Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
440 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 440 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×#390 | C2 |
| prime radical | C22×C5×D4 | C22 |
| hypercenter | #390 | D5 |
| hypocenter | C5 | #2513 |
| LCS | G ▷ C23×C5 ▷ C5 | |
| UCS | C1 ◁ C23 ◁ #390 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. C4⋊C4×Dic5 | C2 | semidirect |
| 5. #65262 | C2 | semidirect |
| 6. #65241 | C2 | semidirect |
| 7. #65241 | C2 | semidirect |
| 8. #65234 | C2 | semidirect |
| 9. #65233 | C2 | semidirect |
| 10. #65225 | C2 | semidirect |
| 11. C4×#683 | C2 | semidirect |
| 240. C5 | #2513 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#390 | 2 |
| #65510 | 2 |
| C4⋊C4×Dic5 | 2 |
| #65262 | 2 |
| #65241 | 2 |
| #65234 | 2 |
| #65233 | 2 |
| #65225 | 2 |
| C4×#683 | 2 |
| #2513 | 5 |