  Multiple-$Q$ states are expressed as a superposition of spin density waves at
multiple ordering wave vectors, which results in unconventional complicated
spin textures, such as skyrmion, hedgehog, and vortex. We investigate the
multiple-$Q$ instability by focusing on the low-symmetric ordering wave vectors
in momentum space. By systematically performing the simulated annealing for
effective spin models with various ordering wave vectors on a two-dimensional
square lattice, we classify the magnetic phase diagram into four types
according to the position of the ordering wave vectors. Three out of four cases
lead to a plethora of isotropic multiple-$Q$ instabilities yielding collinear,
coplanar, and noncoplanar double-$Q$ and quadruple-$Q$ magnetic phases, while
the remaining case leads to an anisotropic double-$Q$ instability when the
multiple-spin interaction is introduced. Our results indicate that exotic
multiple-$Q$ phases distinct from the skyrmion crystal phase are expected when
the ordering wave vectors lie on the low-symmetric positions in the Brillouin
zone.
