Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
482 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 482 conjugacy classes of subgroups — too many to draw. Only its 125 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D4×D5 |
| commutator, cosocle | C2×C4×C5 | C24 |
| Frattini | C2×C4 | C23×D5 |
| Fitting | C5×#466 | C2 |
| socle | C22×C5 | C22×D4 |
| hypercenter | #466 | D5 |
| hypocenter | C5 | #3285 |
| LCS | G ▷ C2×C4×C5 ▷ C2×C5 ▷ C5 | |
| UCS | C1 ◁ C22 ◁ C22×C4 ◁ #466 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#4058 | C2 | semidirect |
| 2. C22×Dic20 | C2 | semidirect |
| 3. #65932 | C2 | semidirect |
| 4. C5×#466 | C2 | semidirect |
| 5. #65444 | C2 | semidirect |
| 6. C8×C22⋊D5 | C2 | semidirect |
| 7. #65329 | C2 | semidirect |
| 8. #65176 | C2 | semidirect |
| 9. #65162 | C2 | semidirect |
| 10. #65072 | C2 | semidirect |
| 11. #65056 | C2 | semidirect |
| 79. Dic20 | D4 | semidirect |
| 86. #466 | D5 | semidirect |
| 157. C22×C5 | #135 | semidirect |
| 247. C5 | #3285 | semidirect |
| 256. C22 | #4058 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4058 | 2 |
| C22×Dic20 | 2 |
| #65932 | 2 |
| C5×#466 | 2 |
| #65444 | 2 |
| C8×C22⋊D5 | 2 |
| #65329 | 2 |
| #65176 | 2 |
| #65162 | 2 |
| #65072 | 2 |
| #65056 | 2 |
| #3285 | 5 |