Let G be a group and let G' be its commutator. Prove there is a one-to-one correspondence between the set of normal subgroups of G whose quotient is abelian and the set of all subgroup of G/G'.
I tried to use the fact that the commutator is a subgroup of any normal subgroup whose quotient is abelian but I can't seem to realize what correspondence I should be looking at. I would appreciate your help.
The allegedly duplicated question does not talk about the correspondence aforementioned nor does it help me in any way getting what I need to do understood.