Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
598 conjugacy classes of subgroups; only the 192 normal subgroups are shown.
This group has 598 conjugacy classes of subgroups — too many to draw. Only its 192 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 |
|---|---|---|
| 3. #10604842 | C2 | semidirect |
| 4. #10604838 | C2 | semidirect |
| 228. C5 | #17961 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10617374 | 2 |
| #10613523 | 2 |
| #10604842 | 2 |
| #10604838 | 2 |
| #10604651 | 2 |
| #10603816 | 2 |
| #10603807 | 2 |
| #17961 | 5 |