Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
346 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 117 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. #65868 | C2 | semidirect |
| 2. C5×#424 | C2 | semidirect |
| 3. #65426 | C2 | semidirect |
| 5. #65403 | C2 | semidirect |
| 6. #65140 | C2 | semidirect |
| 7. #65134 | C2 | semidirect |
| 8. #65133 | C2 | semidirect |
| 9. #65131 | C2 | semidirect |
| 73. #424 | D5 | semidirect |
| 188. C5 | #3263 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #65868 | 2 |
| C5×#424 | 2 |
| #65426 | 2 |
| #65424 | 2 |
| #65403 | 2 |
| #65140 | 2 |
| #65134 | 2 |
| #65133 | 2 |
| #65131 | 2 |
| #3263 | 5 |