$f:G\rightarrow G'$ is a non trivial homomorphism, show that if $ord(G)$ is a prime then $f$ is onto.

Question

Let $f:G\rightarrow G'$ be a non trivial homomorphism,

Prove that if $|G'|$ is prime, then $f$ is onto.

My Attempt:

As $f$ is homomorphism, $f(gg')=f(g)f(g')$ for all $g,g'\in G$. If $|G'|$ is prime then what?

Answer 1

Hint: The image of $f$ is a subgroup of $G'$. What size can a subgorup of $G'$ have?