Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
546 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 546 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 |
|---|---|---|
| 1. #10615048 | C2 | semidirect |
| 3. #10610259 | C2 | semidirect |
| 4. C5×#1980 | C2 | semidirect |
| 5. #10600282 | C2 | semidirect |
| 6. #10600262 | C2 | semidirect |
| 7. #10598159 | C2 | semidirect |
| 81. #1980 | D5 | semidirect |
| 367. C5 | #10196 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10615048 | 2 |
| #10615041 | 2 |
| #10610259 | 2 |
| C5×#1980 | 2 |
| #10600282 | 2 |
| #10600262 | 2 |
| #10598159 | 2 |
| #10196 | 5 |