  We investigate the options for imposing flavor symmetries on a minimal
renormalizable non-supersymmetric $\mathrm{SU}(5)$ grand unified theory,
without introducing additional flavor-related fields. Such symmetries reduce
the number of free parameters in the model and therefore lead to more
predictive models. We consider the Yukawa sector of the Lagrangian, and search
for all possible flavor symmetries. As a result, we find 25 distinct realistic
flavor symmetry cases, with $\mathbb{Z}_2$, $\mathbb{Z}_3$, $\mathbb{Z}_4$, and
$\mathrm{U}(1)$ symmetries, and no non-Abelian cases.
