Using a sample of 4.48 × 10 8 ψð3686Þ events collected with the BESIII detector at the BEPCII collider, we study the two-photon decays of the pseudoscalar mesons π 0 , η, η 0 , ηð1405Þ, ηð1475Þ, ηð1760Þ, and Xð1835Þ in J=ψ radiative decays using ψð3686Þ → π þ π − J=ψ events. The π 0 , η, and η 0 mesons are clearly observed in the two-photon mass spectra, and the branching fractions are determined to be BðJ=ψ → γπ 0 → 3γÞ ¼ ð3.57 AE 0.12 AE 0.16Þ × 10 −5 , BðJ=ψ → γη → 3γÞ ¼ ð4.42 AE 0.04 AE 0.18Þ × 10 −4 , and BðJ=ψ → γη 0 → 3γÞ ¼ ð1.26 AE 0.02 AE 0.05Þ × 10 −4 , where the first error is statistical and the second is systematic. No clear signal for ηð1405Þ, ηð1475Þ, ηð1760Þ or Xð1835Þ is observed in the two-photon mass spectra, and upper limits at the 90% confidence level on the product branching fractions are obtained.