Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
460 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 139 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. C5×#550 | C2 | semidirect |
| 2. #65911 | C2 | semidirect |
| 3. #65362 | C2 | semidirect |
| 4. #65361 | C2 | semidirect |
| 5. Q8×#168 | C2 | semidirect |
| 6. #65304 | C2 | semidirect |
| 7. C4×#686 | C2 | semidirect |
| 47. #550 | D5 | semidirect |
| 55. C5×Q8 | D8 | semidirect |
| 72. #168 | #41 | semidirect |
| 130. Q8 | #686 | semidirect |
| 148. C5 | #3391 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#550 | 2 |
| #65911 | 2 |
| #65362 | 2 |
| #65361 | 2 |
| Q8×#168 | 2 |
| #65304 | 2 |
| C4×#686 | 2 |
| #3391 | 5 |