  Let $C$ be a modular category of Frobenius-Perron dimension $dq^n$, where $q$
is a prime number and $d$ is a square-free integer. We show that if $q>2$ then
$C$ is integral and nilpotent. In particular, $C$ is group-theoretical. In the
general case, we describe the structure of $C$ in terms of equivariantizations
of group-crossed braided fusion categories.
