Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
456 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 90 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. #10617413 | C2 | semidirect |
| 3. #10604788 | C2 | semidirect |
| 4. C2×#64903 | C2 | semidirect |
| 5. #10604781 | C2 | semidirect |
| 6. #10598630 | C2 | semidirect |
| 7. #10598627 | C2 | semidirect |
| 21. C5×#472 | C4 | semidirect |
| 23. #65449 | C4 | semidirect |
| 24. #65432 | C4 | semidirect |
| 25. #65185 | C4 | semidirect |
| 172. #472 | AGL(1,𝔽5) | semidirect |
| 414. C5 | #13070 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10617413 | 2 |
| #10612668 | 2 |
| #10604788 | 2 |
| C2×#64903 | 2 |
| #10604781 | 2 |
| #10598630 | 2 |
| #10598627 | 2 |
| #13070 | 5 |