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The spin-orbit torque in a disordered Co/Pt bilayer is calculated using a first-principles nonequilibrium Green's function formalism. The torque is formally split in the Fermi-sea and Fermi-surface contributions. The Fermi-sea term is important at low temperatures, but the Fermi-surface term dominates at room temperature. In addition to the usual damping-like and field-like terms, the odd torque contains a sizeable planar Hall-like term (m . E)m x (z x m) which contributes to damping. While the torques that contribute to damping are almost entirely due to spin-orbit coupling on the Pt atoms, the field-like torque does not require it.