Find all subgroups of $\mathbb{Z}_5 \times \mathbb{Z}_{125} \times \mathbb{Z}$ up to isomorphism
My try:
I know there are subgroups of the form $H_1 \times H_2 \times H_3 $ when $H_1\le\mathbb{Z}_5 , H_2\le\mathbb{Z}_{125} , H_3\le\mathbb{Z}$.
How can I find the subgroups which are not of this form and how can I know that I found all of them?