Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
988 conjugacy classes of subgroups; only the 549 normal subgroups are shown.
This group has 988 conjugacy classes of subgroups — too many to draw. Only its 549 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D5 |
| commutator, socle, cosocle | C22×C5 | C25 |
| Fitting | C4×C5×#41 | C2 |
| prime radical | C2×C5×#41 | C22 |
| hypercenter | C4×#41 | D5 |
| hypocenter | C5 | #3504 |
| LCS | G ▷ C22×C5 ▷ C5 | |
| UCS | C1 ◁ C22 ◁ C4×#41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #65903 | C2 | semidirect |
| 4. #65873 | C2 | semidirect |
| 5. #65853 | C2 | semidirect |
| 6. #65804 | C2 | semidirect |
| 7. C2×#4016 | C2 | semidirect |
| 29. C5×#41 | Q8 | semidirect |
| 99. #41 | Dic10 | semidirect |
| 136. C5 | #3504 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C5×#41 | 2 |
| #66161 | 2 |
| #65903 | 2 |
| #65873 | 2 |
| #65853 | 2 |
| #65804 | 2 |
| C2×#4016 | 2 |
| #3504 | 5 |