Here is a more in depth post by Duckroll circa when Index was still alive:
There are currently only two development studios in the Index Consumer Software Division. There's the 1st Production Studio and the 2nd Production Studio.
The 1st Production Studio is where most of the games come from. EO games, Devil Survivor games, SMT4, whatever else.
The 2nd Production Studio is Hashino's Persona team which is its own thing now. They produced P4, P3P, P4G, P4 Arena, and Catherine. They are currently working on Persona 5.
In the past it was a single production studio when it was Atlus R&D1. After Cozy Okada left, Hashino produced almost everything for a time, as well as directing many of them - Maken X, SMT3, DDS, P3, EO1, etc. But as they started to have more output, and as Persona became increasingly popular, they split the Persona team into its own secondary studio.
Actual teams seem to be formed on a project to project basis, so there are no fixed teams other than those which make sense when it comes to pumping out sequels. When a series stops getting sequels, the team members are moved onto other projects.