Mwhite4348

I am new here, so I do not really understand how this forum thing works yet, so bare with me. When you are identifying whether something is a subgroup of a group (I can do that part), how do you give a "complete list of all subgroup relations?" I keep thinking that this is the skeleton diagram. i.e. Z4 - {0} - {0,2} That is an example that our professor gave in class, but I am not sure that I understand that very well either. I do, however, understand that Z4 is modulo 4, but how does the {0} and (0,2} get pulled out? There are many more relations.