Finite Group DatabasebetaFinite Group Databasebeta← C5×C7×C5⋊AGL(1,𝔽7) #20301261
Order 7350.
88 conjugacy classes of subgroups.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C7 | C5⋊AGL(1,𝔽7) |
| commutator, hypocenter | C5×C7 | C2×C3×C5×C7 |
| Frattini | C1 | G |
| Fitting, socle | C52×C72 | C2×C3 |
| LCS | G ▷ C5×C7 | |
| UCS | C1 ◁ C5×C7 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C52×C7×ΓL(1,𝔽8) | C2 | semidirect |
| 2. C5×C7×D35 | C3 | semidirect |
| 3. C7×C5⋊AGL(1,𝔽7) | C5 | direct (N × H) |
| 5. C52×C72 | C2×C3 | semidirect |
| 7. C5×C5⋊AGL(1,𝔽7) | C7 | direct (N × H) |
| 9. C5×C7×ΓL(1,𝔽8) | D5 | semidirect |
| 10. C5×C7×ΓL(1,𝔽8) | C2×C5 | semidirect |
| 12. C52×ΓL(1,𝔽8) | C2×C7 | semidirect |
| 13. C7×D35 | C3×C5 | semidirect |
| 15. C5×D35 | C3×C7 | semidirect |
| 19. C5×C72 | C3×D5 | semidirect |
| 20. C5×C72 | C2×C3×C5 | semidirect |
| 23. C5⋊AGL(1,𝔽7) | C5×C7 | direct (N × H) |
| 26. C52×C7 | AGL(1,𝔽7) | semidirect |
| 27. C52×C7 | C2×C3×C7 | semidirect |
| 29. C7×ΓL(1,𝔽8) | C5×D5 | semidirect |
| 34. C5×ΓL(1,𝔽8) | C7×D5 | semidirect |
| 35. C5×ΓL(1,𝔽8) | C2×C5×C7 | semidirect |
| 39. D35 | C3×C5×C7 | semidirect |
| 43. C72 | C3×C5×D5 | semidirect |
| 51. C5×C7 | C5×AGL(1,𝔽7) | semidirect |
| 52. C5×C7 | C5⋊AGL(1,𝔽7) | direct (N × H) |
| 53. C5×C7 | C3×C7×D5 | semidirect |
| 54. C5×C7 | C2×C3×C5×C7 | semidirect |
| 57. C52 | C7×AGL(1,𝔽7) | semidirect |
| 59. ΓL(1,𝔽8) | C5×C7×D5 | semidirect |
| 68. C7 | C5×C5⋊AGL(1,𝔽7) | direct (N × H) |
| 69. C7 | C3×C5×C7×D5 | semidirect |
| 72. C5 | C5×C7×AGL(1,𝔽7) | semidirect |
| 73. C5 | C7×C5⋊AGL(1,𝔽7) | direct (N × H) |