Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
484 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 133 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×#417 | C2 |
| socle | C22×C5 | C22×D4 |
| hypercenter | #417 | D5 |
| hypocenter | C5 | #3061 |
| LCS | G ▷ C2×C4×C5 ▷ C2×C5 ▷ C5 | |
| UCS | C1 ◁ C22 ◁ C22×C4 ◁ #417 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #66167 | C2 | semidirect |
| 2. C2×#4096 | C2 | semidirect |
| 3. C2×#4053 | C2 | semidirect |
| 4. #65844 | C2 | semidirect |
| 5. C5×#417 | C2 | semidirect |
| 6. #65422 | C2 | semidirect |
| 7. C2×#3939 | C2 | semidirect |
| 8. #65102 | C2 | semidirect |
| 9. #65101 | C2 | semidirect |
| 10. #65069 | C2 | semidirect |
| 11. #65064 | C2 | semidirect |
| 83. C2×#168 | D4 | semidirect |
| 98. #417 | D5 | semidirect |
| 276. C5 | #3061 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #66167 | 2 |
| C2×#4096 | 2 |
| C2×#4053 | 2 |
| #65844 | 2 |
| C5×#417 | 2 |
| #65422 | 2 |
| C2×#3939 | 2 |
| #65102 | 2 |
| #65101 | 2 |
| #65069 | 2 |
| #65064 | 2 |
| #3061 | 5 |