Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
340 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 2. C4×C5×Q16 | C2 | semidirect |
| 3. #65477 | C2 | semidirect |
| 4. #65309 | C2 | semidirect |
| 5. #65169 | C2 | semidirect |
| 6. #65103 | C2 | semidirect |
| 8. #64971 | C2 | semidirect |
| 55. C4×Q16 | D5 | semidirect |
| 148. C5 | #3342 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #65918 | 2 |
| C4×C5×Q16 | 2 |
| #65477 | 2 |
| #65309 | 2 |
| #65169 | 2 |
| #65103 | 2 |
| C8×D20 | 2 |
| #64971 | 2 |
| #3342 | 5 |