  & {\mathbb{Z}}^0             & {\mathbb{Z}}^0             & {\mathbb{Z}}^0     & {\mathbb{Z}}^0 \\ \hline                            \mathrm{AIII}   & 0     & 0                 & 0     & 0         & {\mathbb{Z}}^0             & {\mathbb{Z}}^0             & 0         & 0 \\ \hline\hline & {\mathcal{R}}_{q-0} & {\mathcal{R}}_{q-0}^0\times{\mathcal{C}}_{q}^0 & {\mathcal{C}}_{q}^0 &{\mathcal{C}}_{q}^0 & {\mathcal{R}}_{q-0}^0\times{\mathcal{R}}_{q-0}^0 & {\mathcal{R}}_{q-0}^0\times{\mathcal{R}}_{q-0}^0 & {\mathcal{R}}_{q-0}^0 & {\mathcal{R}}_{q-0}^0 \\ \hline\hline \mathrm{AI}     & 0     & {\mathbb{Z}}^0             & {\mathbb{Z}}^0 & {\mathbb{Z}}^0     & {\mathbb{Z}}^0             & {\mathbb{Z}}^0             & 0         & 0  \\ \hline \mathrm{BDI}    & 0     & 0                 & 0     & 0         & 0                 & 0                 & 0         & 0  \\ \hline \mathrm{D}      & {\mathbb{Z}}& {\mathbb{Z}}^0             & {\mathbb{Z}}^0 & {\mathbb{Z}}^0     & 0                 & 0                 & {\mathbb{Z}}^0     & {\mathbb{Z}}^0 \\ \hline \mathrm{DIII}   & {\mathbb{Z}}_0 & {\mathbb{Z}}_0^0           & 0     & 0         & {\mathbb{Z}}^0             & {\mathbb{Z}}^0             & {\mathbb{Z}}_0^0   &{\mathbb{Z}}_0^0 \\ \hline \mathrm{AII}    & {\mathbb{Z}}_0 &{\mathbb{Z}}_0^0\times{\mathbb{Z}}^0 & {\mathbb{Z}}^0 & {\mathbb{Z}}^0     & {\mathbb{Z}}_0^0