Finite Group DatabasebetaFinite Group Databasebeta← C7×C22⋊(C13⋊(C52⋊C3)) #41032074
Order 27300.
80 conjugacy classes of subgroups.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | C22⋊(C13⋊(C52⋊C3)) |
| commutator, cosocle, hypocenter | C22×C52×C13 | C3×C7 |
| Frattini | C1 | G |
| Fitting, socle | C22×C52×C7×C13 | C3 |
| LCS | G ▷ C22×C52×C13 | |
| UCS | C1 ◁ C7 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C52×C7×C13 | C3 | semidirect |
| 4. C22⋊(C13⋊(C52⋊C3)) | C7 | direct (N × H) |
| 5. C52×C7×C13 | A4 | semidirect |
| 8. C22×C52×C13 | C3×C7 | semidirect |
| 12. C22×C52×C7 | C13⋊C3 | semidirect |
| 16. C22×C7×C13 | C52⋊C3 | semidirect |
| 18. C52×C13 | C7×A4 | semidirect |
| 23. C52×C7 | C22⋊(C13⋊C3) | semidirect |
| 27. C22×C52 | C7×C13⋊C3 | semidirect |
| 28. C7×C13 | C22⋊(C52⋊C3) | semidirect |
| 33. C22×C13 | C7×C52⋊C3 | semidirect |
| 37. C22×C7 | C13⋊(C52⋊C3) | semidirect |
| 39. C52 | C7×C22⋊(C13⋊C3) | semidirect |
| 43. C13 | C7×C22⋊(C52⋊C3) | semidirect |
| 46. C7 | C22⋊(C13⋊(C52⋊C3)) | direct (N × H) |
| 48. C22 | C7×C13⋊(C52⋊C3) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C52×C7×C13 | 3 |
| C7×C13⋊(C52⋊C3) | 4 |
| C22⋊(C13⋊(C52⋊C3)) | 7 |
| C7×C22⋊(C52⋊C3) | 13 |
| C7×C22⋊(C13⋊C3) | 25 |