We investigate the quantum Hall (QH) states near the charge neutral Dirac point of a high mobility graphene sample in high magnetic fields. We find that the QH states at filling factors $ u=pm1$ depend only on the perpendicular component of the field with respect to the graphene plane, indicating them to be not spin-related. A non-linear magnetic field dependence of the activation energy gap at filling factor $ u=1$ suggests a many-body origin. We therefore propose that the $ u=0$ and $pm1$ states arise from the lifting of the spin and sub-lattice degeneracy of the $n=0$ LL, respectively.
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