Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
496 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 135 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. C2×#4097 | C2 | semidirect |
| 3. C2×D5×M16 | C2 | semidirect |
| 4. C2×#4043 | C2 | semidirect |
| 5. C5×#417 | C2 | semidirect |
| 6. #65409 | C2 | semidirect |
| 7. #65253 | C2 | semidirect |
| 8. #65105 | C2 | semidirect |
| 9. #65102 | C2 | semidirect |
| 10. #65069 | C2 | semidirect |
| 11. #65067 | C2 | semidirect |
| 20. C2×#689 | C22 | semidirect |
| 25. C2×#687 | C22 | semidirect |
| 39. C5×#103 | C22 | semidirect |
| 40. C5×#102 | C22 | semidirect |
| 41. #3948 | C22 | semidirect |
| 42. #3948 | C22 | semidirect |
| 43. #3940 | C22 | semidirect |
| 44. #3939 | C22 | semidirect |
| 89. #681 | D4 | semidirect |
| 103. #417 | D5 | semidirect |
| 175. #103 | C2×D5 | semidirect |
| 176. #102 | C2×D5 | semidirect |
| 190. C2×D5 | #137 | semidirect |
| 295. C5 | #3056 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #66162 | 2 |
| C2×#4097 | 2 |
| C2×D5×M16 | 2 |
| C2×#4043 | 2 |
| C5×#417 | 2 |
| #65409 | 2 |
| #65253 | 2 |
| #65105 | 2 |
| #65102 | 2 |
| #65069 | 2 |
| #65067 | 2 |
| #3056 | 5 |