  We establish the full list of flavour symmetry groups which may be enforced,
without producing any further accidental symmetry, on the Yukawa-coupling
matrices of an SO(10) Grand Unified Theory with arbitrary numbers of scalar
multiplets in the 10, $\overline{126}$, and 120 representations of SO(10). For
each of the possible discrete non-Abelian symmetry groups, we present examples
of minimal models which do not run into obvious contradiction with the
phenomenological fermion masses and mixings.
