Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
454 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 94 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 |
|---|---|---|
| 3. #10604037 | C2 | semidirect |
| 4. #10603817 | C2 | semidirect |
| 6. #10598597 | C2 | semidirect |
| 7. #10598531 | C2 | semidirect |
| 156. C5×D4 | #108 | semidirect |
| 326. D4 | #3996 | semidirect |
| 361. C5 | #8908 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×#700 | 2 |
| #10604404 | 2 |
| #10604037 | 2 |
| #10603817 | 2 |
| D5×D4⋊C8 | 2 |
| #10598597 | 2 |
| #10598531 | 2 |
| #8908 | 5 |