Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
494 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 141 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. C22×#677 | C2 | semidirect |
| 3. #65860 | C2 | semidirect |
| 4. #65855 | C2 | semidirect |
| 5. C5×#424 | C2 | semidirect |
| 6. #65409 | C2 | semidirect |
| 7. #65402 | C2 | semidirect |
| 8. #65133 | C2 | semidirect |
| 9. #65130 | C2 | semidirect |
| 26. #4021 | C22 | semidirect |
| 28. #4015 | C22 | semidirect |
| 29. C5×C4⋊C8 | C22 | semidirect |
| 30. #3953 | C22 | semidirect |
| 31. #3948 | C22 | semidirect |
| 32. #3948 | C22 | semidirect |
| 74. #424 | D5 | semidirect |
| 125. C4⋊C8 | C2×D5 | semidirect |
| 212. C5 | #3042 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4054 | 2 |
| C22×#677 | 2 |
| #65860 | 2 |
| #65855 | 2 |
| C5×#424 | 2 |
| #65409 | 2 |
| #65402 | 2 |
| #65133 | 2 |
| #65130 | 2 |
| #3042 | 5 |