Metric components of potentials of admissible electromagnetic fields in spaces with simply transitive motion group G4 are found. The components of vector tetrads corresponding to the components of the metric tensors found by Petrov are given. The results obtained complement the coordinate-free classification given in Magazev et al. [Theor. Math. Phys. 156, 1127–1141 (2008)]. Previously, admissible electromagnetic fields were found for the case when three- and four-parameter groups of motions act on hypersurfaces of spacetime. Thus, non-equivalent sets of potentials for all electromagnetic fields that admit three- and four-parameter groups of motions are known now.

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