  Crystal symmetries can enforce all bands of a material to be topological, a
property that is commonly referred to as "supertopology". Here, we determine
the symmetry-enforced $\mathbb{Z}_2$ supertopologies of non-magnetic
centrosymmetric materials with weak and strong spin-orbit coupling (SOC). For
weak (i.e., negligible) SOC, crystal symmetries can enforce Dirac nodal lines
protected by a $\pi$-Berry phase, while for strong SOC, crystal symmetries can
give rise to nontrival weak $\mathbb{Z}_2$ topologies in 2D subplanes of the 3D
Brillouin zone. We catalogue all centrosymmetric space groups whose symmetries
enforce these $\mathbb{Z}_2$ supertopologies. Suitable material realizations
are identified and experimental signatures of the supertopologies, such as
quantum spin Hall states, are being discussed.
