## Automorphism of a subgroup of an abelian group

Let $A \cong C_n^{m}$ be an abelian group consisting of the direct product of $C_n$ $m$-times for $m \in \mathbb{N} \cup \{\infty\}$. Let $H \leq A$.

My question is this: if $\phi$ is an automorphism of $H$ then does $\phi$ extend to an automorphism of $A$? If not in general, what if $n$ is prime?