  We analyze the effects of nearest neighbor repulsive interactions in the
Hofstadter system in a honeycomb lattice. At low fillings, we show that, as the
interaction strength is increased there are two first order transitions, a
Landau transition with translational and rotational symmetries broken, followed
by a topological transition with a jump in the quantized Hall conductivity. We
therefore predict that in physical realizations where the interaction effects
are strong, there would be translation symmetry broken states with quantized
Hall conductivities that differ from those predicted by the non-interacting
theory.
