Let
k
k
be any field and let
G
G
be a connected reductive algebraic
k
k
-group. Associated to
G
G
is an invariant first studied in the 1960s by Satake [Ann. of Math. (2) 71 (1960), 77–110] and Tits [Théorie des Groupes Algébriques (Bruxelles, 1962), Librairie Universitaire, Louvain; Gauthier- Villars, Paris, 1962], [Algebraic Groups and Discontinuous Subgroups (Proc. Sympos. Pure Math., Boulder, Colo., 1965), Amer. Math. Soc., Providence, R.I., 1966, pp. 33–62] that is called the index of
G
G
(a Dynkin diagram along with some additional combinatorial information). Tits [Algebraic Groups and Discontinuous Subgroups (Proc. Sympos. Pure Math., Boulder, Colo., 1965), Amer. Math. Soc., Providence, R.I., 1966, pp. 33–62] showed that the
k
k
-isogeny class of
G
G
is uniquely determined by its index and the
k
k
-isogeny class of its anisotropic kernel
G
a
G_a
. For the cases where
G
G
is absolutely simple, all possibilities for the index of
G
G
have been classified in by Tits [Algebraic Groups and Discontinuous Subgroups (Proc. Sympos. Pure Math., Boulder, Colo., 1965), Amer. Math. Soc., Providence, R.I., 1966, pp. 33–62]. Let
H
H
be a connected reductive
k
k
-subgroup of maximal rank in
G
G
. We introduce an invariant of the
G
(
k
)
G(k)
-conjugacy class of
H
H
in
G
G
called the embedding of indices of
H
⊂
G
H \subset G
. This consists of the index of
H
H
and the index of
G
G
along with an embedding map that satisfies certain compatibility conditions. We introduce an equivalence relation called index-conjugacy on the set of
k
k
-subgroups of
G
G
, and observe that the
G
(
k
)
G(k)
-conjugacy class of
H
H
in
G
G
is determined by its index-conjugacy class and the
G
(
k
)
G(k)
-conjugacy class of
H
a
H_a
in
G
G
. We show that the index-conjugacy class of
H
H
in
G
G
is uniquely determined by its embedding of indices. For the cases where
G
G
is absolutely simple of exceptional type and
H
H
is maximal connected in
G
G
, we classify all possibilities for the embedding of indices of
H
⊂
G
H \subset G
. Finally, we establish some existence results. In particular, we consider which embeddings of indices exist when
k
k
has cohomological dimension 1 (resp.
k
=
R
k=\mathbb {R}
,
k
k
is
p
\mathfrak {p}
-adic).