  The pairing interactions between electrons play an essential role in
determining the properties in superconducting states. Recently, a plethora of
unconventional superconducting states has been extensively explored, which
often emerge owing to multipole fluctuations in the vicinity of multipole
orders. We classify such superconducting states from the viewpoint of the
multipole degrees of freedom by extending its representation to Nambu space. We
clarify that under the crystallographic point group, arbitrary Cooper pairs
between electrons with any angular momenta are systematically classified by
four types of multipoles: electric, magnetic, magnetic toroidal, and electric
toroidal. As examples, we apply our formulation to an $sp$-orbital electron
system, which potentially exhibits exotic Cooper pairs under polar and axial
point groups. Our systematic classification will be useful in characterizing
unconventional superconducting states in multiorbital systems.
