Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
336 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 4. C2×#3948 | C2 | semidirect |
| 5. C2×C8×Dic5 | C2 | semidirect |
| 6. #65266 | C2 | semidirect |
| 7. C2×#3942 | C2 | semidirect |
| 14. #4082 | C4 | semidirect |
| 198. C5 | #1958 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4082 | 2 |
| C2×C5×#102 | 2 |
| C2×#3964 | 2 |
| C2×#3948 | 2 |
| C2×C8×Dic5 | 2 |
| #65266 | 2 |
| C2×#3942 | 2 |
| #1958 | 5 |