For full XP, a group has to have Minions, LTs, and Bosses (EB/AV not required, though any group with EBs/AVs must have the other three to receive full XP on the EBs/AVs as well). This is to discourage people from making an "all boss" group, for example.
As for specific composition, the game "randomly" picks from available units, based on the player's number of teammates (or their difficulty rating, whichever is higher). For 1 player, the game usually picks 3 minions for a group, but a single LT standing by themselves isn't unheard of. At 2 players, you usually add an extra minion or LT in a group, or you'llg et a group of 2 LTs and 2 Minions. At 3, it starts to put bosses in, sometimes at the expense of a minion or LT, but sometimes not (someone feel free to correct me on this point!). Having "bosses disabled" will still spawn bosses, but downgrade them to LTs (and it will downgrade any EBs into Bosses). This is something you can NOT control for. If you want a spawn to have three LTs and only three LTs, someone can come it at x1 and only see 1 LT, while someone else can come it at x8 and see like 6-10 of them.
Some specific missions in the game subvert these rules (TFs with multiple EB/AVs in a group, for example), but those are hand-coded to be exceptions, and are not available for use in AE missions.