I'm supposed to determine the isomorphism type of $G/\langle 15\rangle $ and $G/\langle 9 \rangle$.
I've determined the order of both subgroups ($\langle 15\rangle$ and $\langle 9\rangle$), and it is $2$. Therefore, the order of quotient groups is $4$ and I'm left with two possibilities for the isomorphism type of each quotient group i.e. $Z_4$ and $Z_2 \times Z_2$. However, I'm a bit stuck on how to determine which is which other than simply calculating the actual groups (Which I would like to avoid). I've realized that all the groups in the problem are solvable ($p$-groups) so I guess I should use this somehow, but I'm not really sure how!
Any help would be well appreciated.
Thanks in advance.