Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
600 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 600 conjugacy classes of subgroups — too many to draw. Only its 98 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 |
|---|---|---|
| 1. C2×#65757 | C2 | semidirect |
| 3. C2×#64927 | C2 | semidirect |
| 4. #10604897 | C2 | semidirect |
| 5. #10598722 | C2 | semidirect |
| 59. #4002 | D4 | semidirect |
| 374. C5 | #9124 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#65757 | 2 |
| #10614540 | 2 |
| C2×#64927 | 2 |
| #10604897 | 2 |
| #10598722 | 2 |
| #9124 | 5 |