Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
740 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 740 conjugacy classes of subgroups — too many to draw. Only its 173 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×C5×Q16 | C2 | semidirect |
| 4. C22×#689 | C2 | semidirect |
| 5. C2×#3967 | C2 | semidirect |
| 6. #65475 | C2 | direct (N × H) |
| 8. C2×#3948 | C2 | semidirect |
| 20. C2×C5×Q16 | C22 | semidirect |
| 25. C2×#689 | C22 | semidirect |
| 30. #3967 | C22 | semidirect |
| 32. #3948 | C22 | semidirect |
| 76. C22×Q16 | D5 | semidirect |
| 85. C22×D5 | Q16 | semidirect |
| 130. C2×Q16 | C2×D5 | semidirect |
| 148. C2×D5 | C2×Q16 | semidirect |
| 197. C2×C5 | #451 | semidirect |
| 237. C5 | C2×#451 | semidirect |
| 255. C2 | #65475 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q8×D5 | 2 |
| C22×C5×Q16 | 2 |
| C2×#4092 | 2 |
| C22×#689 | 2 |
| C2×#3967 | 2 |
| #65475 | 2 |
| C2×#3952 | 2 |
| C2×#3948 | 2 |
| C2×#451 | 5 |