Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
482 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 482 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. C2×#4055 | C2 | semidirect |
| 3. D4×Dic10 | C2 | semidirect |
| 4. C5×#436 | C2 | semidirect |
| 5. #65423 | C2 | semidirect |
| 6. #65138 | C2 | semidirect |
| 7. #65137 | C2 | semidirect |
| 8. #65027 | C2 | semidirect |
| 9. #65022 | C2 | semidirect |
| 10. C4×Dic20 | C2 | semidirect |
| 11. #64982 | C2 | semidirect |
| 79. Dic20 | D4 | semidirect |
| 93. #436 | D5 | semidirect |
| 165. C4×C5 | #137 | semidirect |
| 250. C5 | #3278 | semidirect |
| 265. C4 | #4055 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4055 | 2 |
| #65887 | 2 |
| D4×Dic10 | 2 |
| C5×#436 | 2 |
| #65423 | 2 |
| #65138 | 2 |
| #65137 | 2 |
| #65027 | 2 |
| #65022 | 2 |
| C4×Dic20 | 2 |
| #64982 | 2 |
| #3278 | 5 |