Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
494 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 494 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 |
|---|---|---|
| 1. C5×#550 | C2 | semidirect |
| 2. C2×#4096 | C2 | semidirect |
| 3. #65885 | C2 | semidirect |
| 4. #65528 | C2 | semidirect |
| 5. #65365 | C2 | semidirect |
| 6. #65361 | C2 | semidirect |
| 7. #65330 | C2 | semidirect |
| 8. #65326 | C2 | semidirect |
| 9. #65320 | C2 | semidirect |
| 10. C4×#688 | C2 | semidirect |
| 11. D4×#168 | C2 | semidirect |
| 70. #688 | D4 | semidirect |
| 84. #550 | D5 | semidirect |
| 171. C4×C5 | #135 | semidirect |
| 255. C5 | #3284 | semidirect |
| 272. C4 | #4096 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#550 | 2 |
| C2×#4096 | 2 |
| #65885 | 2 |
| #65528 | 2 |
| #65365 | 2 |
| #65361 | 2 |
| #65330 | 2 |
| #65326 | 2 |
| #65320 | 2 |
| C4×#688 | 2 |
| D4×#168 | 2 |
| #3284 | 5 |