  We calculate the electronic spectrum of bilayer graphene in perpendicular
magnetic fields nonperturbatively. To accommodate arbitrary displacements
between the two layers, we apply a periodic gauge based on singular flux
vortices of phase $2\pi$. The resulting Hofstadter-like butterfly plots show a
reduced symmetry, depending on the relative position of the two layers against
each other. The split of the zero-energy relativistic Landau level differs by
one order of magnitude between Bernal and non-Bernal stacking.
