Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
460 conjugacy classes of subgroups; only the 237 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 237 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D5 |
| commutator | C22×C5 | C23×C4 |
| Fitting | C2×C5×C4⋊Q8 | C2 |
| socle, prime radical, cosocle | C23×C5 | C24 |
| hypercenter | C2×C4⋊Q8 | D5 |
| hypocenter | C5 | #2331 |
| LCS | G ▷ C22×C5 ▷ C5 | |
| UCS | C1 ◁ C23 ◁ C2×C4⋊Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 9. C5×C4⋊Q8 | C4 | semidirect |
| 41. C4×Dic5 | Q8 | semidirect |
| 71. C4⋊Q8 | Dic5 | semidirect |
| 141. C5 | #2331 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×C4⋊Q8 | 2 |
| #65519 | 2 |
| #65274 | 2 |
| #65270 | 2 |
| C4⋊C4×Dic5 | 2 |
| #65225 | 2 |
| #65221 | 2 |
| #2331 | 5 |