Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
396 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 79 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. #10600405 | C2 | semidirect |
| 3. #10599484 | C2 | semidirect |
| 5. C5×#1271 | C2 | semidirect |
| 6. #10597971 | C2 | semidirect |
| 64. #1271 | D5 | semidirect |
| 338. C5 | #7834 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10607916 | 2 |
| #10600405 | 2 |
| #10599484 | 2 |
| #10599475 | 2 |
| C5×#1271 | 2 |
| #10597971 | 2 |
| #10597970 | 2 |
| #7834 | 5 |