Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
294 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 61 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×D5×Q32 | C2 | semidirect |
| 2. C2×#64741 | C2 | semidirect |
| 3. C2×#64669 | C2 | semidirect |
| 5. C5×#1416 | C2 | semidirect |
| 6. #10598085 | C2 | semidirect |
| 7. #10598069 | C2 | semidirect |
| 34. C5×Q32 | D4 | semidirect |
| 41. Dic40 | D4 | semidirect |
| 53. #1416 | D5 | semidirect |
| 129. Q32 | D20 | semidirect |
| 146. C2×D5 | SD64 | semidirect |
| 204. C5 | #13662 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D5×Q32 | 2 |
| C2×#64741 | 2 |
| C2×#64669 | 2 |
| #10600120 | 2 |
| C5×#1416 | 2 |
| #10598085 | 2 |
| #10598069 | 2 |
| #13662 | 5 |