  We show that the solutions to the non-stationary Navier-Stokes equations in
$R^d$, $d=2,3$ which are left invariant under the action of discrete subgroups
of the orthogonal group $O(d)$ decay much faster as $|x|\to\infty$ or $ t
\to\infty$ than in the generic case and we compute, for each subgroup, the
precise decay rates in space-time of the velocity field.
