Search for rare and lepton flavor violating decays of the Higgs boson with the ATLAS detector

The Standard Model (SM) predicts several rare Higgs boson decay channels, which have not yet been observed, but could be enhanced in theories beyond the Standard Model. Among these are decays to second and first generation fermions. In addition, theories beyond the Standard Model may predict lepton-flavor violating (LFV) decays of the Higgs boson. This presentation summarises current results of the ATLAS experiment on searches for the decays of the SM Higgs boson to muons and electrons $H\rightarrow\mu\mu$ and $ee$ and LFV modes, meson resonances $J/\psi\gamma$, $\Upsilon\gamma$, $\rho\gamma$, $\phi\gamma$ and decays into charm quarks $c\bar{c}$, as well as into a pair of $Z$-boson and photon $H\rightarrow Z\gamma$. The presented searches are based on the full and partial Run-2 dataset collected at a centre-of-mass energy of $13\;\mathrm{TeV}$.