Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
464 conjugacy classes of subgroups; only the 160 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 160 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. #65759 | C2 | semidirect |
| 3. #65756 | C2 | semidirect |
| 4. #65754 | C2 | semidirect |
| 5. D5⋊(C22⋊C8) | C2 | semidirect |
| 6. #65705 | C2 | semidirect |
| 7. #65704 | C2 | semidirect |
| 8. #65702 | C2 | semidirect |
| 11. C2×#700 | C22 | semidirect |
| 12. C2×D5⋊C8 | C22 | semidirect |
| 25. #4004 | C22 | semidirect |
| 26. #4003 | C22 | semidirect |
| 27. #4003 | C22 | semidirect |
| 28. #4002 | C22 | semidirect |
| 29. C4⋊#170 | C22 | semidirect |
| 30. C4×#170 | C22 | semidirect |
| 90. D20 | M16 | semidirect |
| 203. C5 | #2974 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4039 | 2 |
| #65759 | 2 |
| #65756 | 2 |
| #65754 | 2 |
| D5⋊(C22⋊C8) | 2 |
| #65705 | 2 |
| #65704 | 2 |
| #65702 | 2 |
| #2974 | 5 |