Finite Group DatabasebetaFinite Group Databasebeta← C5×C3⋊(C3⋊#10596814) #39908193
Order 26100.
156 conjugacy classes of subgroups.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | C3⋊(C3⋊#10596814) |
| commutator, hypocenter | C32×C5×C29 | C4×C5 |
| Frattini | C1 | G |
| Fitting, socle | C32×C52×C29 | C4 |
| prime radical | C32×C5×D145 | C2 |
| cosocle | C32×D145 | C2×C5 |
| LCS | G ▷ C32×C5×C29 | |
| UCS | C1 ◁ C5 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C32×C52×C29 | C4 | semidirect |
| 4. C3⋊(C3⋊#10596814) | C5 | direct (N × H) |
| 10. C3×C52×C29 | Dic3 | semidirect |
| 15. C32×C5×C29 | C4×C5 | semidirect |
| 16. C32×C5×C29 | AGL(1,𝔽5) | semidirect |
| 21. C52×C29 | C3⋊Dic3 | semidirect |
| 27. C3×C5×C29 | C5×Dic3 | semidirect |
| 28. C3×C5×C29 | ΓL(1,𝔽16) | semidirect |
| 33. C32×C29 | C5×AGL(1,𝔽5) | semidirect |
| 34. C32×C52 | #1181 | semidirect |
| 40. C5×C29 | C5×C3⋊Dic3 | semidirect |
| 41. C5×C29 | C3⋊ΓL(1,𝔽16) | semidirect |
| 46. C3×C29 | C5×ΓL(1,𝔽16) | semidirect |
| 47. C3×C52 | C3⋊#1181 | semidirect |
| 53. C32×C5 | C5×#1181 | semidirect |
| 54. C32×C5 | #10596814 | semidirect |
| 58. C29 | C5×C3⋊ΓL(1,𝔽16) | semidirect |
| 59. C52 | C3⋊(C3⋊#1181) | semidirect |
| 64. C3×C5 | C5×C3⋊#1181 | semidirect |
| 65. C3×C5 | C3⋊#10596814 | semidirect |
| 69. C32 | C5×#10596814 | semidirect |
| 72. C5 | C5×C3⋊(C3⋊#1181) | semidirect |
| 73. C5 | C3⋊(C3⋊#10596814) | direct (N × H) |
| 75. C3 | C5×C3⋊#10596814 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C5×D145 | 2 |
| C5×C3⋊#10596814 | 3 |
| C3⋊(C3⋊#10596814) | 5 |
| C5×C3⋊(C3⋊#1181) | 5 |
| C5×C3⋊ΓL(1,𝔽16) | 29 |