We investigate the ferromagnetic resonance modes of the magnetic vortex states on Ni81Fe19 ellipses using broadband ferromagnetic resonance measurements and micromagnetic simulations. Experiments show a rich structure of modes in the resonance absorption spectra, with absorption peak amplitudes dependent on the direction of the probing radio-frequency field. The evolution of the resonant modes is observed to be symmetric around zero field, due to the reversibility of the vortex core motion. The simulated absorption spectra reproduce the main features of the experimental results. A detailed analysis of the resonant modes at zero field shows that the observed absorption profiles result from the overlap of resonant modes which have an increasing complexity with the frequency. Besides, the simplest resonant modes are not those that exhibit the larger absorption amplitudes. Furthermore, the observed frequency splitting of some of the oscillation modes with the external field is correlated to the symmetry breaking during the vortex motion.