Finite Group DatabasebetaFinite Group DatabasebetaOrder 1760.
216 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 80 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C4×C11⋊AGL(1,𝔽5) | C2 | semidirect |
| 4. C4×C11×AGL(1,𝔽5) | C2 | semidirect |
| 5. AGL(1,𝔽5)×Dic11 | C2 | semidirect |
| 9. AGL(1,𝔽5)×D11 | C4 | direct (N × H) |
| 10. C4×D55 | C4 | semidirect |
| 12. C4×C5×D11 | C4 | semidirect |
| 13. #89166 | C4 | semidirect |
| 15. Dic5×D11 | C4 | semidirect |
| 21. C11⋊AGL(1,𝔽5) | C2×C4 | semidirect |
| 22. C11×AGL(1,𝔽5) | C2×C4 | semidirect |
| 23. C4×C5×C11 | C2×C4 | semidirect |
| 24. Dic55 | C2×C4 | semidirect |
| 25. C5×Dic11 | C2×C4 | semidirect |
| 26. C11×Dic5 | C2×C4 | semidirect |
| 34. D55 | C42 | semidirect |
| 35. C5×D11 | C42 | semidirect |
| 46. C4×D11 | AGL(1,𝔽5) | direct (N × H) |
| 51. C4×AGL(1,𝔽5) | D11 | direct (N × H) |
| 52. C5×C11 | C2×C42 | semidirect |
| 59. C4×C11 | C2×AGL(1,𝔽5) | semidirect |
| 62. Dic11 | C2×AGL(1,𝔽5) | semidirect |
| 77. D11 | C4×AGL(1,𝔽5) | direct (N × H) |
| 83. AGL(1,𝔽5) | C4×D11 | direct (N × H) |
| 85. C4×C5 | C4×D11 | semidirect |
| 87. Dic5 | C4×D11 | semidirect |
| 93. C11 | C2×C4×AGL(1,𝔽5) | semidirect |
| 108. C5 | C42×D11 | semidirect |
| 118. C4 | 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 |
|---|---|
| C2×AGL(1,𝔽5)×D11 | 2 |
| C4×D5×D11 | 2 |
| C4×C11⋊AGL(1,𝔽5) | 2 |
| C4×C11×AGL(1,𝔽5) | 2 |
| AGL(1,𝔽5)×Dic11 | 2 |
| C42×D11 | 5 |
| C2×C4×AGL(1,𝔽5) | 11 |