All external electromagnetic fields in which the Klein-Gordon-Fock equation admits the first-order symmetry operators are found, provided that in the space-time V 4 a group of motion G 3 acts simply transitively on a non-null subspace of transitivity V 3 . It is shown that in the case of a Riemannian space V n , in which the group G r acts simply transitively, the algebra of symmetry operators of the n-dimensional Klein-Gordon-Fock equation in an external admissible electromagnetic field coincides with the algebra of operators of the group G r .