Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
400 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 78 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. #10604732 | C2 | semidirect |
| 3. C2×#64887 | C2 | semidirect |
| 4. #10598814 | C2 | semidirect |
| 5. #10598613 | C2 | semidirect |
| 305. C5 | #11893 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10612489 | 2 |
| #10604732 | 2 |
| C2×#64887 | 2 |
| #10598814 | 2 |
| #10598613 | 2 |
| #11893 | 5 |