Finite Group DatabasebetaFinite Group Databasebeta← C2×C3×C29⋊((C5⋊D5)⋊C3) #39908070
Order 26100.
160 conjugacy classes of subgroups.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | C29⋊((C5⋊D5)⋊C3) |
| commutator, cosocle, hypocenter | C52×C29 | C22×C32 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C52×C29 | C2×C3 |
| LCS | G ▷ C52×C29 | |
| UCS | C1 ◁ C2×C3 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C3×C29×C52⋊C3 | C2 | semidirect |
| 2. C3×C29⋊((C5⋊D5)⋊C3) | C2 | direct (N × H) |
| 3. C2×C3×C5⋊D145 | C3 | semidirect |
| 4. C2×C29⋊((C5⋊D5)⋊C3) | C3 | direct (N × H) |
| 5. C3×C29×C52⋊C3 | C22 | semidirect |
| 6. C3×C5⋊D145 | C2×C3 | semidirect |
| 7. C2×C29×C52⋊C3 | C2×C3 | semidirect |
| 8. C29⋊((C5⋊D5)⋊C3) | C2×C3 | direct (N × H) |
| 9. C2×C3×C52×C29 | C2×C3 | semidirect |
| 10. C2×C5⋊D145 | C32 | semidirect |
| 11. C29×C52⋊C3 | C22×C3 | semidirect |
| 12. C3×C52×C29 | C22×C3 | semidirect |
| 14. C2×C52×C29 | C2×C32 | semidirect |
| 15. C5⋊D145 | C2×C32 | semidirect |
| 20. C52×C29 | C22×C32 | semidirect |
| 24. C2×C3×C52⋊C3 | D29 | semidirect |
| 34. C3×C52⋊C3 | C2×D29 | semidirect |
| 36. C2×C3×C29 | (C5⋊D5)⋊C3 | semidirect |
| 39. C2×C3×C52 | C3×D29 | semidirect |
| 41. C2×C52⋊C3 | C3×D29 | semidirect |
| 47. C3×C29 | C2×(C5⋊D5)⋊C3 | semidirect |
| 48. C3×C52 | C2×C3×D29 | semidirect |
| 49. C52⋊C3 | C2×C3×D29 | semidirect |
| 51. C2×C29 | C3×(C5⋊D5)⋊C3 | semidirect |
| 53. C2×C52 | C32×D29 | semidirect |
| 58. C29 | C2×C3×(C5⋊D5)⋊C3 | semidirect |
| 59. C52 | C2×C32×D29 | semidirect |
| 72. C2×C3 | C29⋊((C5⋊D5)⋊C3) | direct (N × H) |
| 76. C3 | C2×C29⋊((C5⋊D5)⋊C3) | direct (N × H) |
| 78. C2 | C3×C29⋊((C5⋊D5)⋊C3) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C29×C52⋊C3 | 2 |
| C3×C29⋊((C5⋊D5)⋊C3) | 2 |
| C2×C3×C5⋊D145 | 3 |
| C2×C29⋊((C5⋊D5)⋊C3) | 3 |
| C2×C32×D29 | 25 |
| C2×C3×(C5⋊D5)⋊C3 | 29 |