Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
360 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 89 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. #10610903 | C2 | semidirect |
| 5. C5×#1384 | C2 | semidirect |
| 6. #10598305 | C2 | semidirect |
| 7. #10598217 | C2 | semidirect |
| 33. C2×Dic20 | Q8 | semidirect |
| 38. C2×D40 | Q8 | semidirect |
| 69. #1384 | D5 | semidirect |
| 291. C5 | #13374 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10610903 | 2 |
| C2×#64738 | 2 |
| #10601451 | 2 |
| #10601449 | 2 |
| C5×#1384 | 2 |
| #10598305 | 2 |
| #10598217 | 2 |
| #13374 | 5 |