Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
378 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 378 conjugacy classes of subgroups — too many to draw. Only its 67 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. #10613509 | C2 | semidirect |
| 2. C5×#2246 | C2 | semidirect |
| 3. #10602086 | C2 | semidirect |
| 4. #10602079 | C2 | semidirect |
| 5. #10598281 | C2 | semidirect |
| 6. #10597997 | C2 | semidirect |
| 7. #10597995 | C2 | semidirect |
| 56. #2246 | D5 | semidirect |
| 143. Dic10 | D16 | semidirect |
| 272. C5 | #12328 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10613509 | 2 |
| C5×#2246 | 2 |
| #10602086 | 2 |
| #10602079 | 2 |
| #10598281 | 2 |
| #10597997 | 2 |
| #10597995 | 2 |
| #12328 | 5 |