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.

None of the terms you use is standard. Indeed, I can't decide what you mean and I'm a group theorist.

 

Are you asking for all subgroups of a given group?

 

Well, obviously {0} is a subgroup of Z_4, as is {0,2}, and there can be no other subgroups for many reasons (simplest is because if the subgroup contained 1 or -1 then it is the whole of Z_4). What exactly do you mean be "realations"? what do the - symbols you've used signify?