Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
460 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 141 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 |
| 4. #65514 | C2 | semidirect |
| 5. #65478 | C2 | semidirect |
| 6. #65477 | C2 | semidirect |
| 7. #65395 | C2 | semidirect |
| 53. C22×Q16 | D5 | semidirect |
| 161. C5 | #3059 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×Q16 | 2 |
| #66150 | 2 |
| C2×#4047 | 2 |
| #65514 | 2 |
| #65478 | 2 |
| #65477 | 2 |
| #65395 | 2 |
| #3059 | 5 |