Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
436 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 436 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 | C22 | C2×D4×D5 |
| commutator, cosocle | C2×C4×C5 | C24 |
| Frattini | C2×C4 | C23×D5 |
| Fitting | C5×#459 | C2 |
| socle | C22×C5 | C22×D4 |
| hypercenter | #459 | D5 |
| hypocenter | C5 | #3245 |
| LCS | G ▷ C2×C4×C5 ▷ C2×C5 ▷ C5 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #459 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #66050 | C2 | semidirect |
| 2. #65882 | C2 | semidirect |
| 3. C5×#459 | C2 | semidirect |
| 4. #65446 | C2 | semidirect |
| 5. #65439 | C2 | semidirect |
| 6. #65361 | C2 | semidirect |
| 7. #65296 | C2 | semidirect |
| 8. #65135 | C2 | semidirect |
| 9. D5×C4⋊C8 | C2 | semidirect |
| 10. #65064 | C2 | semidirect |
| 11. #65048 | C2 | semidirect |
| 93. #459 | D5 | semidirect |
| 127. C4×D5 | D8 | semidirect |
| 270. C5 | #3245 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #66050 | 2 |
| #65882 | 2 |
| C5×#459 | 2 |
| #65446 | 2 |
| #65439 | 2 |
| #65361 | 2 |
| #65296 | 2 |
| #65135 | 2 |
| D5×C4⋊C8 | 2 |
| #65064 | 2 |
| #65048 | 2 |
| #3245 | 5 |