Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
896 conjugacy classes of subgroups; only the 469 normal subgroups are shown.
This group has 896 conjugacy classes of subgroups — too many to draw. Only its 469 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C23 | C23×D5 |
| commutator, cosocle | C22×C5 | C25 |
| Frattini | C22 | C24×D5 |
| Fitting | C2×C5×#125 | C2 |
| socle, prime radical | C23×C5 | C24 |
| hypercenter | C2×#125 | D5 |
| hypocenter | C5 | C2×#564 |
| LCS | G ▷ C22×C5 ▷ C5 | |
| UCS | C1 ◁ C23 ◁ C2×#125 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C5⋊#564 | C2 | direct (N × H) |
| 97. C2×C5 | #564 | semidirect |
| 111. C5 | C2×#564 | semidirect |
| 120. C2 | C5⋊#564 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#125 | 2 |
| C5⋊#564 | 2 |
| C2×#4036 | 2 |
| C2×#4035 | 2 |
| C2×#4016 | 2 |
| C2×#564 | 5 |