Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
412 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 412 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×#389 | C2 |
| prime radical | C23×D5 | C23 |
| hypercenter | #389 | D5 |
| hypocenter | C5 | #2495 |
| LCS | G ▷ C23×C5 ▷ C5 | |
| UCS | C1 ◁ C23 ◁ #389 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C5×#389 | C2 | semidirect |
| 5. #65271 | C2 | semidirect |
| 6. C4⋊C4×Dic5 | C2 | semidirect |
| 7. #65262 | C2 | semidirect |
| 9. #65225 | C2 | semidirect |
| 11. #64940 | C2 | semidirect |
| 66. #389 | D5 | semidirect |
| 234. C5 | #2495 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#389 | 2 |
| #65279 | 2 |
| #65276 | 2 |
| #65271 | 2 |
| C4⋊C4×Dic5 | 2 |
| #65262 | 2 |
| C4×#685 | 2 |
| #65225 | 2 |
| #64964 | 2 |
| #64940 | 2 |
| #2495 | 5 |