Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
402 conjugacy classes of subgroups; only the 146 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 146 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. #65787 | C2 | semidirect |
| 3. #65775 | C2 | semidirect |
| 4. #65695 | C2 | semidirect |
| 5. #65694 | C2 | semidirect |
| 6. #65693 | C2 | semidirect |
| 7. #65692 | C2 | semidirect |
| 8. #65684 | C2 | semidirect |
| 9. #65680 | C2 | semidirect |
| 224. C5 | #2981 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #66002 | 2 |
| #65787 | 2 |
| #65775 | 2 |
| #65695 | 2 |
| #65694 | 2 |
| #65693 | 2 |
| #65692 | 2 |
| #65684 | 2 |
| #65680 | 2 |
| #2981 | 5 |