Let $G$ be a finite abelian group of order $p^n$, where $p$ is a prime number. How to find the number of subgroups of order $p$?
i.e. find a formula for the number of subgroups of order $p$.
I know that $G$ is isomorphic to a direct product of cyclic $p$-groups. There are too many cases. I don't know the appropriate approach. It seems that there should be a formula that works universally.