  On the basis of group theory and the first-principles calculations, we
investigate high-rank multipole orderings in URu2Si2, which have been proposed
as a genuine primary order parameter in the hidden order phase below 17.5K. We
apply Shubnikov group theory to the multipole ordered states characterized by
the wave vector Q = (0, 0, 1) and specify the global/site symmetry and the
secondary order parameters, such as induced dipole moments and change in charge
distribution. We find that such antiferroic magnetic multipole orderings have
particularly advantageous to conceal the primary order parameter due to
preserving high symmetry in charge distribution. Experimental observations of
the inherent low-rank multipoles, which are explicitly classified in this
paper, will be key pieces to understand the puzzling hidden order phase.
