With a sample of (225.2±2.8)×10(6) J/ψ events registered in the BESIII detector, J/ψ→γπ(+)π(-)η(') is studied using two η(') decay modes: η(')→π(+)π(-)η and η(')→γρ(0). The X(1835), which was previously observed by BESII, is confirmed with a statistical significance that is larger than 20σ. In addition, in the π(+)π(-)η(') invariant-mass spectrum, the X(2120) and the X(2370), are observed with statistical significances larger than 7.2σ and 6.4σ, respectively. For the X(1835), the angular distribution of the radiative photon is consistent with expectations for a pseudoscalar.