A few notes on the 4 groups - from their respective Wiki pages ...
10 Group
The group was re-formed on 1 June 1940 within Fighter Command to enable neighbouring No. 11 Group to function more efficiently. Its area of operation was the south-western region of England.
10 Group supported 11 Group in the Battle of Britain by rotating squadrons, providing additional fighter support when needed, and supplying additional pilots.
As well as providing support for 11 Group, 10 Group also had some squadrons of aircraft that could not be risked in the Battle of Britain (Gloster Gladiator, Boulton Paul Defiant).
11 Group
11 Group's most famous period was during the Battle of Britain when, due to its position, 11 Group bore the brunt of the German aerial assault. Pilots posted to squadrons in 11 Group knew that they would be sent into certain action while pilots and squadrons transferring out of 11 Group knew that they were going to comparatively safer duty.
12 Group
It was the group responsible for aerial defence of the Midlands, Norfolk, Lincolnshire and North Wales.
As well as regional defence, 12 Group were also supposed to fly cover for 11 Group airfields during the Battle of Britain, but several times, these fields were left undefended. When Park complained about it, Leigh-Mallory responded that in order to test his Big Wing theory (espoused by Squadron Leader Douglas Bader), more time was needed to get the necessary squadrons airborne.
13 Group
As well as guarding the north during the Battle of Britain, 13 Group also provided reserve squadrons and pilots to the more beleaguered 11 Group, and provided quieter bases for squadrons to recuperate from operations.
From this it's obvious that 11 Group was the main front-line formation, with the other 3 groups providing various degrees of support. You'll find the complete order of battle here ...
https://en.wikipedia.org/wiki/RAF_Fighter_Command_Order_of_Battle_1940#Fighter_Command
It shows that 11 Group contained many more squadrons than the other groups.
Hope this is useful rather than annoying.
