Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
698 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 698 conjugacy classes of subgroups — too many to draw. Only its 145 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | C2×#4083 |
| commutator, cosocle | C2×C4×C5 | C24 |
| Frattini | C2×C4 | C23×D5 |
| Fitting | C5×#575 | C2 |
| socle | C2×C5 | C2×#120 |
| hypercenter | #575 | D5 |
| hypocenter | C5 | #3020 |
| LCS | G ▷ C2×C4×C5 ▷ C2×C5 ▷ C5 | |
| UCS | C1 ◁ C2 ◁ C22×C4 ◁ #575 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#4150 | C2 | semidirect |
| 2. C5×#575 | C2 | semidirect |
| 3. #66159 | C2 | semidirect |
| 4. #66156 | C2 | semidirect |
| 5. #65525 | C2 | semidirect |
| 6. #65494 | C2 | semidirect |
| 7. #65490 | C2 | semidirect |
| 8. #65428 | C2 | semidirect |
| 9. C2×#3956 | C2 | semidirect |
| 24. C5×#137 | C22 | semidirect |
| 26. C5×AGL(1,ℤ/8) | C22 | semidirect |
| 32. #4090 | C22 | semidirect |
| 33. #4088 | C22 | semidirect |
| 34. #4082 | C22 | semidirect |
| 36. #4078 | C22 | semidirect |
| 40. #3969 | C22 | semidirect |
| 41. #3957 | C22 | semidirect |
| 42. #3956 | C22 | semidirect |
| 111. #575 | D5 | semidirect |
| 185. #137 | C2×D5 | semidirect |
| 189. AGL(1,ℤ/8) | C2×D5 | semidirect |
| 344. C5 | #3020 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4150 | 2 |
| C5×#575 | 2 |
| #66159 | 2 |
| #66156 | 2 |
| #65525 | 2 |
| #65494 | 2 |
| #65490 | 2 |
| #65428 | 2 |
| C2×#3956 | 2 |
| #3020 | 5 |