi. Other examples of elementals include archons (elemental warriors unrelated to the angelic archons of earlier editions), genies and the tarrasque.
Fey
Fey creatures are native to the Feywild. Elves, Drow, Eladrin and Gnomes are considered Fey in 4th Edition, other examples of Fey include displacer beasts, owlbears, cyclopses and treants.
Immortal
Immortal creatures are native to the Astral Sea. Many outsiders from earlier editions have been converted to immortal humanoids or immortal magical beasts. Examples of immortals include angels, devils.
Natural
Creatures with the natural origin are native to the natural world. Examples include humans, orcs, and many (but not all) varieties of giants, dragons and monstrous animals.
Shadow
Shadow creatures are native to or otherwise connected to the Shadowfell. Examples include ghosts, nightmares, specters and wraiths.
Keywords

The Construct, Dragon, Giant, Ooze, Plant, Shapechanger and Undead creature types were converted to keywords in 4th edition, as were many subtypes.
5th edition
Fifth edition's approach to creature types is similar to third edition's. The outsider type has been split into celestials and fiends, animal and vermin type have been combined into beast type, and several types have been removed (magical beast, monstrous humanoid, etc.) and the catch-all monstrosity type has been added.
Aberrations
Beasts
Celestials
Constructs
Dragons
Elemental
Fey
Fiends
Giants
Humanoids
Monstrosities
Oozes
Plants
Undead