Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
494 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 109 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. #10601571 | C2 | semidirect |
| 5. #10600615 | C2 | semidirect |
| 6. C5×#1275 | C2 | semidirect |
| 7. #10598229 | C2 | semidirect |
| 23. #64983 | C4 | semidirect |
| 24. #64971 | C4 | semidirect |
| 75. #1275 | D5 | semidirect |
| 337. C5 | #9291 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10610999 | 2 |
| #10610222 | 2 |
| #10601583 | 2 |
| #10601571 | 2 |
| #10600615 | 2 |
| C5×#1275 | 2 |
| #10598229 | 2 |
| #9291 | 5 |