Question: Which battle occurred first, the Battle of Cold Harbor or Operation Diadem?

Context paragraphs:
Cold Harbor Union order of battle: The following Union Army units and commanders fought in the Battle of Cold Harbor (May 31–June 12, 1864) of the American Civil War.  The Confederate order of battle is listed separately.  Order of battle compiled from the army organization May 31, 1864, army organization May 26-June 3, 1864, the casualty returns and the reports.

Battle of Gaines's Mill: The Battle of Gaines's Mill, sometimes known as the First Battle of Cold Harbor or the Battle of Chickahominy River, took place on June 27, 1862, in Hanover County, Virginia, as the third of the Seven Days Battles (Peninsula Campaign) of the American Civil War.  Following the inconclusive Battle of Beaver Dam Creek (Mechanicsville) the previous day, Confederate General Robert E. Lee renewed his attacks against the right flank of the Union Army, relatively isolated on the northern side of the Chickahominy River.  There, Brig. Gen. Fitz John Porter's V Corps had established a strong defensive line behind Boatswain's Swamp.  Lee's force was destined to launch the largest Confederate attack of the war, about 57,000 men in six divisions.  Porter's reinforced V Corps held fast for the afternoon as the Confederates attacked in a disjointed manner, first with the division of Maj. Gen. A.P. Hill, then Maj. Gen. Richard S. Ewell, suffering heavy casualties.  The arrival of Maj. Gen. Stonewall Jackson's command was delayed, preventing the full concentration of Confederate force before Porter received some reinforcements from the VI Corps.

Shohola train wreck: The Great Shohola train wreck occurred on July 15, 1864 during the American Civil War on the broad gauge Erie Railroad 1⁄ miles (1.5 mi ) west of Shohola, Pennsylvania, killing at least 60 people.  Aboard the 18 car train were 833 Confederate prisoners of war (many captured at the Battle of Cold Harbor) and 128 Union guards from the Veteran Reserve Corps.  The prisoners were being taken from Point Lookout, Maryland to newly constructed Camp Rathbun at Elmira, New York, built to house 10,000 inmates.  They had begun their journey by steamer, traveling along the Atlantic coast from Maryland to New Jersey.  Here they were switched to railroad for the final 273 mi to Elmira.

Operation Diadem order of battle: Operation Diadem order of battle is a listing of the significant formations that were involved in the fighting on the Winter Line and at the Anzio bridgehead south of Rome during "Operation Diadem" in May - June 1944 which resulted in the Allied breakthrough at Cassino and the breakout at Anzio leading to the capture of Rome.

Cold Harbor, Virginia: Cold Harbor is an unincorporated community in Hanover County, Virginia.  The Battle of Cold Harbor was fought in the area in 1864, during the American Civil War.

Battle of Cold Harbor: The Battle of Cold Harbor was fought from May 31 to June 12, 1864, with the most significant fighting occurring on June 3.  It was one of the final battles of Union Lt. Gen. Ulysses S. Grant's Overland Campaign during the American Civil War, and is remembered as one of American history's bloodiest, most lopsided battles.  Thousands of Union soldiers were killed or wounded in a hopeless frontal assault against the fortified positions of Confederate Gen. Robert E. Lee's army.

Operation Diadem: Operation Diadem, also referred to as the Fourth Battle of Monte Cassino or, in Canada, the Battle of the Liri Valley, was an offensive operation undertaken by the Allies of World War II (U.S. Fifth Army and British Eighth Army in May 1944, as part of the Italian Campaign of World War II.  "Diadem" was supported by air attacks called Operation Strangle.  The opposing force was the German 10th Army.

Battle of Alhandic: The Battle of Alhandic (Spanish: "Batalla de Alhandic" ), also known as Zamora's trench Battle ("Batalla del Foso de Zamora"), was a battle that occurred on August 5, 939 in the city of Zamora, Spain.  The battle occurred when the troops of Abd-ar-Rahman III assaulted the walls of Zamora.  The defending troops were those loyal to Ramiro II of León, King of the Kingdom of Leon.  The fighting was so bloody that the tide of the battle did not turn until the ditch surrounding the city walls was entirely filled with corpses.  The troops of Aberraman III won the day and were able to seize the city of Zamora.  This battle should not be confused with the Day of Zamora ("Día de Zamora" or "Jornada del Foso de Zamora") which took place a few decades before in the year 901.

Terrence Begley: Sergeant Terrence Begley (died 25 August 1864) was an Irish soldier who fought in the American Civil War.  Begley was awarded the United States' highest award for bravery during combat, the Medal of Honor, for his action during the Battle of Cold Harbor in Cold Harbor, Virginia on 3 June 1864.  He was honored posthumously with the award on 1 December 1864.

Cold Harbor Confederate order of battle: The following Confederate States Army units and commanders fought in the Battle of Cold Harbor (May 31–June 12, 1864) of the American Civil War.  The Union order of battle is listed separately.  Order of battle compiled from the army organization during the battle and the reports.

Supporting paragraphs: Battle of Cold Harbor Operation Diadem
Answer: Battle of Cold Harbor