Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
1260 conjugacy classes of subgroups; only the 485 normal subgroups are shown.
This group has 1260 conjugacy classes of subgroups — too many to draw. Only its 485 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C23 | C23×D5 |
| commutator, cosocle | C22×C5 | C25 |
| Frattini | C22 | C24×D5 |
| Fitting | C2×C5×#117 | C2 |
| socle | C23×C5 | C24 |
| hypercenter | C2×#117 | D5 |
| hypocenter | C5 | C2×#540 |
| LCS | G ▷ C22×C5 ▷ C5 | |
| UCS | C1 ◁ C23 ◁ C2×#117 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C5×#117 | C2 | semidirect |
| 2. C2×#4076 | C2 | semidirect |
| 3. #65869 | C2 | direct (N × H) |
| 4. C2×#4040 | C2 | semidirect |
| 5. C2×#4030 | C2 | semidirect |
| 6. C2×#4020 | C2 | semidirect |
| 7. C2×C4×D20 | C2 | semidirect |
| 8. C2×#4016 | C2 | semidirect |
| 14. C5×#117 | C22 | semidirect |
| 19. #4076 | C22 | semidirect |
| 24. #4040 | C22 | semidirect |
| 25. #4030 | C22 | semidirect |
| 26. #4020 | C22 | semidirect |
| 27. C4×D20 | C22 | semidirect |
| 28. #4016 | C22 | semidirect |
| 62. C2×#117 | D5 | semidirect |
| 97. #117 | C2×D5 | semidirect |
| 147. C2×C5 | #540 | semidirect |
| 174. C5 | C2×#540 | semidirect |
| 192. C2 | #65869 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#117 | 2 |
| C2×#4076 | 2 |
| #65869 | 2 |
| C2×#4040 | 2 |
| C2×#4030 | 2 |
| C2×#4020 | 2 |
| C2×C4×D20 | 2 |
| C2×#4016 | 2 |
| C2×#540 | 5 |