Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
374 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 374 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. #66064 | C2 | semidirect |
| 2. D4×Dic10 | C2 | semidirect |
| 3. C5×#476 | C2 | semidirect |
| 4. #65368 | C2 | semidirect |
| 6. #65159 | C2 | semidirect |
| 7. #65145 | C2 | semidirect |
| 8. #65135 | C2 | semidirect |
| 9. #65120 | C2 | semidirect |
| 11. #65055 | C2 | semidirect |
| 60. #686 | Q8 | semidirect |
| 80. #476 | D5 | semidirect |
| 102. D20 | C2×Q8 | semidirect |
| 110. #168 | C2×Q8 | semidirect |
| 220. C5 | #3384 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #66064 | 2 |
| D4×Dic10 | 2 |
| C5×#476 | 2 |
| #65368 | 2 |
| C4×#686 | 2 |
| #65159 | 2 |
| #65145 | 2 |
| #65135 | 2 |
| #65120 | 2 |
| #65074 | 2 |
| #65055 | 2 |
| #3384 | 5 |