  The symmetry-based indicator [H. C. Po, A. Vishwanath, H. Watanabe, Nat.
Commun. 8, 50 (2017)] is a practical tool to diagnose topological materials in
the band theory. In this note, we present two directions to generalize the
symmetry-based indicator for other classes of topological materials. The one is
for superconductors. The careful definition of the atomic insulators and the
trivial vacuum Hamiltonian yields the symmetry-based indicators specific to
superconductors. The other is for ingap boundary states. The quotient of the
group of atomic insulators by a subset of atomic insulators such as those
localized at the interior of the unit cell gives us the symmetry-based
indicator for detecting ingap corner, hinge, and surface states.
