There exists a homomorphism $f : G \to H$ with $|G| = 20$ and $|im f | = 6$

Question

There exists a homomorphism $f : G \to H$ with $|G| = 20$ and $|im f | = 6$?

Is this true? I know that I have to use the first isomorphism theorem but I don't know what to do next?

Answer 1

Hint: the first isomorphism theorem tells you that $|\text{im}(f)|$ is equal to the index in $G$ of $\ker f$.