Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
548 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 135 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×#65414 | C2 | semidirect |
| 3. C2×#64783 | C2 | semidirect |
| 4. C2×#64773 | C2 | semidirect |
| 5. #10598211 | C2 | semidirect |
| 48. #3951 | D4 | semidirect |
| 273. C5 | #13010 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#469 | 2 |
| C2×#65414 | 2 |
| C2×#64783 | 2 |
| C2×#64773 | 2 |
| #10598211 | 2 |
| #13010 | 5 |