Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
668 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 668 conjugacy classes of subgroups — too many to draw. Only its 145 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×#393 | C2 |
| prime radical | #65249 | C2 |
| hypercenter | #393 | D5 |
| hypocenter | C5 | #2463 |
| LCS | G ▷ C23×C5 ▷ C5 | |
| UCS | C1 ◁ C23 ◁ #393 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#4092 | C2 | semidirect |
| 2. C2×#4027 | C2 | semidirect |
| 3. C5×#393 | C2 | semidirect |
| 4. #65250 | C2 | semidirect |
| 6. #65235 | C2 | semidirect |
| 7. #64958 | C2 | semidirect |
| 8. #64954 | C2 | semidirect |
| 9. #64944 | C2 | semidirect |
| 64. #683 | D4 | semidirect |
| 69. #393 | D5 | semidirect |
| 235. C5 | #2463 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4092 | 2 |
| C2×#4027 | 2 |
| C5×#393 | 2 |
| #65250 | 2 |
| #65249 | 2 |
| #65235 | 2 |
| #64958 | 2 |
| #64954 | 2 |
| #64944 | 2 |
| #2463 | 5 |