CONTENTS

ABSTRACT. Determining the subgroup structure of algebraic groups (over an algebraically closed field K of arbitrary characteristic) often requires an understanding of those instances when a group Y and a closed subgroup G both act irreducibly on some module V, which is rational for G and Y. In this paper and [4], we give a classification of all such triples G Y V when G is a non-connected algebraic group with simple identity component X, V is an irreducible G-module with restricted X-high weight(s), and Y is a simple algebrai