  Let $G$ be a simple algebraic group of exceptional type, over an
algebraically closed field of characteristic $p \ge 0$. A closed subgroup $H$
of $G$ is called $G$-completely reducible ($G$-cr) if whenever $H$ is contained
in 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 simple
connected 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 the
connected 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 among
connected reductive subgroups, but not maximal among all connected subgroups.

Group Theory;Representation Theory