Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
372 conjugacy classes of subgroups; only the 150 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 150 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. #65788 | C2 | semidirect |
| 3. #65773 | C2 | semidirect |
| 4. #65697 | C2 | semidirect |
| 5. #65694 | C2 | semidirect |
| 6. #65692 | C2 | semidirect |
| 7. #65691 | C2 | semidirect |
| 8. #65678 | C2 | semidirect |
| 9. #65676 | C2 | semidirect |
| 201. C5 | #2968 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #66014 | 2 |
| #65788 | 2 |
| #65773 | 2 |
| #65697 | 2 |
| #65694 | 2 |
| #65692 | 2 |
| #65691 | 2 |
| #65678 | 2 |
| #65676 | 2 |
| #2968 | 5 |