Let
n
∈
N
n\in \mathbb {N}
and let
Θ
⊂
{
1
,
…
,
n
}
\Theta \subset \{1,\dots ,n\}
be a nonempty subset. We prove that if
Θ
\Theta
contains an odd integer, then any
P
Θ
P_\Theta
-Anosov subgroup of
Sp
(
2
n
,
R
)
\operatorname {Sp}(2n,\mathbb {R})
is virtually isomorphic to a free group or a surface group. In particular, any Borel Anosov subgroup of
Sp
(
2
n
,
R
)
\operatorname {Sp}(2n,\mathbb {R})
is virtually isomorphic to a free or surface group. On the other hand, if
Θ
\Theta
does not contain any odd integers, then there exists a
P
Θ
P_\Theta
-Anosov subgroup of
Sp
(
2
n
,
R
)
\operatorname {Sp}(2n,\mathbb {R})
which is not virtually isomorphic to a free or surface group. We also exhibit new examples of maximally antipodal subsets of certain flag manifolds; these arise as limit sets of rank
1
1
subgroups.