abstract algebra question

Is there a shortcut to prove that Z, Q, R, S are pairwise nonisomorphic? I can split it into three proofs and do them individually, but I feel like there has to be some property that covers all the cases.

It can't be just the fact that Z < Q < R < S because the subset of even integers is isomorphic to the set of all integers.

Anyone care to push me in the right direction, if there is one?

>>11
This needs a proper demonstration. I don't see how they can be isomorph, even as Z-modules. I mean, C is of dimension 2 over R as his algebraic closure (cloture ?)... And if you have example of space, set, etc that are isomorph as certain type of structure but not for other type, I'd be glad to acknowledge them.