Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
492 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 181 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C23×D5 |
| commutator, socle | C22×C5 | C23×C4 |
| Fitting | C5×#424 | C2 |
| prime radical | #65858 | C2 |
| cosocle | C2×C4×C5 | C24 |
| hypercenter | #424 | D5 |
| hypocenter | C5 | #2930 |
| LCS | G ▷ C22×C5 ▷ C5 | |
| UCS | C1 ◁ C2×C4 ◁ #424 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#4053 | C2 | semidirect |
| 2. C22×#676 | C2 | semidirect |
| 4. C5×#424 | C2 | semidirect |
| 5. #65415 | C2 | semidirect |
| 6. #65399 | C2 | semidirect |
| 7. #65286 | C2 | semidirect |
| 8. #65127 | C2 | semidirect |
| 9. #65125 | C2 | semidirect |
| 21. C2×#676 | C22 | semidirect |
| 22. C2×C8×D5 | C22 | semidirect |
| 28. C5×C4⋊C8 | C22 | semidirect |
| 30. #3952 | C22 | semidirect |
| 31. #3935 | C22 | semidirect |
| 32. C4×#168 | C22 | semidirect |
| 59. C2×#168 | D4 | semidirect |
| 72. #424 | D5 | semidirect |
| 121. C4⋊C8 | C2×D5 | semidirect |
| 206. C5 | #2930 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4053 | 2 |
| C22×#676 | 2 |
| #65858 | 2 |
| C5×#424 | 2 |
| #65415 | 2 |
| #65399 | 2 |
| #65286 | 2 |
| #65127 | 2 |
| #65125 | 2 |
| #2930 | 5 |