  Using a general symmetry-based approach, we provide a classification of
generic miniband structures for electrons in graphene placed on substrates with
the hexagonal Bravais symmetry. In particular, we identify conditions at which
the first moir\'e miniband is separated from the rest of the spectrum by either
one or a group of three isolated mini Dirac points and is not obscured by
dispersion surfaces coming from other minibands. In such cases the Hall
coefficient exhibits two distinct alternations of its sign as a function of
charge carrier density.
