Question: What is the abbreviation of the military entity the Saint Patrick's Battalion fought as?

Context paragraphs:
15th Battalion (Australia): The 15th Battalion was an infantry battalion of the Australian Army.  Formed in 1914 as part of the all-volunteer Australian Imperial Force from Queensland and Tasmanian recruits, the battalion fought during the Gallipoli Campaign and on the Western Front during the First World War.  It was disbanded after the war in 1919, but later re-raised as a part-time Citizens Forces unit based in Queensland in 1921, consisting of a mixture of volunteers and conscripts.  Economic pressures and limited manpower resulted in the battalion being amalgamated with other battalions a couple of times during the inter-war years.  In mid-1939, as rising tensions in Europe led to an expansion of the Australian military, the battalion was re-formed in its own right.  During the Second World War the 15th Battalion was mobilised for wartime service and initially undertook defensive duties in Australia before taking part in the fighting against the Japanese in New Guinea and Bougainville in 1943–1945.  The battalion was disbanded in 1946 and never re-raised.

22nd Battalion (New Zealand): The 22nd Battalion, also known as the "Wellington Battalion", was an infantry battalion of the New Zealand Military Forces, which served during the Second World War.  After undertaking defensive duties in the United Kingdom from mid-1940 until early 1941, the battalion then fought in the Battles of Greece and Crete where it suffered heavy casualties and lost a large number of men who were taken as prisoners of war.  After being rebuilt, the battalion fought in North Africa, fighting in Operation Crusader, before undertaking garrison duties in Syria.  It later fought in the First Battle of El Alamein during which they suffered heavy casualties at Ruweisat Ridge.  Re-formed, the battalion later fought in the Second Battle of El Alamein.  In late 1943, the battalion was transferred to Italy where it fought for the remainder of the war, fighting battles around Cassino and along the Adriatic coast, before entering Trieste in the final days of the war.  After the war, it performed occupation duties in Japan until it was disbanded in 1948.

2/29th Battalion (Australia): The 2/29th Battalion was an infantry battalion of the Australian Army, which served during the Second World War.  Formed in October 1940, the battalion served in Malaya as part of the 27th Brigade, which was assigned to the 8th Division.  Recruited mainly from volunteers drawn from the state of Victoria, after completing its training around Bonegilla and then Bathurst, the 2/29th Battalion was sent to Malaya in August 1941 along with the rest of the 27th Brigade to bolster the Australian force there and subsequently fought in the Malayan Campaign following the Japanese attack in December 1941.  The battalion fought several delaying actions along the west coast, including fighting around Bakri and Muar, and in Johore, before Allied forces withdrew across the Causeway to Singapore.  The battalion later took part in the defence of Singapore in February 1942, but was captured after the garrison capitulated on 15 February.  They spent the remainder of the war as prisoners of war, with many dying in captivity.

Saint Patrick's Battalion: The Saint Patrick's Battalion (Spanish: "Batallón de San Patricio" ), formed and led by John Riley, was a unit of 175 to several hundred immigrants (accounts vary) and expatriates of European descent who fought as part of the Mexican Army against the United States in the Mexican–American War of 1846–8.  Most of the battalion's members had deserted or defected from the United States Army.  The Battalion served as an artillery unit for much of the war.  Despite later being formally designated as two infantry companies, it still retained artillery pieces throughout the conflict.  In many ways, the battalion acted as the sole Mexican counterbalance to the recent U.S. innovation of horse artillery.  The "San Patricios" were responsible for the toughest battles encountered by the United States in its invasion of Mexico, with Ulysses S. Grant remarking that "Churubusco proved to be about the severest battle fought in the valley of Mexico".

Mexican Armed Forces: The Mexican Armed Forces ("Fuerzas Armadas de México") are composed of two independent entities: the Mexican Army and the Mexican Navy.  The Mexican Army includes the Mexican Air Force ("FAM").  The Presidential Guard, Military Police, and Special Forces are part of the Army, but have their own chains of command.  The Mexican Navy includes the Naval Infantry Force and the Naval Aviation ("FAN").

4th Battalion (Australia): The 4th Battalion was an infantry battalion of the Australian Army.  Originally raised as part of the First Australian Imperial Force during the First World War, the battalion formed part of the 1st Brigade, attached to the 1st Division.  During the war the battalion fought at Gallipoli and in the trenches on the Western Front, before being disbanded in 1919.  In 1921, the battalion was re-raised as a militia unit and designated as the "4th Battalion (Australian Rifles)", adopting the designation of the Australian Rifles militia unit from which many of the battalion's recruits had come during the war.  In 1930, the battalion was amalgamated with the 3rd Battalion (Werriwa Regiment) and they remained linked until 1936, when they were delinked.

Saul, County Down: The townland lies to the east of Downpatrick and has strong links with Saint Patrick.  It is claimed that when Saint Patrick arrived in Ireland in 432, strong currents swept his boat through the Strangford Lough tidal narrows and he landed where the Slaney River flows into the lough.  The local chieftain, Dichu, was quickly converted and gave him a barn for holding services.  Allegedly, Saint Patrick died in Saul on 17 March 461 and is buried in nearby Downpatrick.  The modern "Saint Patrick's Memorial Church" is built on the reputed spot of this building and includes a replica round tower.  To the east of the parish is Saint Patrick's Catholic Church.

Saint Patrick's Breastplate: Saint Patrick's Breastplate, a Prayer of Protection, also known as The Deer's Cry or The Lorica of Saint Patrick or Saint Patrick's Hymn is a lorica whose original Old Irish lyrics were traditionally attributed to Saint Patrick during his Irish ministry in the 5th century.  In 1889 it was adapted into the hymn I Bind Unto Myself Today.  A number of other adaptions have been made.

25th Battalion (Australia): The 25th Battalion was an infantry unit of the Australian Army.  Raised in early 1915 as part of the Australian Imperial Force during the First World War, the battalion fought at Gallipoli and in the trenches along the Western Front, before being disbanded in early 1919.  In mid-1921, it was re-formed as a part-time unit based in the state of Queensland.  Throughout the 1930s, the battalion was merged briefly with the 49th Battalion as a result of manpower shortages, but was later re-raised in its own right.  During the Second World War, the 25th deployed to New Guinea where they fought the Battle of Milne Bay in August and September 1942.  Later in the war, the 25th took part in the Bougainville Campaign.  During the post-war period, the 25th Battalion became part of the Royal Queensland Regiment, variously forming battalion or company-sized elements, before being merged with the 49th Battalion to form the 25th/49th Battalion, Royal Queensland Regiment.

Saint Patrick's Saltire: Saint Patrick's Saltire or Saint Patrick's Cross is a red saltire (X-shaped cross) on a white field, used to represent the island of Ireland or Saint Patrick, the patron saint of Ireland.  In heraldic language, it may be blazoned "Argent, a saltire gules".  Saint Patrick's Flag ("Bratach Naomh Pádraig") is a flag composed of Saint Patrick's Saltire.

Supporting paragraphs: Saint Patrick's Battalion Mexican Armed Forces
Answer: FAM