Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
482 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 482 conjugacy classes of subgroups — too many to draw. Only its 125 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. C2×#4061 | C2 | semidirect |
| 2. #66061 | C2 | semidirect |
| 4. C5×#492 | C2 | semidirect |
| 5. #65463 | C2 | semidirect |
| 6. #65462 | C2 | semidirect |
| 7. #65459 | C2 | semidirect |
| 8. #65379 | C2 | semidirect |
| 9. #65364 | C2 | semidirect |
| 10. C4×Dic20 | C2 | semidirect |
| 11. #64977 | C2 | semidirect |
| 81. Dic20 | D4 | semidirect |
| 86. #492 | D5 | semidirect |
| 165. C4×C5 | #137 | semidirect |
| 250. C5 | #3278 | semidirect |
| 265. C4 | #4061 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4061 | 2 |
| #66061 | 2 |
| #66052 | 2 |
| C5×#492 | 2 |
| #65463 | 2 |
| #65462 | 2 |
| #65459 | 2 |
| #65379 | 2 |
| #65364 | 2 |
| C4×Dic20 | 2 |
| #64977 | 2 |
| #3278 | 5 |