Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
388 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 125 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. #66064 | C2 | semidirect |
| 3. C5×#498 | C2 | semidirect |
| 4. #65383 | C2 | semidirect |
| 5. #65373 | C2 | semidirect |
| 6. #65153 | C2 | semidirect |
| 7. #65152 | C2 | semidirect |
| 8. #65151 | C2 | semidirect |
| 9. D5×#106 | C2 | semidirect |
| 10. C4×#677 | C2 | semidirect |
| 11. C8×D20 | C2 | semidirect |
| 77. #498 | D5 | semidirect |
| 102. D20 | SD16 | semidirect |
| 111. C5×C8 | #41 | semidirect |
| 223. C8 | #713 | semidirect |
| 224. C5 | #3335 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #66064 | 2 |
| #66060 | 2 |
| C5×#498 | 2 |
| #65383 | 2 |
| #65373 | 2 |
| #65153 | 2 |
| #65152 | 2 |
| #65151 | 2 |
| D5×#106 | 2 |
| C4×#677 | 2 |
| C8×D20 | 2 |
| #3335 | 5 |