Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
500 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 500 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. C22×C5×Q16 | C2 | semidirect |
| 3. C2×Q8×Dic5 | C2 | semidirect |
| 5. C2×#3967 | C2 | semidirect |
| 6. #65474 | C2 | direct (N × H) |
| 8. C2×#3946 | C2 | semidirect |
| 13. C2×C5×Q16 | C22 | semidirect |
| 18. Q8×Dic5 | C22 | semidirect |
| 28. #3967 | C22 | semidirect |
| 30. #3946 | C22 | semidirect |
| 65. C22×Q16 | D5 | semidirect |
| 107. C2×Q16 | C2×D5 | semidirect |
| 174. C2×C5 | #464 | semidirect |
| 209. C5 | C2×#464 | semidirect |
| 227. C2 | #65474 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×Q16 | 2 |
| C2×#4093 | 2 |
| C2×Q8×Dic5 | 2 |
| C22×#688 | 2 |
| C2×#3967 | 2 |
| #65474 | 2 |
| C2×#3953 | 2 |
| C2×#3946 | 2 |
| C2×#464 | 5 |