I am not really sure if this is the correct section for this question, but the question I am given is this:

Describe all the subgroups of the group Z^2 which consists from all 2 dimensional vectors with integer components.

I am not looking for an answer at all.

I just don't really understand the question, know where to start, or even a method to do this. Any help that you are able to give would be most appreciated.