Large magnetic saturation field in the antiferromagnet EuIrSi3

•The magnetic phase diagram of non-centrosymmetric antiferromagnet is established by high field magnetization up to 57 Tesla.•Magnetic saturation at 41 T, one of the largest for a S-state (L = 0) magnetic ion is observed in EuIrSi3.•A large electronic density of states at the Fermi energy may enhance the magnetic ordering temperature as well as the critical field for magnetic saturation.