Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
362 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 115 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. #65895 | C2 | semidirect |
| 2. C4×C5×D8 | C2 | semidirect |
| 4. #65444 | C2 | semidirect |
| 5. #65307 | C2 | semidirect |
| 6. #65176 | C2 | semidirect |
| 7. #65163 | C2 | semidirect |
| 8. #65069 | C2 | semidirect |
| 9. #65054 | C2 | semidirect |
| 10. C4×Dic20 | C2 | semidirect |
| 11. #64978 | C2 | semidirect |
| 81. C4×D8 | D5 | semidirect |
| 212. C5 | #3175 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #65895 | 2 |
| C4×C5×D8 | 2 |
| #65446 | 2 |
| #65444 | 2 |
| #65307 | 2 |
| #65176 | 2 |
| #65163 | 2 |
| #65069 | 2 |
| #65054 | 2 |
| C4×Dic20 | 2 |
| #64978 | 2 |
| #3175 | 5 |