Finite Group DatabasebetaFinite Group DatabasebetaOrder 20624.
20 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | Dic2578 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | D5156 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | C8×C1289 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C2×D1289 | — | 2 | 1 | no | — |
| 5 | C4×C1289 | C22 | 1 | 1 | yes | characteristic |
| 6 | Dic1289 | — | 2 | 1 | no | — |
| 7 | C2×C1289 | D4 | 1 | 1 | yes | characteristic |
| 8 | D1289 | — | 4 | 1 | no | — |
| 9 | C1289 | SD16 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 10 | SD16 | — | 1289 | 1 | no | maximal, Sylow |
| 11 | Q8 | — | 1289 | 1 | no | — |
| 12 | D4 | — | 1289 | 1 | no | — |
| 13 | C8 | D1289 | 1 | 1 | yes | characteristic, complemented |
| 14 | C22 | — | 2578 | 1 | no | — |
| 15 | C4 | — | 2578 | 1 | no | — |
| 16 | C4 | C2×D1289 | 1 | 1 | yes | characteristic |
| 17 | C2 | — | 5156 | 1 | no | — |
| 18 | C2 | D5156 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. Dic2578 | C2 | semidirect |
| 3. C8×C1289 | C2 | semidirect |
| 9. C1289 | SD16 | semidirect |
| 13. C8 | D1289 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Dic2578 | 2 |
| D5156 | 2 |
| C8×C1289 | 2 |
| SD16 | 1289 |