Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
508 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 508 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, Frattini | C23 | C23×D5 |
| commutator, socle, cosocle | C23×C5 | C24 |
| Fitting | C2×C5×C22⋊Q8 | C2 |
| prime radical | C24×C5 | C23 |
| hypercenter | C2×C22⋊Q8 | D5 |
| hypocenter | C5 | #2627 |
| LCS | G ▷ C23×C5 ▷ C5 | |
| UCS | C1 ◁ C23 ◁ C2×C22⋊Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #65518 | C2 | semidirect |
| 5. #65273 | C2 | semidirect |
| 6. #65271 | C2 | semidirect |
| 41. C22×Dic5 | Q8 | semidirect |
| 179. C5 | #2627 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×C22⋊Q8 | 2 |
| C22×#683 | 2 |
| #65518 | 2 |
| #65501 | 2 |
| #65273 | 2 |
| #65271 | 2 |
| #65235 | 2 |
| #65232 | 2 |
| #2627 | 5 |