Finite Group DatabasebetaFinite Group DatabasebetaOrder 10432.
66 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C4×C163⋊C8 | C2 | 1 | 2 | yes | maximal |
| 2 | C4×C8×C163 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | C2×C163⋊C8 | C4 | 1 | 4 | yes | — |
| 4 | C2×C8×C163 | C4 | 1 | 2 | yes | — |
| 5 | C42×C163 | C22 | 1 | 1 | yes | characteristic |
| 6 | C163⋊C8 | — | 2 | 4 | no | — |
| 7 | C2×C4×C163 | C2×C4 | 1 | 2 | yes | — |
| 8 | C2×C4×C163 | C2×C4 | 1 | 1 | yes | characteristic |
| 9 | C8×C163 | C8 | 1 | 4 | yes | complemented |
| 10 | C22×C163 | C42 | 1 | 1 | yes | characteristic |
| 11 | C4×C163 | C2×C8 | 1 | 2 | yes | — |
| 12 | C4×C163 | M16 | 1 | 4 | yes | — |
| 13 | C2×C163 | C4×C8 | 1 | 1 | yes | characteristic |
| 14 | C2×C163 | #97 | 1 | 2 | yes | — |
| 15 | C163 | #322 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 16 | #322 | — | 163 | 1 | no | maximal, Sylow |
| 17 | C4×C8 | — | 163 | 2 | no | — |
| 18 | C4×C8 | D163 | 1 | 1 | yes | characteristic |
| 19 | C2×C8 | — | 163 | 4 | no | — |
| 20 | C2×C8 | Dic163 | 1 | 2 | yes | — |
| 21 | C42 | C2×D163 | 1 | 1 | yes | characteristic |
| 22 | C2×C4 | C4×D163 | 1 | 2 | yes | — |
| 23 | C2×C4 | C2×Dic163 | 1 | 1 | yes | characteristic |
| 24 | C8 | — | 326 | 4 | no | — |
| 25 | C8 | C163⋊C8 | 1 | 4 | yes | complemented |
| 26 | C22 | C4×Dic163 | 1 | 1 | yes | characteristic |
| 27 | C4 | C2×C163⋊C8 | 1 | 2 | yes | — |
| 28 | C4 | #14579682 | 1 | 4 | yes | — |
| 29 | C2 | C4×C163⋊C8 | 1 | 1 | yes | characteristic |
| 30 | C2 | #19104645 | 1 | 2 | yes | — |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 9. C8×C163 | C8 | semidirect |
| 15. C163 | #322 | semidirect |
| 25. C8 | C163⋊C8 | semidirect |