Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
384 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 115 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. #66061 | C2 | semidirect |
| 2. #66047 | C2 | semidirect |
| 3. C5×#486 | C2 | semidirect |
| 4. #65383 | C2 | semidirect |
| 6. #65076 | C2 | semidirect |
| 7. #65074 | C2 | semidirect |
| 8. #65054 | C2 | semidirect |
| 9. #65050 | C2 | semidirect |
| 10. C4×#677 | C2 | semidirect |
| 11. #64968 | C2 | semidirect |
| 78. #486 | D5 | semidirect |
| 226. C5 | #3373 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #66061 | 2 |
| #66047 | 2 |
| C5×#486 | 2 |
| #65383 | 2 |
| #65361 | 2 |
| #65076 | 2 |
| #65074 | 2 |
| #65054 | 2 |
| #65050 | 2 |
| C4×#677 | 2 |
| #64968 | 2 |
| #3373 | 5 |