Clean superconductors with weakly coupled conducting planes have been suggested as promising candidates for observing the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state. We consider here a layered superconductor in a magnetic field of arbitrary orientation with respect to the conducting plane. In this case there is competition of Pauli spin-pair-breaking effects, favoring the FFLO state, and orbital-pair-breaking effects, favoring the Abrikosov vortex state. In previous work, phase transitions to phases with paitring in Landau levels with quantum numbers n > 0 have been predicted. Here, we calculate the actual structure of the stable states below Hc2 by minimizing the free energy. We find new order parameter structures differing from both the traditional Abrikosov and FFLO solutions. These include two-dimensional periodic structures with several zeros of the order parameteer, as well as quasi-one-dimentional structures consisting of vortex chains separated by FFLO domains. We discuss the limit of high n, where some interesting but yet unsolved questions appear.