Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
372 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 123 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. #65918 | C2 | semidirect |
| 2. Q8×D20 | C2 | semidirect |
| 3. C5×#446 | C2 | semidirect |
| 4. #65139 | C2 | semidirect |
| 5. #65135 | C2 | semidirect |
| 7. #65130 | C2 | semidirect |
| 8. #65003 | C2 | semidirect |
| 9. #64999 | C2 | semidirect |
| 11. #64970 | C2 | semidirect |
| 83. #446 | D5 | semidirect |
| 222. C5 | #3367 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #65918 | 2 |
| Q8×D20 | 2 |
| C5×#446 | 2 |
| #65139 | 2 |
| #65135 | 2 |
| #65133 | 2 |
| #65130 | 2 |
| #65003 | 2 |
| #64999 | 2 |
| C4×D40 | 2 |
| #64970 | 2 |
| #3367 | 5 |