Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
458 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 105 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. #10601573 | C2 | semidirect |
| 5. #10601301 | C2 | semidirect |
| 6. C5×#1286 | C2 | semidirect |
| 7. #10598122 | C2 | semidirect |
| 76. #1286 | D5 | semidirect |
| 345. C5 | #9194 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10610770 | 2 |
| #10605925 | 2 |
| #10601575 | 2 |
| #10601573 | 2 |
| #10601301 | 2 |
| C5×#1286 | 2 |
| #10598122 | 2 |
| #9194 | 5 |