  We study discrete flavor symmetries of the models based on a ten-dimensional
supersymmetric Yang-Mills (10D SYM) theory compactified on magnetized tori. We
assume non-vanishing non-factorizable fluxes as well as the orbifold
projections. These setups allow model-building with more various flavor
structures. Indeed, we show that there exist various classes of non-Abelian
discrete flavor symmetries. In particular, we find that $S_3$ flavor symmetries
can be realized in the framework of the magnetized 10D SYM theory for the first
time.
