Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
400 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 48. #4015 | Q8 | semidirect |
| 333. C5 | #10359 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10605949 | 2 |
| #10600621 | 2 |
| #10600615 | 2 |
| #10600348 | 2 |
| C5×#1295 | 2 |
| #10598150 | 2 |
| #10359 | 5 |