Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
500 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 500 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 |
|---|---|---|
| 3. #10604680 | C2 | semidirect |
| 4. #10604646 | C2 | semidirect |
| 6. #10598531 | C2 | semidirect |
| 7. #10598530 | C2 | semidirect |
| 19. C5×#492 | C4 | semidirect |
| 22. #65370 | C4 | semidirect |
| 23. #65359 | C4 | semidirect |
| 25. #64969 | C4 | semidirect |
| 114. #700 | SD16 | semidirect |
| 141. #492 | AGL(1,𝔽5) | semidirect |
| 369. C5 | #9055 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10617363 | 2 |
| #10613483 | 2 |
| #10604680 | 2 |
| #10604646 | 2 |
| #10604593 | 2 |
| #10598531 | 2 |
| #10598530 | 2 |
| #9055 | 5 |