Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
1008 conjugacy classes of subgroups; only the 234 normal subgroups are shown.
This group has 1008 conjugacy classes of subgroups — too many to draw. Only its 234 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. C22×#704 | C2 | semidirect |
| 3. #65755 | C2 | direct (N × H) |
| 4. C2×#4003 | C2 | semidirect |
| 14. C2×#704 | C22 | semidirect |
| 15. C22×#170 | C22 | semidirect |
| 16. #4003 | C22 | semidirect |
| 40. C2×#170 | C23 | semidirect |
| 54. C22×D5 | M16 | semidirect |
| 92. C2×D5 | C2×M16 | semidirect |
| 121. C2×C5 | #407 | semidirect |
| 150. C5 | C2×#407 | semidirect |
| 168. C2 | #65755 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C4×D5 | 2 |
| C22×#704 | 2 |
| #65755 | 2 |
| C2×#4003 | 2 |
| C2×#407 | 5 |