Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
420 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 139 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. D4×Dic10 | C2 | semidirect |
| 3. C5×C8×D4 | C2 | semidirect |
| 4. #65403 | C2 | semidirect |
| 5. C2×#3948 | C2 | semidirect |
| 6. #65140 | C2 | semidirect |
| 7. #65130 | C2 | semidirect |
| 8. #65027 | C2 | semidirect |
| 9. #65010 | C2 | semidirect |
| 10. C4×#677 | C2 | semidirect |
| 11. #64970 | C2 | semidirect |
| 87. C8×D4 | D5 | semidirect |
| 91. C5×D4 | SD16 | semidirect |
| 114. Dic10 | #41 | semidirect |
| 216. D4 | #677 | semidirect |
| 234. C5 | #3298 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #65889 | 2 |
| D4×Dic10 | 2 |
| C5×C8×D4 | 2 |
| #65403 | 2 |
| C2×#3948 | 2 |
| #65140 | 2 |
| #65130 | 2 |
| #65027 | 2 |
| #65010 | 2 |
| C4×#677 | 2 |
| #64970 | 2 |
| #3298 | 5 |