Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
568 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 157 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C22×D5 |
| commutator, socle, cosocle | C23×C5 | C24 |
| Frattini | C23 | C23×D5 |
| Fitting | C5×#376 | C2 |
| prime radical | C22×D20 | C22 |
| hypercenter | #376 | D5 |
| hypocenter | C5 | #2398 |
| LCS | G ▷ C23×C5 ▷ C5 | |
| UCS | C1 ◁ C22×C4 ◁ #376 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C4×Dic10 | C2 | semidirect |
| 3. C5×#376 | C2 | semidirect |
| 4. C4×#685 | C2 | semidirect |
| 5. #64963 | C2 | semidirect |
| 6. #64962 | C2 | semidirect |
| 8. #64948 | C2 | semidirect |
| 58. #376 | D5 | semidirect |
| 171. C5 | #2398 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D20 | 2 |
| C2×C4×Dic10 | 2 |
| C5×#376 | 2 |
| C4×#685 | 2 |
| #64963 | 2 |
| #64962 | 2 |
| #64961 | 2 |
| #64948 | 2 |
| #2398 | 5 |