Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
534 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 534 conjugacy classes of subgroups — too many to draw. Only its 95 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×C5×#509 | C2 | semidirect |
| 2. #10615659 | C2 | semidirect |
| 3. C2×#65449 | C2 | semidirect |
| 4. #10602873 | C2 | semidirect |
| 5. C2×#64783 | C2 | semidirect |
| 6. #10602228 | C2 | semidirect |
| 7. #10598312 | C2 | semidirect |
| 82. C2×#509 | D5 | semidirect |
| 393. C5 | #13323 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#509 | 2 |
| #10615659 | 2 |
| C2×#65449 | 2 |
| #10602873 | 2 |
| C2×#64783 | 2 |
| #10602228 | 2 |
| #10598312 | 2 |
| #13323 | 5 |