  We classify integral modular categories of dimension pq^4 and p^2q^2 where p
and q are distinct primes. We show that such categories are always
group-theoretical except for categories of dimension 4q^2. In these cases there
are well-known examples of non-group-theoretical categories, coming from
centers of Tambara-Yamagami categories and quantum groups. We show that a
non-group-theoretical integral modular category of dimension 4q^2 is equivalent
to either one of these well-known examples or is of dimension 36 and is
twist-equivalent to fusion categories arising from a certain quantum group.
