  In this paper, we develop an algebraic approach to classifying contact
symmetries of the second-order nonlinear evolution equations. Up to contact
isomorphisms, all inequivalent PDEs admitting semi-simple algebras, solvable
algebras of dimension $n\leq4$, and algebras having nontrivial Levi factors,
belonging to the class under consideration, and corresponding contact
symmetries they admitted are listed.
