Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
348 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 69 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. #66150 | C2 | semidirect |
| 2. C2×#4088 | C2 | semidirect |
| 4. C5×#419 | C2 | semidirect |
| 5. #65295 | C2 | semidirect |
| 6. #65294 | C2 | semidirect |
| 7. #64776 | C2 | semidirect |
| 80. #419 | D5 | semidirect |
| 249. C5 | #2009 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #66150 | 2 |
| C2×#4088 | 2 |
| #66082 | 2 |
| C5×#419 | 2 |
| #65295 | 2 |
| #65294 | 2 |
| #64776 | 2 |
| #2009 | 5 |