Finite Group DatabasebetaFinite Group DatabasebetaOrder 26100.
128 conjugacy classes of subgroups.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C29 | #3874⋊C2 |
| commutator, cosocle, hypocenter | C52⋊C3 | C22×C3×C29 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C29 | C2×D3 |
| LCS | G ▷ C52⋊C3 | |
| UCS | C1 ◁ C3×C29 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×C29×(C5⋊D5)⋊C3 | C2 | semidirect |
| 2. C3×C29×#3874 | C2 | semidirect |
| 4. C29×#3874⋊C2 | C3 | direct (N × H) |
| 5. C3×C29×C52⋊C3 | C22 | semidirect |
| 6. C3×C29×C5⋊D5 | D3 | semidirect |
| 9. C29×(C5⋊D5)⋊C3 | C2×C3 | semidirect |
| 10. C29×#3874 | C2×C3 | semidirect |
| 13. C29×C52⋊C3 | C22×C3 | semidirect |
| 14. C3×C52×C29 | C2×D3 | semidirect |
| 16. C29×C5⋊D5 | C3×D3 | semidirect |
| 19. C3×#3874⋊C2 | C29 | direct (N × H) |
| 23. C52×C29 | C2×C3×D3 | semidirect |
| 27. C3×(C5⋊D5)⋊C3 | C2×C29 | semidirect |
| 28. C3×#3874 | C2×C29 | semidirect |
| 33. #3874⋊C2 | C3×C29 | direct (N × H) |
| 38. C3×C52⋊C3 | C22×C29 | semidirect |
| 44. C3×C5⋊D5 | D3×C29 | semidirect |
| 47. (C5⋊D5)⋊C3 | C2×C3×C29 | semidirect |
| 48. #3874 | C2×C3×C29 | semidirect |
| 54. C3×C29 | #3874⋊C2 | direct (N × H) |
| 55. C3×C52 | C2×D3×C29 | semidirect |
| 57. C52⋊C3 | C22×C3×C29 | semidirect |
| 61. C5⋊D5 | C3×D3×C29 | semidirect |
| 67. C29 | C3×#3874⋊C2 | direct (N × H) |
| 68. C52 | C2×C3×D3×C29 | semidirect |
| 88. C3 | C29×#3874⋊C2 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C29×(C5⋊D5)⋊C3 | 2 |
| C3×C29×#3874 | 2 |
| C3×D52×C29 | 3 |
| C29×#3874⋊C2 | 3 |
| C2×C3×D3×C29 | 25 |
| C3×#3874⋊C2 | 29 |