We examine the behaviour of Killing spinors on AdS(5) under various discret
e symmetries of the spacetime. In this way we discover a number of supersym
metric orbifolds, reproducing the known ones and adding a few novel ones to
the list. These orbifolds break the SO(4; 2) invariance of AdS(5) down to
subgroups. We also make some comments on the non-compact Stiefel manifold W
-4,W-2.