Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
472 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 472 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. #65426 | C2 | semidirect |
| 6. #65138 | C2 | semidirect |
| 7. #65130 | C2 | semidirect |
| 8. #65028 | C2 | semidirect |
| 9. #65022 | C2 | semidirect |
| 10. #64988 | C2 | semidirect |
| 11. C4×#677 | C2 | semidirect |
| 82. #677 | D4 | semidirect |
| 93. #436 | D5 | semidirect |
| 163. C4×C5 | #137 | semidirect |
| 246. C5 | #3276 | semidirect |
| 261. 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 |
| #65885 | 2 |
| D4×Dic10 | 2 |
| C5×#436 | 2 |
| #65426 | 2 |
| #65138 | 2 |
| #65130 | 2 |
| #65028 | 2 |
| #65022 | 2 |
| #64988 | 2 |
| C4×#677 | 2 |
| #3276 | 5 |