Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
420 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 85 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. #10601630 | C2 | semidirect |
| 5. #10601608 | C2 | semidirect |
| 6. C5×#1291 | C2 | semidirect |
| 7. #10598157 | C2 | semidirect |
| 20. #64983 | C4 | semidirect |
| 21. #64982 | C4 | semidirect |
| 22. #64971 | C4 | semidirect |
| 23. #64970 | C4 | semidirect |
| 73. #1291 | D5 | semidirect |
| 296. C5 | #9415 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10611068 | 2 |
| #10610264 | 2 |
| #10601630 | 2 |
| #10601628 | 2 |
| #10601608 | 2 |
| C5×#1291 | 2 |
| #10598157 | 2 |
| #9415 | 5 |