We analyze the symmetry properties of the dipolar Hamiltonian as the main relaxation mechanism responsible for the observed NMR spectra of long lived states in methyl groups. Long lived states exhibit relaxation times that are considerably longer than the spin-lattice relaxation time, T1. The analysis brings clarity to the key components of the relaxation mechanism of long lived states by focusing exclusively on the symmetry of the spin Hamiltonian. Our study shows that the dipole-dipole coupling between protons of a methyl group and between the protons and an external spin are both symmetry breaking interactions that can lead to relaxation pathways that transform the polarization from symmetry order to Zeeman order, but the net contribution of the internal dipolar interaction to the NMR observation of long lived states is zero. Our calculation is in agreement with the reported features of the observed spectra.