Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
696 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 696 conjugacy classes of subgroups — too many to draw. Only its 114 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. C22×#4002 | C2 | semidirect |
| 3. C2×#64921 | C2 | semidirect |
| 4. #10604897 | C2 | semidirect |
| 5. #10598722 | C2 | semidirect |
| 61. #4002 | D4 | semidirect |
| 248. C22×C5 | #329 | semidirect |
| 380. C5 | #9119 | semidirect |
| 394. C22 | #64921 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#4002 | 2 |
| #10614429 | 2 |
| C2×#64921 | 2 |
| #10604897 | 2 |
| #10598722 | 2 |
| #9119 | 5 |