Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
520 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 121 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×#381 | C2 |
| prime radical | #65249 | C2 |
| hypercenter | #381 | D5 |
| hypocenter | C5 | #2760 |
| LCS | G ▷ C23×C5 ▷ C5 | |
| UCS | C1 ◁ C23 ◁ #381 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C5×#381 | C2 | semidirect |
| 2. #65502 | C2 | semidirect |
| 4. #65245 | C2 | semidirect |
| 5. #65236 | C2 | semidirect |
| 6. #64962 | C2 | semidirect |
| 7. #64954 | C2 | semidirect |
| 8. #64953 | C2 | semidirect |
| 9. C5⋊#401 | C2 | semidirect |
| 69. #381 | D5 | semidirect |
| 225. C5 | #2760 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#381 | 2 |
| #65502 | 2 |
| #65249 | 2 |
| #65245 | 2 |
| #65236 | 2 |
| #64962 | 2 |
| #64954 | 2 |
| #64953 | 2 |
| C5⋊#401 | 2 |
| #2760 | 5 |