Group classification and conservation laws of nonlinear filtration equation with a small parameter

•Group classification of perturbed nonlinear filtration equations is performed.•The nonlinearly self-adjoint perturbed equations are singled out.•Conservation laws are constructed for self-adjoint equations. Group classification of the perturbed nonlinear filtration equation is performed assuming that the perturbation is an arbitrary function of the dependent variable. The nonlinear self-adjointness of the equation under consideration is investigated. Using these results, the approximate conservation laws are constructed.