$Z_{2}$ topological invariant exist for Kitaev model.
What symmetries does it conserve? And to what symmetry class it belongs to? The hamiltonian for kitaev model can be written as $$ H=\sum_k \phi_k^\dagger \begin{pmatrix} \xi(k) & 2i\Delta \sin(k)\\ -2i\Delta \sin(k ) & -\xi(k)\end{pmatrix}\phi(k) $$
It belongs to the symmetry class of no symmetry. i.e. the only symmetry is the fermion-number-parity conservation $Z_2^f$, which is always the symmetry of fermionic systems. See my paper http://arxiv.org/abs/1111.6341 for a discussion on the full-symmetry group $G_f$ for fermion systems.
The Kitaev model belongs to class D of the Altland-Zirnbauer classification. Here's the periodic table of non-interacting (gapped) fermionic topological systems.
The one circled in red corresponds to the 1D $p$-wave superconductor (or Kitaev chain). As you can see from the symmetry columns, it only possesses particle-hole symmetry ($\Xi$), while the time-reversal symmetry ($\Theta$) and the so-called chiral symmetry ($\Pi = \Theta \Xi$) are explicitly broken.
