In this paper we describe the implementation of the complete next-to-leading order electroweak calculations for the various cross channels of the process f₁f̄₁HA→0 in the framework of the SANC system. Here A stands for a photon and f₁ for a fermion whose mass is neglected everywhere besides arguments of logarithmic functions. The symbol →0 means that all 4-momenta of the external particles flow inwards. The derived one-loop scalar form factors can be used for any cross channel after an appropriate permutation of their arguments s,t,u. We present the complete analytical results for the covariant and helicity amplitudes for three cross channels: f₁f̄₁→Hγ, H→f₁f̄₁γ and f₁γ→f₁H. For checking of the correctness of the results first of all we observe the independence of the scalar form factors on the gauge parameters and the validity of the Ward identity (external photon transversality), and, secondly, we make an extensive comparison of our numerical results with other independent calculations.