Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
510 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 510 conjugacy classes of subgroups — too many to draw. Only its 98 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. C22×#3990 | C2 | semidirect |
| 3. C2×#64907 | C2 | semidirect |
| 4. #10604722 | C2 | semidirect |
| 5. #10598621 | C2 | semidirect |
| 15. C5×#467 | C4 | semidirect |
| 16. #65477 | C4 | semidirect |
| 17. #65404 | C4 | semidirect |
| 19. #65172 | C4 | semidirect |
| 59. #3990 | D4 | semidirect |
| 129. #467 | AGL(1,𝔽5) | semidirect |
| 222. C22×C5 | #360 | semidirect |
| 338. C5 | #13065 | semidirect |
| 351. C22 | #64907 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#3990 | 2 |
| #10612489 | 2 |
| C2×#64907 | 2 |
| #10604722 | 2 |
| #10598621 | 2 |
| #13065 | 5 |