I'm trying to solve the problem of finding all groups $G$ such that there exists a surjective homomorphism $\mathbb Z/n\mathbb Z \to G$, if $n$ is greater than or equal to 2.
I'm really not sure where to start, is the First Isomorphism Theorem applicable in this case?
Hint: Since $\Bbb Z/n\Bbb Z$ is cyclic, so is $G$. Use Lagrange's theorem and the First Isomorphism Theorem to look at normal subgroups of $\Bbb Z/n\Bbb Z$. Also, note that all subgroups of an abelian group are normal.