For each of the following values of $x$ in $\mathbb{Z}_{20}$, determines the number of group homomorphisms

$f: \mathbb{Z}_{20} \rightarrow \mathbb{Z}_{8}$

whose image has the following prescribed sizes; if there is none, enter $0$.

$\# \operatorname{image}(f)$	number of functions $f$
$5$
$2$
$25$
$4$
$10$
$8$