  We consider a random Schro\"dinger operator in an external magnetic field.
The random potential consists of delta functions of random strengths situated
on the sites of a regular two-dimensional lattice. We characterize the spectrum
in the lowest N Landau bands of this random Hamiltonian when the magnetic field
is sufficiently strong, depending on N. We show that the spectrum in these
bands is entirely pure point, that the energies coinciding with the Landau
levels are infinitely degenerate and that the eigenfunctions corresponding to
energies in the remainder of the spectrum are localized with a uniformly
bounded localization length. By relating the Hamiltonian to a lattice operator
we are able to use the Aizenman-Molchanov method to prove localization.
