Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
362 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 123 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. #65919 | C2 | semidirect |
| 2. #65913 | C2 | semidirect |
| 3. C5×C8×Q8 | C2 | semidirect |
| 4. #65139 | C2 | semidirect |
| 5. #65136 | C2 | semidirect |
| 6. #65133 | C2 | semidirect |
| 8. #64986 | C2 | semidirect |
| 9. #64983 | C2 | semidirect |
| 10. C4×D40 | C2 | semidirect |
| 11. C4×#677 | C2 | semidirect |
| 82. C8×Q8 | D5 | semidirect |
| 222. C5 | #3361 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #65919 | 2 |
| #65913 | 2 |
| C5×C8×Q8 | 2 |
| #65139 | 2 |
| #65136 | 2 |
| #65133 | 2 |
| #65132 | 2 |
| #64986 | 2 |
| #64983 | 2 |
| C4×D40 | 2 |
| C4×#677 | 2 |
| #3361 | 5 |