Search for rare 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, $H\rightarrow Z\gamma$, and to a low-mass lepton pair and a photon $H→\ell\ell\gamma$. 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. Results based on 139 $\text{fb}^{-1}$ of $pp$ collision data collected at 13 TeV will be presented.