Finite Group DatabasebetaFinite Group DatabasebetaOrder 1760.
472 conjugacy classes of subgroups; only the 166 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 166 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | AGL(1,𝔽5)×D11 |
| commutator, hypocenter | C5×C11 | C23×C4 |
| Frattini | C1 | G |
| Fitting, socle | C22×C5×C11 | C2×C4 |
| prime radical | C22×D5×D11 | C2 |
| cosocle | D5×C11 | C24 |
| LCS | G ▷ C5×C11 | |
| UCS | C1 ◁ C22 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C22×C11⋊AGL(1,𝔽5) | C2 | semidirect |
| 3. C22×C11×AGL(1,𝔽5) | C2 | semidirect |
| 4. C2×AGL(1,𝔽5)×D11 | C2 | direct (N × H) |
| 5. C22×D55 | C4 | semidirect |
| 7. C22×C5×D11 | C4 | semidirect |
| 8. C2×D5×D11 | C4 | semidirect |
| 10. C2×C11⋊AGL(1,𝔽5) | C22 | semidirect |
| 11. C2×C11×AGL(1,𝔽5) | C22 | semidirect |
| 12. AGL(1,𝔽5)×D11 | C22 | direct (N × H) |
| 14. C22×C5×C11 | C2×C4 | semidirect |
| 15. C2×D55 | C2×C4 | semidirect |
| 16. C2×D5×C11 | C2×C4 | semidirect |
| 18. C2×C5×D11 | C2×C4 | semidirect |
| 19. D5×D11 | C2×C4 | semidirect |
| 21. C11⋊AGL(1,𝔽5) | C23 | semidirect |
| 22. C11×AGL(1,𝔽5) | C23 | semidirect |
| 28. C2×C5×C11 | C22×C4 | semidirect |
| 29. D55 | C22×C4 | semidirect |
| 30. C5×D11 | C22×C4 | semidirect |
| 31. D5×C11 | C22×C4 | semidirect |
| 37. C22×D11 | AGL(1,𝔽5) | direct (N × H) |
| 44. C22×AGL(1,𝔽5) | D11 | direct (N × H) |
| 45. C5×C11 | C23×C4 | semidirect |
| 48. C22×C11 | C2×AGL(1,𝔽5) | semidirect |
| 52. C2×D11 | C2×AGL(1,𝔽5) | direct (N × H) |
| 62. C2×AGL(1,𝔽5) | C2×D11 | direct (N × H) |
| 66. C2×C11 | C22×AGL(1,𝔽5) | semidirect |
| 68. D11 | C22×AGL(1,𝔽5) | direct (N × H) |
| 70. C22×C5 | C4×D11 | semidirect |
| 74. C2×D5 | C4×D11 | semidirect |
| 77. AGL(1,𝔽5) | C22×D11 | direct (N × H) |
| 82. C11 | C23×AGL(1,𝔽5) | semidirect |
| 84. C2×C5 | C2×C4×D11 | semidirect |
| 86. D5 | C2×C4×D11 | semidirect |
| 96. C5 | C22×C4×D11 | semidirect |
| 103. C22 | AGL(1,𝔽5)×D11 | direct (N × H) |
| 110. C2 | C2×AGL(1,𝔽5)×D11 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D5×D11 | 2 |
| C22×C11⋊AGL(1,𝔽5) | 2 |
| C22×C11×AGL(1,𝔽5) | 2 |
| C2×AGL(1,𝔽5)×D11 | 2 |
| C22×C4×D11 | 5 |
| C23×AGL(1,𝔽5) | 11 |