  We study the single particle entanglement spectrum in 2D topological
insulators which possess $n$-fold rotation symmetry. By defining a series of
special choices of subsystems on which the entanglement is calculated, or real
space cuts, we find that the number of protected in-gap states for each type of
these real space cuts is a quantum number indexing (if any) non-trivial
topology in these insulators. We explicitly show the number of protected in-gap
states is determined by a $Z^n$-index, $(z_1,...,z_n)$, where $z_m$ is the
number of occupied states that transform according to $m$-th one-dimensional
representation of the $C_n$ point group. We find that the entanglement spectrum
contains in-gap states pinned in an interval of entanglement eigenvalues
$[1/n,1-1/n]$. We determine the number of such in-gap states for an exhaustive
variety of cuts, in terms of the $Z_m$ quantum numbers. Furthermore, we show
that in a homogeneous system, the $Z^n$ index can be determined through an
evaluation of the eigenvalues of point group symmetry operators at all
high-symmetry points in the Brillouin zone. When disordered $n$-fold
rotationally symmetric systems are considered, we find that the number of
protected in-gap states is identical to that in the clean limit as long as the
disorder preserves the underlying point group symmetry and does not close the
bulk insulating gap.
