Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
376 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 141 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 |
|---|---|---|
| 2. #65853 | C2 | semidirect |
| 3. C5×#424 | C2 | semidirect |
| 5. #65410 | C2 | semidirect |
| 7. C2×#3950 | C2 | semidirect |
| 8. #65139 | C2 | semidirect |
| 9. #65136 | C2 | semidirect |
| 10. #65135 | C2 | semidirect |
| 11. #65118 | C2 | semidirect |
| 47. #709 | Q8 | semidirect |
| 84. #424 | D5 | semidirect |
| 224. C5 | #3083 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #65857 | 2 |
| #65853 | 2 |
| C5×#424 | 2 |
| #65422 | 2 |
| #65410 | 2 |
| #65402 | 2 |
| C2×#3950 | 2 |
| #65139 | 2 |
| #65136 | 2 |
| #65135 | 2 |
| #65118 | 2 |
| #3083 | 5 |