  We compute the $E_2$ pages of the momentum-space and real-space
Atiyah-Hirzebruch spectral sequence (AHSS) for topological crystalline
insulators and superconductors up to three spatial dimensions, considering the
cell decomposition in which if a group action fixes a cell setwise then its
group action fixes the same cell pointwise. We provide a detailed description
of the implementation for computing the $E_2$ pages of AHSS. Under a physically
reasonable assumption, we enumerate all possible $K$-groups that are compatible
with the $E_2$ pages for both momentum and real-space AHSS. As a result, we
determine the $K$-groups for approximately 59\% of symmetry settings in three
spatial dimensions. All the results can be found at this http
\href{https://www2.yukawa.kyoto-u.ac.jp/~ken.shiozaki/ahss/e2.html}{URL}.
