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. #10610841 | C2 | semidirect |
| 5. C5×#1386 | C2 | semidirect |
| 6. #10598304 | C2 | semidirect |
| 7. #10598216 | C2 | semidirect |
| 34. C2×Dic20 | Q8 | semidirect |
| 39. C2×D40 | Q8 | semidirect |
| 68. #1386 | 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 |
|---|---|
| #10610841 | 2 |
| #10602243 | 2 |
| #10601451 | 2 |
| C2×#64708 | 2 |
| C5×#1386 | 2 |
| #10598304 | 2 |
| #10598216 | 2 |
| #13374 | 5 |