Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
496 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 143 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. C2×C5×#137 | C2 | semidirect |
| 3. C2×#4092 | C2 | semidirect |
| 4. C2×D5×M16 | C2 | semidirect |
| 5. #65521 | C2 | semidirect |
| 6. #65514 | C2 | semidirect |
| 7. #65478 | C2 | semidirect |
| 8. #65477 | C2 | semidirect |
| 9. #65463 | C2 | semidirect |
| 10. #65460 | C2 | semidirect |
| 11. #65410 | C2 | semidirect |
| 16. C2×C5×Q16 | C22 | semidirect |
| 17. C2×C5×SD16 | C22 | semidirect |
| 39. #3967 | C22 | semidirect |
| 40. #3967 | C22 | semidirect |
| 41. #3967 | C22 | semidirect |
| 42. #3964 | C22 | semidirect |
| 43. #3950 | C22 | semidirect |
| 44. #3949 | C22 | semidirect |
| 71. C5×M16 | D4 | semidirect |
| 93. C2×#137 | D5 | semidirect |
| 148. C2×Q16 | C2×D5 | semidirect |
| 149. C2×SD16 | C2×D5 | semidirect |
| 190. C2×D5 | #137 | semidirect |
| 228. M16 | C22⋊D5 | semidirect |
| 295. C5 | #3056 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#137 | 2 |
| #66162 | 2 |
| C2×#4092 | 2 |
| C2×D5×M16 | 2 |
| #65521 | 2 |
| #65514 | 2 |
| #65478 | 2 |
| #65477 | 2 |
| #65463 | 2 |
| #65460 | 2 |
| #65410 | 2 |
| #3056 | 5 |