Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
414 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 107 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. C4×C5×#108 | C2 | semidirect |
| 3. #10600655 | C2 | semidirect |
| 5. #10600649 | C2 | semidirect |
| 7. #10600518 | C2 | semidirect |
| 77. C4×#108 | D5 | semidirect |
| 328. C5 | #9728 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10610199 | 2 |
| C4×C5×#108 | 2 |
| #10600655 | 2 |
| #10600652 | 2 |
| #10600649 | 2 |
| #10600646 | 2 |
| #10600518 | 2 |
| #9728 | 5 |