Let $H$ be a group and suppose that $f\colon D_{10} \to H$ is a homomorphism. Describe all the possible images of $f$.
I know by definition, $\operatorname{Im} (f) = \{h \in H \mid h=f(g) \text{ for some } g \in G\}$ and I have all the elements of $D_{10}$ but I have no idea how to start to answer the question. I hope you can help me.