Now, the question asks me what the subgroups of order $4$ are of this relation and then to give them as sets and identify the group of order $4$ that each of the subgroups is isomorphic to. How do I go about doing that? Here is what I got.
I know this relation has $8$ elements: $(0,0),\ (0,1),\ (0,2),\ (0,2),\ (0,3),\ (1,0),\ (1,1),\ (1,2),\ (1,3),$
I'm completely lost from this point. How do I find a subgroup of a relation like this?