We report on magnetic-torque and resistivity measurements of the heavy-fermion compound CeCoIn5 in static magnetic fields up to 36 T and temperatures down to 50 mK. While quantum oscillations of the de Haas-van Alphen (dHvA) as well as the Shubnikov-de Haas (SdH) effect confirm the previously reported Fermi surfaces, an analysis of the field dependence reveals two anomalous features. The first is seen at about 22 T as a sharp anomaly in the resistivity for current applied along the a direction. The second appears as nonmonotonic field-dependent oscillation frequencies and amplitudes in both dHvA and SdH signals. This second feature emerges at about 28 T. This field is close to that of the nematic transition reported for CeRhIn5 and the proposed Lifshitz transition in CeIrIn5. We discuss possible common grounds of these latter features that might originate from the very similar band structures of these materials.