Classes of Maxwell spaces that admit subgroups of the Poincaré group

A Maxwell space is a triple $(M,g,F)$, where $M$ is the four-dimensional Minkowski space or a domain in it, $g$ is a pseudo-Euclidean metric on $M$, and $F$ is a closed exterior 2-form on $M$. In this paper, we give an exhaustive description of classes of Maxwell spaces that admit subgroups of the Poincaré group. Representatives of all classes are constructed.