Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
480 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 137 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 | C5×#386 | C2 |
| prime radical | C22×C5×D4 | C22 |
| hypercenter | #386 | D5 |
| hypocenter | C5 | #2804 |
| LCS | G ▷ C23×C5 ▷ C5 | |
| UCS | C1 ◁ C23 ◁ #386 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #65499 | C2 | semidirect |
| 5. #65236 | C2 | semidirect |
| 6. #65236 | C2 | semidirect |
| 7. #65235 | C2 | semidirect |
| 8. #64949 | C2 | semidirect |
| 9. #64935 | C2 | semidirect |
| 36. C2×C5×D4 | Q8 | semidirect |
| 156. C2×D4 | Dic10 | semidirect |
| 221. C5 | #2804 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#386 | 2 |
| #65510 | 2 |
| #65509 | 2 |
| #65499 | 2 |
| #65236 | 2 |
| #65235 | 2 |
| #64949 | 2 |
| #64935 | 2 |
| #2804 | 5 |