According to wikipedia (sorry) the 1st army was 4 divisions, pattons 3rd army had 19 divisions, the 9th army had 16 and the 15th army had 9. Plus the corps sizes are all over the place. I was wondering why this was the case?
My understand, which could be very wrong, is with the British and Canadians generally 2 divisions make a corps, 2 corps make an army, and 2 armies make an army group.
During WWII, the United States generally had no fixed size for the number of divisions within a corps (as few as 2, as many as 6), or the number of corps within an Army. More corps arrived later on in order to manage the increasing number of divisions (eventually 42 infantry, 16 armored, and 4 airborne) that were in the ETO. Divisions were often moved between corps in order to give them more punching power for an attack, or to assign them to a quieter area where they could recuperate. When a corps boundary was moved, which happened quite often, the division that got "jumped" over was often just reassigned.
Corps were even moved between armies. As new corps moved up and were inserted into the line, more space was needed. Whole armies were even shifted; the Ninth Army initially moved up to the line in between First and Third Armies in September 1944, but was shifted to the very north of the American lines, abutting the British, in November.
These movements could also happen in the case of emergencies, such as during the Battle of the Bulge, where a frantic series of movements took place in the opening days of the battle. The US First and Ninth Armies were actually placed under administrative control of the British; the First Army until the Battle of the Bulge ended, and the Ninth Army until the British crossed the Weser River. This resulted in the 8th Infantry Division being by far the furthest north US unit, in the vicinity of Schwerin in far northeastern Germany when the war ended.
The US had the following army corps in the European Theater when the war ended:
V, VI, VII, VIII, XII, XIII, XV, XVI, XVIII Airborne, XIX, XX, XXI, XXIII
Let's take a look at General Joseph Lawton Collins' VIII Corps. It pinged around between the First, Third, and Ninth Armies during its service in the ETO.
VIII Corps was a part of the following armies while in the ETO:
| Army | Dates |
|---|---|
| First | 15 June-31 July 1944 |
| Third | 1 August-4 September 1944 |
| Ninth | 5 September-21 October 1944 |
| First | 22 October-19 December 1944 |
| Third | 20 December 1944-21 April 1945 |
| First | 22 April-5 May 1945 |
| Ninth | 6-8 May 1945 |
At some point or another, all the following divisions were assigned to VIII Corps. I have just included the time that they were with VIII Corps and not noted the superordinate Army.
| Division | First Time | Second Time | Third Time | Fourth Time | Fifth Time |
|---|---|---|---|---|---|
| 1st Infantry Division | 27-28 April 1945 | ||||
| 2nd Infantry Division | 18 August-21 October 1944 | ||||
| 4th Armored Division | 22 January-8 March 44 | 15-31 July 1944 | 2-11 January 1945 | 4-8 April 1945 | 17-21 April 1945 |
| 4th Infantry Division | 16-18 July 1944 | 7 December 1944 | 27 January-19 March 1945 | ||
| 6th Armored Division | 8 February-3 March 44 | 25 July-19 September 1944 | 11 February-5 March 1945 | 17 April 1945-VE Day | |
| 8th Infantry Division | 1 August-21 October 1944 | ||||
| 10th Armored Division | 17-19 December 1944 | ||||
| 11th Armored Division | 23-30 December 1944 | 15 January-11 March 1945 | |||
| 17th Airborne Division | 1-25 January 1945 | ||||
| 28th Infantry Division | 19 November 1944-6 January 1945 | ||||
| 29th Infantry Division | 19 August-4 September 1944 | ||||
| 65th Infantry Division | 4-16 April 1945 | ||||
| 76th Infantry Division | 19-24 January 1945 | 22 April 1945-VE Day | |||
| 79th Infantry Division | 1-31 July 1944 | ||||
| 82nd Airborne Division | 19 February-12 March 1945 | 19 June-11 August 1944 | 17 December 1944 | ||
| 83rd Infantry Division | 8 April-24 June 1944 | 15-31 July 1944 | 3 August-4 September 1944 | 11-21 October 1944 | 11 November 1944 |
| 87th Infantry Division | 29 December 1944-13 January 1945 | 25 January 1945-VE Day | |||
| 89th Infantry Division | 23 March 1945-VE Day | ||||
| 90th Infantry Division | 19 June-31 July 1944 | 26 January-11 March 1945 | |||
| 95th Infantry Division | 29 January-12 February 1945 | ||||
| 101st Airborne Division | 15 June-11 August 1944 | 17-20 December 1944 | 29 December 1944-19 January 1945 | ||
| 106th Infantry Division | 29 November-19 December 1944 |
Sources:
ETO Order of Battle- DIVISIONS
US Army in World War II, by Rich Anderson
Corps, Armies, and Army Groups, have no fixed organization. They are task organized depending on the situation, and changed as as the situation changes. This is true of British organizations as well as US.
You don't say which Wiki article you are looking at, but those numbers are only good for a very small timeframe in any case. For example, First Army had 15 divisions in 3 corps in December 1945, while Third Army had 16 divisions in 3 corps.
The idea that the the British used a 2-2-2 formation is wrong. For example, XXX Corps had 3 divisions (Guards Armoured Division, 43rd (Wessex) Infantry Division, 50th (Northumbrian) Infantry Division) plus an additional armoured brigade (8th) assigned to it during Market Garden, while the UK Second Army had 3 corps assigned (XXX, XII, and VIII). 21st Army Group had at least 4 armies assigned to it during the Battle of the Bulge, as the US First and Ninth Armies were temporarily attached.