Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
182 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 182 conjugacy classes of subgroups — too many to draw. Only its 63 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×#436 | C2 | semidirect |
| 3. C8×D20 | C2 | semidirect |
| 4. D4⋊#168 | C2 | semidirect |
| 5. #64703 | C2 | semidirect |
| 6. #64700 | C2 | semidirect |
| 7. #64674 | C2 | semidirect |
| 44. #436 | D5 | semidirect |
| 62. D20 | M16 | semidirect |
| 147. C5 | #1586 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#436 | 2 |
| C4×#686 | 2 |
| C8×D20 | 2 |
| D4⋊#168 | 2 |
| #64703 | 2 |
| #64700 | 2 |
| #64674 | 2 |
| #1586 | 5 |