  Theories of symmetry-based indicators and topological quantum chemistry,
while powerful in diagnosing gapped topological materials, cannot be directly
applied to diagnosing band degeneracies at high-symmetry momenta due to the
violation of the compatibility conditions. Here we design a recursive protocol
that utilizes indicators of maximal subgroups to infer the topological nature
of band degeneracies at high-symmetry lines. For demonstration, the method is
used to predict the existence of iso-energy Weyl points and a node-line cage,
respectively, in the phonon bands of In2Te and ZrSiO.
