Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
316 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 99 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. C4×C5×#108 | C2 | semidirect |
| 4. #10601476 | C2 | semidirect |
| 6. #10598225 | C2 | semidirect |
| 7. #10598149 | C2 | semidirect |
| 20. #64716 | C4 | semidirect |
| 21. #64715 | C4 | semidirect |
| 61. C4×#108 | D5 | semidirect |
| 264. C5 | #13137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C5×#108 | 2 |
| #10601483 | 2 |
| #10601480 | 2 |
| #10601476 | 2 |
| #10600588 | 2 |
| #10598225 | 2 |
| #10598149 | 2 |
| #13137 | 5 |