**5. Conclusions**

The performed classification of admissible electromagnetic fields will be used in the search for electrovacuum solutions of the Einstein–Maxwell equations. As is already known, the components of the Ricci tensor of a homogeneous space in the frame (2) depend only on time. In order for Einstein's equations with matter to be proven as an integrable system of ordinary differential equations, the equations of motion of matter must be subordinated to the conditions of space symmetry. These conditions were fulfilled first by the potentials of the electromagnetic fields determined in this work.

**Funding:** This research received no external funding.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The data that support the findings of this study are available within the article.

**Acknowledgments:** The work is partially supported by the Ministry of Education of the Russian Federation, Project No. FEWF-2020-003.

**Conflicts of Interest:** The author declares no conflict of interest.
