Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
1708 conjugacy classes of subgroups; only the 288 normal subgroups are shown.
This group has 1708 conjugacy classes of subgroups — too many to draw. Only its 288 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C24×#170 | C2 | semidirect |
| 2. C2×#65773 | C2 | semidirect |
| 4. #10605025 | C2 | semidirect |
| 5. #10604946 | C2 | semidirect |
| 6. #10604230 | C2 | semidirect |
| 7. #10604226 | C2 | semidirect |
| 9. C22×#704 | C22 | semidirect |
| 17. C2×C22⋊#170 | C22 | semidirect |
| 19. C2×#4004 | C22 | semidirect |
| 20. C2×#4002 | C22 | semidirect |
| 25. #64918 | C22 | semidirect |
| 39. C22×#170 | D4 | semidirect |
| 68. C24×C5 | M16 | semidirect |
| 155. #170 | #120 | semidirect |
| 196. C22×C5 | #435 | semidirect |
| 208. C24 | #704 | semidirect |
| 283. C5 | #21440 | semidirect |
| 292. C22 | #65773 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×#170 | 2 |
| C2×#65773 | 2 |
| Dic5×#120 | 2 |
| #10605025 | 2 |
| #10604946 | 2 |
| #10604230 | 2 |
| #10604226 | 2 |
| #21440 | 5 |