Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
340 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 133 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. Q8×Dic10 | C2 | semidirect |
| 3. #65380 | C2 | semidirect |
| 4. #65367 | C2 | semidirect |
| 5. #65354 | C2 | semidirect |
| 6. #65352 | C2 | semidirect |
| 7. #65313 | C2 | semidirect |
| 61. #687 | Q8 | semidirect |
| 211. C5 | #3385 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#554 | 2 |
| Q8×Dic10 | 2 |
| #65380 | 2 |
| #65367 | 2 |
| #65354 | 2 |
| #65352 | 2 |
| #65313 | 2 |
| #65307 | 2 |
| C4×#687 | 2 |
| #65297 | 2 |
| #65296 | 2 |
| #3385 | 5 |