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5 of 8 edited title

Finding the number of subgroups of order $p^2$ of $\mathbb{Z}_{p^3} \bigoplus \mathbb{Z}_{p^2} $.

What is the number of subgroups of $\mathbb{Z}_{p^3} \bigoplus \mathbb{Z}_{p^2} $?

I'm not really sure how to figure it out. I tried seeing subgroups of each $\Bbb Z_{p^n}$ but I'm not sure I'm going to get them all.