Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
322 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 161 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×#432 | C2 |
| prime radical | C23×C5 | C22×C4 |
| cosocle | C2×C4×C5 | C24 |
| hypercenter | #432 | D5 |
| hypocenter | C5 | #2985 |
| LCS | G ▷ C22×C5 ▷ C5 | |
| UCS | C1 ◁ C2×C4 ◁ #432 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #65120 | C2 | semidirect |
| 5. #65119 | C2 | semidirect |
| 7. #64990 | C2 | semidirect |
| 146. C5 | #2985 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #65804 | 2 |
| C5×#432 | 2 |
| #65214 | 2 |
| #65120 | 2 |
| #65119 | 2 |
| #65009 | 2 |
| #64990 | 2 |
| #2985 | 5 |