  The study of improper phases in the context of multiferroic materials has a
long history, but superconductivity has yet to be connected to the network of
ferroic orders. In this work, we highlight an overlooked mechanism that couples
superconducting order parameters to odd-parity orders in the charge or spin
sectors such that the latter emerge as improper orders. For that, we explore a
novel perspective of nonsymmorphic symmetries based on extended symmetry groups
in real space. We highlight how nonsymmorphic symmetries can generate rather
nonintuitive couplings between order parameters. In particular, we find that a
bilinear in the superconducting order parameter can couple linearly to
odd-parity orders in centrosymmetric systems. Our findings can account for the
unusual phenomenology of CeRh$_2$As$_2$, a recently discovered heavy fermion
superconductor, and open the door for exploring nonsymmorphic symmetries in the
broader context of improper orders with potential applications to functional
materials.
