Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
536 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 98 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×#3990 | C2 | semidirect |
| 3. C2×#64906 | C2 | semidirect |
| 4. #10604731 | C2 | semidirect |
| 5. #10598622 | C2 | semidirect |
| 59. #3990 | D4 | semidirect |
| 228. C22×C5 | #361 | semidirect |
| 347. C5 | #13067 | semidirect |
| 364. C22 | #64906 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#3990 | 2 |
| D5×#466 | 2 |
| C2×#64906 | 2 |
| #10604731 | 2 |
| #10598622 | 2 |
| #13067 | 5 |