The processes hc→ γP (P = η′, η, π0) are studied with a sample of (27.12 ± 0.14) × 108ψ(3686) events collected by the BESIII detector at the BEPCII collider. The decay hc→ γη is observed for the first time with the significance of 9.0 σ, and the branching fraction is determined to be (3.77 ± 0.55 ± 0.13 ± 0.26) × 10−4, while B (hc→ γη′) is measured to be (1.40 ± 0.11 ± 0.04 ± 0.10) × 10−3, where the first uncertainties are statistical, the second systematic, and the third from the branching fraction of ψ(3686) → π0hc. The combination of these results allows for a precise determination of Rhc=Bhc→γηBhc→γη′, which is calculated to be (27.0 ± 4.4 ± 1.0)%. The results are valuable for gaining a deeper understanding of η − η′ mixing, and its manifestation within quantum chromodynamics. No significant signal is found for the decay hc → γπ0, and an upper limit is placed on its branching fraction of B(hc → γπ0) < 5.0 × 10−5, at the 90% confidence level.