Let
F
F
be a locally compact non-archimedean field,
p
p
its residue characteristic, and
G
\textbf {G}
a connected reductive group over
F
F
. Let
C
C
be an algebraically closed field of characteristic
p
p
. We give a complete classification of irreducible admissible
C
C
-representations of
G
=
G
(
F
)
G=\mathbf {G}(F)
, in terms of supercuspidal
C
C
-representations of the Levi subgroups of
G
G
, and parabolic induction. Thus we push to their natural conclusion the ideas of the third author, who treated the case
G
=
G
L
m
\mathbf {G}=\mathrm {GL}_m
, as further expanded by the first author, who treated split groups
G
\mathbf {G}
. As in the split case, we first get a classification in terms of supersingular representations of Levi subgroups, and as a consequence show that supersingularity is the same as supercuspidality.