Finite Group DatabasebetaFinite Group DatabasebetaOrder 30656.
252 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 91 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D479 |
| commutator, socle, cosocle | C22×C479 | C24 |
| Fitting | #120×C479 | C2 |
| hypercenter | #120 | D479 |
| hypocenter | C479 | #560 |
| LCS | G ▷ C22×C479 ▷ C479 | |
| UCS | C1 ◁ C22 ◁ #120 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #29506378 | C2 | semidirect |
| 2. #29506375 | C2 | semidirect |
| 3. #29506364 | C2 | semidirect |
| 4. #29506363 | C2 | semidirect |
| 5. #29506355 | C2 | semidirect |
| 6. #29506354 | C2 | semidirect |
| 7. #29506353 | C2 | semidirect |
| 8. #29506351 | C2 | semidirect |
| 9. #120×C479 | C2 | semidirect |
| 10. C2×D1916 | C22 | semidirect |
| 14. C2×C22⋊D479 | C22 | semidirect |
| 15. C22×Dic479 | C22 | semidirect |
| 16. C2×C4×D479 | C22 | semidirect |
| 17. C4⋊Dic479 | C22 | semidirect |
| 18. Dic479⋊C4 | C22 | semidirect |
| 19. Dic479⋊C4 | C22 | semidirect |
| 23. C22⋊Dic479 | C22 | semidirect |
| 24. (C2×D479)⋊C4 | C22 | semidirect |
| 25. C4×Dic479 | C22 | semidirect |
| 74. C479 | #560 | semidirect |
| 84. #120 | D479 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #29506378 | 2 |
| #29506375 | 2 |
| #29506364 | 2 |
| #29506363 | 2 |
| #29506355 | 2 |
| #29506354 | 2 |
| #29506353 | 2 |
| #29506351 | 2 |
| #120×C479 | 2 |
| #560 | 479 |