Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
414 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 74 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 |
|---|---|---|
| 3. #10604666 | C2 | semidirect |
| 4. #10604655 | C2 | semidirect |
| 6. #10598548 | C2 | semidirect |
| 7. #10598543 | C2 | semidirect |
| 20. C5×#491 | C4 | semidirect |
| 21. #65375 | C4 | semidirect |
| 22. #65354 | C4 | semidirect |
| 27. #65003 | C4 | semidirect |
| 150. #491 | AGL(1,𝔽5) | semidirect |
| 371. C5 | #8998 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10617342 | 2 |
| #10613459 | 2 |
| #10604666 | 2 |
| #10604655 | 2 |
| #10604573 | 2 |
| #10598548 | 2 |
| #10598543 | 2 |
| #8998 | 5 |