Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
494 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 133 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 |
|---|---|---|
| 1. #66150 | C2 | semidirect |
| 2. C22×#688 | C2 | semidirect |
| 4. #65855 | C2 | semidirect |
| 5. C5×#419 | C2 | semidirect |
| 6. #65408 | C2 | semidirect |
| 7. #65291 | C2 | semidirect |
| 8. #65108 | C2 | semidirect |
| 9. #65107 | C2 | semidirect |
| 15. #4093 | C22 | semidirect |
| 17. #4090 | C22 | semidirect |
| 29. C5×#103 | C22 | semidirect |
| 30. #3946 | C22 | semidirect |
| 31. #3942 | C22 | semidirect |
| 32. #3941 | C22 | semidirect |
| 75. #419 | D5 | semidirect |
| 127. #103 | 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 |
|---|---|
| #66150 | 2 |
| C22×#688 | 2 |
| C2×#4054 | 2 |
| #65855 | 2 |
| C5×#419 | 2 |
| #65408 | 2 |
| #65291 | 2 |
| #65108 | 2 |
| #65107 | 2 |
| #3042 | 5 |