The photoproduction of isolated photons, both inclusive and together with a jet, has been measured with the ZEUS detector at HERA using an integrated luminosity of 374 pb(-1). Differential cross sections are presented in the isolated-photon transverse-energy and pseudorapidity ranges 6 < E-T(gamma) < 15 GeV and -0.7 < eta(gamma) < 0.9, and for jet transverse-energy and pseudorapidity ranges 4 < E-T(jet) < 35 GeV and -1.5 < eta(jet) < 1.8, for exchanged-photon virtualities Q(2) < 1 GeV2. Differential cross sections are also presented for inclusive isolated-photon production as functions of the transverse energy and pseudorapidity of the photon. Higher-order theoretical calculations are compared to the results. (C) 2014 The Authors. Published by Elsevier B.V.