Recently, hydrogen sulfide has attracted enormous attention due to the record high-temperature superconductivity of H3S with Tc=203 K at a pressure of 155 GPa. In addition to H3S, there are many theoretically and experimentally confirmed compositions and crystal structures forming under high pressure. Here, using the ab initio variable-composition evolutionary algorithm USPEX, we performed a comprehensive search for new phases in the H-S system and built a refined composition-pressure phase diagram. For H3S2, a new stable semiconducting P21 phase was found. We predicted a new sulfur-rich stable HS2 phase and metastable compound H5S8 and calculated their Tc using superconducting density functional theory (11 K at 100 GPa and 9.2 K at 80 GPa, respectively). Our results show that among stable phases only H3S is a high-Tc superconductor, and highlight that compositional descriptors alone are insufficient for indicating superconductivity, and crystal structure plays an essential role.