Searches for rare and lepton flavour violating decays of the Higgs boson with the ATLAS detector

The Standard Model predicts several rare Higgs boson decay channels, among which are decays to a $Z$ boson and a photon, $H \to Z\gamma$, and to a low-mass lepton pair and a photon $H \to \ell\ell\gamma$. The observation of these decays could open the possibility of studying the CP and coupling properties of the Higgs boson in a complementary way to other analyses. In addition, lepton-flavor-violating decays of the observed Higgs boson are searched for, where on observation would be a clear sign of physics effects beyond the Standard Model. Several results for decays based on pp collision data collected at 13 TeV will be presented.