Complete reducibility in good characteristic

Let G be a simple algebraic group of exceptional type, over analgebraically closed field of characteristic p ≥ 0. A closed subgroup H of G is called G-completely reducible (G-cr) if whenever H is containedin a parabolic subgroup P of G, it is contained in a Levi subgroup of P. In this paper we determine the G-conjugacy classes of non-G-cr simpleconnected subgroups of G when p is good for G. For each such subgroup X, we determine the action of X on the adjoint module L(G) and theconnected centraliser of X in G. As a consequence we classify all non-G-cr connected reductive subgroups of G, and determine their connected centralisers. We also classify the subgroups of G which are maximal amongconnected reductive subgroups, but not maximal among all connected subgroups.