Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
396 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 89 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. #10610997 | C2 | semidirect |
| 4. #10600594 | C2 | semidirect |
| 6. C5×#1275 | C2 | semidirect |
| 7. #10598238 | C2 | semidirect |
| 78. #1275 | D5 | semidirect |
| 302. C5 | #9284 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10611001 | 2 |
| #10610997 | 2 |
| #10601558 | 2 |
| #10600594 | 2 |
| #10600591 | 2 |
| C5×#1275 | 2 |
| #10598238 | 2 |
| #9284 | 5 |