Low-temperature magnetic resonance study of the quasi-two-dimensional antiferromagnet Cu(en)(H$_2$O)$_2$SO$_4$ (en = C$_2$H$_8$N$_2$) was performed down to 0.45~K. This compound orders antiferromagnetically at 0.9K. The analysis of the resonance data within the hydrodynamic approach allowed to identify anisotropy axes and to estimate the anisotropy parameters for the antiferromagnetic phase. Dipolar spin-spin coupling turns out to be the main contribution to the anisotropy of the antiferromagnetic phase. The splitting of the resonance modes and its non-monotonous dependency on the applied frequency was observed below 0.6K in all three field orientations. Several models were discussed to explain the origin of the nontrivial splitting and the existence of inequivalent magnetic subsystems in Cu(en)(H$_2$O)$_2$SO$_4$ was chosen as the most probable source.
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