Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
402 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 144 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. #65776 | C2 | semidirect |
| 3. #65775 | C2 | semidirect |
| 4. #65756 | C2 | semidirect |
| 5. #65705 | C2 | semidirect |
| 6. #65704 | C2 | semidirect |
| 7. #65697 | C2 | semidirect |
| 8. #65695 | C2 | semidirect |
| 9. #65693 | C2 | semidirect |
| 12. C2×#704 | C22 | semidirect |
| 13. C22×#170 | C22 | semidirect |
| 16. C2×#700 | C22 | semidirect |
| 17. C2×D5⋊C8 | C22 | semidirect |
| 29. C22⋊#170 | C22 | semidirect |
| 30. #4004 | C22 | semidirect |
| 33. #4003 | C22 | semidirect |
| 34. #4002 | C22 | semidirect |
| 35. C4⋊#170 | C22 | semidirect |
| 36. C4×#170 | C22 | semidirect |
| 239. C5 | #2978 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #65990 | 2 |
| #65776 | 2 |
| #65775 | 2 |
| #65756 | 2 |
| #65705 | 2 |
| #65704 | 2 |
| #65697 | 2 |
| #65695 | 2 |
| #65693 | 2 |
| #2978 | 5 |