Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
390 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 390 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. C5×#533 | C2 | semidirect |
| 3. #65378 | C2 | semidirect |
| 4. #65375 | C2 | semidirect |
| 5. #65336 | C2 | semidirect |
| 6. #65320 | C2 | semidirect |
| 7. #65316 | C2 | semidirect |
| 8. #65215 | C2 | semidirect |
| 65. #533 | D5 | semidirect |
| 197. C5 | #3216 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#533 | 2 |
| #65811 | 2 |
| #65378 | 2 |
| #65375 | 2 |
| #65336 | 2 |
| #65320 | 2 |
| #65316 | 2 |
| #65215 | 2 |
| #3216 | 5 |