Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
312 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 312 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. #10604113 | C2 | semidirect |
| 4. #10604092 | C2 | semidirect |
| 6. #10598677 | C2 | semidirect |
| 7. #10598626 | C2 | semidirect |
| 23. C5×#362 | C4 | semidirect |
| 24. #64785 | C4 | semidirect |
| 25. #64736 | C4 | semidirect |
| 26. #64715 | C4 | semidirect |
| 124. #362 | AGL(1,𝔽5) | semidirect |
| 284. C5 | #13146 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10604847 | 2 |
| C2×#64909 | 2 |
| #10604113 | 2 |
| #10604092 | 2 |
| #10600059 | 2 |
| #10598677 | 2 |
| #10598626 | 2 |
| #13146 | 5 |