Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
350 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 125 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. C5×Q82 | C2 | semidirect |
| 3. #65380 | C2 | semidirect |
| 4. #65378 | C2 | semidirect |
| 6. #65376 | C2 | semidirect |
| 7. C4×#689 | C2 | semidirect |
| 8. #65317 | C2 | semidirect |
| 10. #65315 | C2 | semidirect |
| 11. #65313 | C2 | semidirect |
| 75. Q82 | D5 | semidirect |
| 217. C5 | #3375 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×Q82 | 2 |
| #65919 | 2 |
| #65380 | 2 |
| #65378 | 2 |
| #65377 | 2 |
| #65376 | 2 |
| C4×#689 | 2 |
| #65317 | 2 |
| #65316 | 2 |
| #65315 | 2 |
| #65313 | 2 |
| #3375 | 5 |