Maximal subalgebras of simple modular Lie algebras

The maximal graded subalgebras of the restricted simple Lie algebras of Cartan type Wn, Sn, Hn, and Kn are studied. The notion of an R-subalgebra and that of an S-subalgebra are introduced for maximal subalgebras. All maximal R-subalgebras are described completely. The number of conjugacy classes, representatives of conjugacy classes and the dimensions of all R-subalgebras are found. An invariant description of graded S-subalgebras is also obtained.