Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
454 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 97 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. #10605128 | C2 | semidirect |
| 4. C5×#1274 | C2 | semidirect |
| 5. #10598237 | C2 | semidirect |
| 33. #4020 | Q8 | semidirect |
| 35. #4015 | Q8 | semidirect |
| 53. #1274 | D5 | semidirect |
| 258. C5 | #10370 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10605128 | 2 |
| #10601582 | 2 |
| #10600233 | 2 |
| C5×#1274 | 2 |
| #10598237 | 2 |
| #10370 | 5 |