  The honeycomb lattice sets the basic arena for numerous ideas to implement
electronic, photonic, or phononic topological bands in (meta-)materials. Novel
opportunities to manipulate Dirac electrons in graphene through band
engineering arise from superlattice potentials as induced by a substrate such
as hexagonal boron-nitride. Making use of the general form of a weak substrate
potential as dictated by symmetry, we analytically derive the low-energy
minibands of the superstructure, including a characteristic 1.5 Dirac cone
deriving from a three-band crossing at the Brillouin zone edge. Assuming a
large supercell, we focus on a single Dirac cone (or valley) and find all
possible arrangements of the low-energy electron and hole bands in a complete
six-dimensional parameter space. We identify the various symmetry planes in
parameter space inducing gap closures and find the sectors hosting topological
minibands, including also complex band crossings that generate a valley Chern
number atypically larger than one. Our map provides a starting point for the
systematic design of topological bands by substrate engineering.
