Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
360 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 100 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. #10604152 | C2 | semidirect |
| 3. C4×#3998 | C2 | semidirect |
| 4. #10598581 | C2 | semidirect |
| 5. #10598579 | C2 | semidirect |
| 133. D20 | M32 | semidirect |
| 139. Dic10 | M32 | semidirect |
| 269. C5 | #11615 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10611007 | 2 |
| #10604152 | 2 |
| C4×#3998 | 2 |
| #10598581 | 2 |
| #10598579 | 2 |
| #11615 | 5 |