Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
400 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 100 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 |
|---|---|---|
| 4. #10603840 | C2 | semidirect |
| 5. C8×#700 | C2 | semidirect |
| 6. #10598590 | C2 | semidirect |
| 7. #10598584 | C2 | semidirect |
| 13. C5×#446 | C4 | semidirect |
| 14. Q8×#168 | C4 | semidirect |
| 18. #65123 | C4 | semidirect |
| 21. #64977 | C4 | semidirect |
| 23. #64927 | C4 | semidirect |
| 29. #64870 | C4 | semidirect |
| 123. #446 | AGL(1,𝔽5) | semidirect |
| 315. C5 | #8250 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10611670 | 2 |
| #10604431 | 2 |
| #10604423 | 2 |
| #10603840 | 2 |
| C8×#700 | 2 |
| #10598590 | 2 |
| #10598584 | 2 |
| #8250 | 5 |