Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
324 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 61 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. #10611445 | C2 | semidirect |
| 2. C5×#2207 | C2 | semidirect |
| 4. #10602080 | C2 | semidirect |
| 5. #10598255 | C2 | semidirect |
| 6. #10598053 | C2 | semidirect |
| 7. #10598050 | C2 | semidirect |
| 66. #2207 | D5 | semidirect |
| 289. C5 | #12337 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10611445 | 2 |
| C5×#2207 | 2 |
| #10602085 | 2 |
| #10602080 | 2 |
| #10598255 | 2 |
| #10598053 | 2 |
| #10598050 | 2 |
| #12337 | 5 |