Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
604 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 604 conjugacy classes of subgroups — too many to draw. Only its 105 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. C5×#3078 | C2 | semidirect |
| 4. #10602628 | C2 | semidirect |
| 5. #10602414 | C2 | semidirect |
| 7. #10598206 | C2 | semidirect |
| 79. #3078 | D5 | semidirect |
| 93. C2×C5×Q8 | SD16 | semidirect |
| 286. C2×Q8 | #688 | semidirect |
| 385. C5 | #10250 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3078 | 2 |
| #10615086 | 2 |
| #10614207 | 2 |
| #10602628 | 2 |
| #10602414 | 2 |
| #10601295 | 2 |
| #10598206 | 2 |
| #10250 | 5 |