Classitification of group subschemes in $\operatorname{GL}_n$, that contain a split maximal torus

We describe group subschemes of $\operatorname{GL}_n$ over an arbitrary field, that contain a split maximal torus. This is a joint generalization of the papers by Z. I. Borewicz, G. M. Seitz, N. A. Vavilov and others on description of overgroups of maximal torus and the works by Ch. Wenzel on parabolic subschemes.