Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
738 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 738 conjugacy classes of subgroups — too many to draw. Only its 157 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. C23×Dic10 | C2 | semidirect |
| 3. C2×#4097 | C2 | semidirect |
| 4. #65496 | C2 | semidirect |
| 5. #65339 | C2 | semidirect |
| 6. #65329 | C2 | semidirect |
| 7. #65293 | C2 | semidirect |
| 23. C2×#689 | C22 | semidirect |
| 24. C2×#687 | C22 | semidirect |
| 27. #3942 | C22 | semidirect |
| 50. C2×Dic10 | D4 | semidirect |
| 123. C22×C5 | #137 | semidirect |
| 196. C5 | #3004 | semidirect |
| 204. C22 | #4097 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Dic10 | 2 |
| C5×#525 | 2 |
| C2×#4097 | 2 |
| #65496 | 2 |
| #65339 | 2 |
| #65329 | 2 |
| #65293 | 2 |
| #3004 | 5 |