The number of subgroups of $\mathbb{Z}_3\times \mathbb{Z}_{16}$ I want to calculate the number of subgroups of $\mathbb{Z}_3\times \mathbb{Z}_{16}$. But it is just that to calculate the number of subgroups of $\mathbb{Z}_3$ and $\mathbb{Z}_{16}$. It is easy to calculate $Z_3$, but how to deal with $\mathbb{Z}_{16}$

Hint:  $\mathbb{Z}_3\times \mathbb{Z}_{16} \cong \mathbb{Z}_{48}  $ and calculate the number of divisors of 48.
