Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
380 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 75 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 |
|---|---|---|
| 2. C5×#1569 | C2 | semidirect |
| 4. #10601303 | C2 | semidirect |
| 5. #10600655 | C2 | semidirect |
| 7. #10598244 | C2 | semidirect |
| 78. #1569 | D5 | semidirect |
| 337. C5 | #10498 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10611082 | 2 |
| C5×#1569 | 2 |
| #10601316 | 2 |
| #10601303 | 2 |
| #10600655 | 2 |
| #10600653 | 2 |
| #10598244 | 2 |
| #10498 | 5 |