  Though symmetry-based indicators formulae are powerful in diagnosing
topological states with a gapped band structure at/between any high-symmetry
points, it fails in diagnosing topological degeneracies when the compatibility
condition is violated. In such cases, we can only obtain information of whether
there is a band degeneracy at some high-symmetry points or along some
high-symmetry lines by the compatibility condition. Under the framework of
symmetry-based indicator theories, we proposed an algorithm to diagnose the
topological band crossings in the compatibility condition-violating systems to
obtain the whole topological information, by using the symmetry-based indicator
formulae of their subgroups. In this paper, we reinterpret the algorithm in a
simpler way with two material examples preserving different topological states
in spinless systems with time-reversal symmetry, discuss the limitation of the
symmetry-based indicator theories, and make further discussions on the
algorithm applying in spinful systems with time-reversal symmetry.
