Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
482 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 482 conjugacy classes of subgroups — too many to draw. Only its 125 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×#4064 | C2 | semidirect |
| 2. #66061 | C2 | semidirect |
| 4. C5×#462 | C2 | semidirect |
| 5. #65476 | C2 | semidirect |
| 6. #65374 | C2 | semidirect |
| 7. C4×#689 | C2 | semidirect |
| 8. #65137 | C2 | semidirect |
| 9. #65127 | C2 | semidirect |
| 10. #65101 | C2 | semidirect |
| 11. #65095 | C2 | semidirect |
| 68. #689 | D4 | semidirect |
| 88. #462 | D5 | semidirect |
| 167. C4×C5 | #137 | semidirect |
| 250. C5 | #3278 | semidirect |
| 265. C4 | #4064 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4064 | 2 |
| #66061 | 2 |
| #65911 | 2 |
| C5×#462 | 2 |
| #65476 | 2 |
| #65374 | 2 |
| C4×#689 | 2 |
| #65137 | 2 |
| #65127 | 2 |
| #65101 | 2 |
| #65095 | 2 |
| #3278 | 5 |