Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
390 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 99 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. #10601546 | C2 | semidirect |
| 4. #10601311 | C2 | semidirect |
| 6. C5×#1299 | C2 | semidirect |
| 7. #10598158 | C2 | semidirect |
| 72. #1299 | D5 | semidirect |
| 155. D20 | #108 | semidirect |
| 310. C5 | #8898 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10610782 | 2 |
| #10601547 | 2 |
| #10601546 | 2 |
| #10601311 | 2 |
| #10600647 | 2 |
| C5×#1299 | 2 |
| #10598158 | 2 |
| #8898 | 5 |