Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
712 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 712 conjugacy classes of subgroups — too many to draw. Only its 137 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. C2×#65297 | C2 | semidirect |
| 3. C2×D4⋊#168 | C2 | semidirect |
| 4. #10600372 | C2 | semidirect |
| 5. #10598125 | C2 | semidirect |
| 42. #4015 | D4 | semidirect |
| 48. C4⋊#168 | D4 | semidirect |
| 289. C5 | #10235 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2537 | 2 |
| C2×#65297 | 2 |
| C2×D4⋊#168 | 2 |
| #10600372 | 2 |
| #10598125 | 2 |
| #10235 | 5 |