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