Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
650 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 650 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. C2×#65197 | C2 | semidirect |
| 2. C2×#64984 | C2 | semidirect |
| 3. C2×#64736 | C2 | semidirect |
| 4. #10600588 | C2 | semidirect |
| 5. C5×#1376 | C2 | semidirect |
| 29. C2×Dic20 | D4 | semidirect |
| 41. C2×D40 | D4 | semidirect |
| 46. C5×M32 | D4 | semidirect |
| 58. #1376 | D5 | semidirect |
| 172. M32 | D20 | semidirect |
| 272. C5 | #13331 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#65197 | 2 |
| C2×#64984 | 2 |
| C2×#64736 | 2 |
| #10600588 | 2 |
| C5×#1376 | 2 |
| #13331 | 5 |