A convective motion model for a binary mixture with thermal diffusion effect is considered. The Oberbeck–Boussinesq approximation that describes convection in natural earth’s conditions is used. The Lie group of transformations allowed by the motion equations and the corresponding Lie algebra of generators \(L=L_5\oplus L_\infty\) are found. An optimal system of subalgebras for the finite Lie algebra \(L_5\) and an optimal system of one-dimensional subalgebras for the Lie algebra \(L\) are constructed.