Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
560 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 560 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, Frattini | C23 | C23×D5 |
| commutator, socle, cosocle | C23×C5 | C24 |
| Fitting | C5×#393 | C2 |
| prime radical | C24×D5 | C22 |
| hypercenter | #393 | D5 |
| hypocenter | C5 | #2736 |
| 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. C5×#393 | C2 | semidirect |
| 2. #65520 | C2 | semidirect |
| 5. #65242 | C2 | semidirect |
| 6. #65234 | C2 | semidirect |
| 7. #64964 | C2 | semidirect |
| 8. #64959 | C2 | semidirect |
| 9. #64958 | C2 | semidirect |
| 11. C22×C5×Q8 | C22 | semidirect |
| 22. C2×C4⋊Dic5 | C22 | semidirect |
| 23. C2×#683 | C22 | semidirect |
| 24. C2×C4×Dic5 | C22 | semidirect |
| 25. C5×#95 | C22 | semidirect |
| 26. C5×#95 | C22 | semidirect |
| 27. #3963 | C22 | semidirect |
| 28. #3963 | C22 | semidirect |
| 29. #3963 | C22 | semidirect |
| 30. #3963 | C22 | semidirect |
| 64. #393 | D5 | semidirect |
| 109. C22×Q8 | C2×D5 | semidirect |
| 127. #95 | C2×D5 | semidirect |
| 128. #95 | C2×D5 | semidirect |
| 228. C5 | #2736 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#393 | 2 |
| #65520 | 2 |
| #65244 | 2 |
| #65242 | 2 |
| #65234 | 2 |
| #64964 | 2 |
| #64959 | 2 |
| #64958 | 2 |
| #2736 | 5 |