Here
https://www2.bc.edu/~reederma/Groups.pdf
on page $112$, a table of the number of groups of order $p^2q$ is given. In the explanations, there is a typo ($\frac{q+5}{5}$ instead of $\frac{q+5}{2}$)
Can someone approve the following formula for $f(p,q)$, the number of groups of order $p^2q$ ?
If $p$ does not divide $q-1$ and $q$ does not divide $p^2-1$, then $f(p,q)=2$
If $p|q-1$ and $p^2$ does not divide $q-1$, then $f(p,q)=4$
If $p^2|q-1$ , then $f(p,q)=5$
If $q=2$ , then $f(p,q)=5$
If $q>2$ and $q|p+1$ , then $f(p,q)=3$
If $q>2$ and $q|p-1$ , then $f(p,q)=\frac{q+9}{2}$
Does anyone know a similar formula for the number of groups of order $p^2q^2$ ?