I don't really get the problem you are having. You already answered your question yourself. Add a `mapping(uint => uint) mintGroup` or whatever variable type you need to map the specific `tokenId` to the group.
Transfering the token does not change its id and thus will not change the mapping.

You could also add it as a variable in the token itself but handling those is really uncomfortable in comparison to using `mapping`.

EDIT: Beware that a token standard like [ERC721][1] is needed to accomplish that. ERC20 standard will not work because every token is the same and therefore cannot store information about the reason of minting it.


  [1]: https://github.com/ethereum/EIPs/pull/841