What are all the homomorphic images of Z15 (up to isomorphism)?
a homomorphic image of a group G is a group in the form G/K, where K is a normal subgroup of G. in your case $\displaystyle G=\mathbb{Z}/15 \mathbb{Z}$ is abelian. so K is any subgroup of G. find the subgroups of G and then
see what G/K are! the final answer is:
Spoiler: