Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
360 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 129 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | C22×#686 |
| commutator, cosocle | C5×C8 | C24 |
| Frattini | C8 | C23×D5 |
| Fitting | C5×#576 | C2 |
| socle | C2×C5 | C22×D8 |
| hypercenter | #576 | D5 |
| hypocenter | C5 | #3416 |
| LCS | G ▷ C5×C8 ▷ C4×C5 ▷ C2×C5 ▷ C5 | |
| UCS | C1 ◁ C2 ◁ #41 ◁ #131 ◁ #576 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C5×#576 | C2 | semidirect |
| 2. #66087 | C2 | semidirect |
| 3. #65484 | C2 | semidirect |
| 4. #65483 | C2 | semidirect |
| 5. C2×#3959 | C2 | semidirect |
| 6. #65436 | C2 | semidirect |
| 7. #65429 | C2 | semidirect |
| 15. C2×Dic20 | C22 | semidirect |
| 16. #4050 | C22 | semidirect |
| 17. #3961 | C22 | semidirect |
| 18. #3960 | C22 | semidirect |
| 19. #3959 | C22 | semidirect |
| 20. #3959 | C22 | semidirect |
| 21. #3958 | C22 | semidirect |
| 22. #3944 | C22 | semidirect |
| 23. C2×#672 | C22 | semidirect |
| 47. #576 | D5 | semidirect |
| 136. C5 | #3416 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#576 | 2 |
| #66087 | 2 |
| #65484 | 2 |
| #65483 | 2 |
| C2×#3959 | 2 |
| #65436 | 2 |
| #65429 | 2 |
| #3416 | 5 |