Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
334 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 121 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. C2×C5×#125 | C2 | semidirect |
| 3. #65357 | C2 | semidirect |
| 4. #65355 | C2 | semidirect |
| 5. #65353 | C2 | semidirect |
| 6. #65352 | C2 | semidirect |
| 7. #65260 | C2 | semidirect |
| 8. #65259 | C2 | semidirect |
| 11. #65214 | C2 | semidirect |
| 80. C2×#125 | D5 | semidirect |
| 227. C5 | #3232 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#125 | 2 |
| #65813 | 2 |
| #65357 | 2 |
| #65355 | 2 |
| #65353 | 2 |
| #65352 | 2 |
| #65260 | 2 |
| #65259 | 2 |
| #65257 | 2 |
| #65256 | 2 |
| #65214 | 2 |
| #3232 | 5 |