Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
406 conjugacy classes of subgroups; only the 168 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 168 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 |
|---|---|---|
| 2. D4×#170 | C2 | semidirect |
| 3. #65759 | C2 | semidirect |
| 4. C2×#4002 | C2 | semidirect |
| 5. #65709 | C2 | semidirect |
| 6. #65693 | C2 | semidirect |
| 7. #65683 | C2 | semidirect |
| 8. C4×#700 | C2 | semidirect |
| 71. C5×D4 | M16 | semidirect |
| 91. #170 | #41 | semidirect |
| 168. D4 | #700 | semidirect |
| 187. C5 | #2970 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#711 | 2 |
| D4×#170 | 2 |
| #65759 | 2 |
| C2×#4002 | 2 |
| #65709 | 2 |
| #65693 | 2 |
| #65683 | 2 |
| C4×#700 | 2 |
| #2970 | 5 |