Finite Group DatabasebetaFinite Group DatabasebetaOrder 1760.
184 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 60 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. C11×C4⋊AGL(1,𝔽5) | C2 | semidirect |
| 5. Dic11⋊AGL(1,𝔽5) | C2 | semidirect |
| 10. C4×D55 | C4 | semidirect |
| 12. C4×C5×D11 | C4 | semidirect |
| 13. #89166 | C4 | semidirect |
| 15. Dic5×D11 | C4 | semidirect |
| 24. C4×C5×C11 | C2×C4 | semidirect |
| 25. Dic55 | C2×C4 | semidirect |
| 26. C5×Dic11 | C2×C4 | semidirect |
| 27. C11×Dic5 | C2×C4 | semidirect |
| 35. D55 | C4⋊C4 | semidirect |
| 36. C5×D11 | C4⋊C4 | semidirect |
| 48. C4×D11 | AGL(1,𝔽5) | semidirect |
| 53. C4⋊AGL(1,𝔽5) | D11 | direct (N × H) |
| 54. C5×C11 | C2×C4⋊C4 | semidirect |
| 62. C4×C11 | C2×AGL(1,𝔽5) | semidirect |
| 65. Dic11 | C2×AGL(1,𝔽5) | semidirect |
| 81. D11 | C4⋊AGL(1,𝔽5) | direct (N × H) |
| 90. C4×C5 | C4×D11 | semidirect |
| 92. Dic5 | C4×D11 | semidirect |
| 98. C11 | C2×C4⋊AGL(1,𝔽5) | semidirect |
| 114. C5 | C4⋊C4×D11 | semidirect |
| 125. C4 | AGL(1,𝔽5)×D11 | semidirect |
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 |
| C11×C4⋊AGL(1,𝔽5) | 2 |
| Dic11⋊AGL(1,𝔽5) | 2 |
| C4⋊C4×D11 | 5 |
| C2×C4⋊AGL(1,𝔽5) | 11 |