Currently, there is only the addGroup method which adds a group to a player. I want to set a players group, is this hidden in the code, or is it currently not possible.

please see:
https://github.com/MilkBowl/Vault/blob/master/src/net/milkbowl/vault/permission/Permission.java#L491

I don't believe you looked through all of the permission interface.

That adds a Sub-Group to a player. It doesn't set the Primary group of a player, which is what I want.

Vault does not recognize sub-groups. There are only groups. How this interfaces with whatever permission manager is for you to figure out. I assume you're using GM. If this is the case, GM uses special methods to make it so a player has a 'primary' group and all groups are sub-groups. If you're looking to support this, hook GM directly not Vault.