Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
366 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 366 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. #65376 | C2 | semidirect |
| 4. #65373 | C2 | semidirect |
| 5. #65356 | C2 | semidirect |
| 6. #65354 | C2 | semidirect |
| 7. #65292 | C2 | semidirect |
| 8. #65215 | C2 | semidirect |
| 63. #533 | D5 | semidirect |
| 191. C5 | #3235 | 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 |
| #65376 | 2 |
| #65373 | 2 |
| #65356 | 2 |
| #65354 | 2 |
| #65292 | 2 |
| #65215 | 2 |
| #3235 | 5 |