Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
490 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 490 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 |
|---|---|---|
| 2. C2×#4097 | C2 | semidirect |
| 3. C22×#677 | C2 | semidirect |
| 4. #65850 | C2 | semidirect |
| 5. C5×#416 | C2 | semidirect |
| 6. #65391 | C2 | semidirect |
| 7. #65290 | C2 | semidirect |
| 8. #65087 | C2 | semidirect |
| 9. #65051 | C2 | semidirect |
| 17. C2×#689 | C22 | semidirect |
| 20. C2×#687 | C22 | semidirect |
| 26. #4033 | C22 | semidirect |
| 29. C5×#103 | C22 | semidirect |
| 30. C5×#102 | C22 | semidirect |
| 31. #3946 | C22 | semidirect |
| 50. C2×Dic10 | D4 | semidirect |
| 76. #416 | D5 | semidirect |
| 126. #103 | C2×D5 | semidirect |
| 128. #102 | C2×D5 | semidirect |
| 212. C5 | #3043 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #66164 | 2 |
| C2×#4097 | 2 |
| C22×#677 | 2 |
| #65850 | 2 |
| C5×#416 | 2 |
| #65391 | 2 |
| #65290 | 2 |
| #65087 | 2 |
| #65051 | 2 |
| #3043 | 5 |