  All non-equivalent solutions of vacuum Maxwell equations are found for the
case when space-time manifolds admit simply transitive four-parameter groups of
motions $G_4(N)$. The potentials of the admissible electromagnetic fields admit
the existence of the algebra of motion integrals of the Hamilton-Jacobi and
Klein-Gordon-Fock equations which is isomorphic to the algebra of the group
operators for the same group $G_4(N)$
