Finite Group DatabasebetaFinite Group DatabasebetaOrder 5280.
656 conjugacy classes of subgroups; only the 201 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 201 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 |
|---|---|---|
| 1. C3×Q8×AGL(1,𝔽11) | C2 | semidirect |
| 2. #72216866 | C2 | semidirect |
| 3. #72216864 | C2 | semidirect |
| 4. #72216859 | C2 | semidirect |
| 5. #239×C11⋊C5 | C2 | semidirect |
| 6. D12×AGL(1,𝔽11) | C2 | semidirect |
| 7. C4×D3×AGL(1,𝔽11) | C2 | semidirect |
| 10. C3×Q8×C11⋊C5 | C22 | semidirect |
| 11. C4⋊(C3⋊AGL(1,𝔽11)) | C22 | semidirect |
| 12. C4×C3⋊AGL(1,𝔽11) | C22 | semidirect |
| 13. D12×C11⋊C5 | C22 | semidirect |
| 14. C4×D3×C11⋊C5 | C22 | semidirect |
| 16. C3×(C11⋊C5)⋊Q8 | C22 | semidirect |
| 17. #63142⋊C5 | C22 | semidirect |
| 18. (D33⋊C4)⋊C5 | C22 | semidirect |
| 19. D3×Dic11⋊C5 | C22 | semidirect |
| 21. D11×#239 | C5 | semidirect |
| 24. Q8×AGL(1,𝔽11) | D3 | semidirect |
| 37. #10587283 | C2×C5 | semidirect |
| 38. C11×#239 | C2×C5 | semidirect |
| 39. C3×Q8×D11 | C2×C5 | semidirect |
| 40. D11×D12 | C2×C5 | semidirect |
| 41. C4×D3×D11 | C2×C5 | semidirect |
| 42. #10587231 | C2×C5 | semidirect |
| 43. #10587230 | C2×C5 | semidirect |
| 46. Q8×C11⋊C5 | C2×D3 | semidirect |
| 56. (C11⋊C5)⋊Q8 | C2×D3 | semidirect |
| 61. C3×AGL(1,𝔽11) | #41 | semidirect |
| 63. C3×Q8×C11 | C22×C5 | semidirect |
| 64. D132 | C22×C5 | semidirect |
| 65. C4×D33 | C22×C5 | semidirect |
| 66. C11×D12 | C22×C5 | semidirect |
| 67. C4×D3×C11 | C22×C5 | semidirect |
| 69. C3×Dic22 | C22×C5 | semidirect |
| 70. #63142 | C22×C5 | semidirect |
| 71. D33⋊C4 | C22×C5 | semidirect |
| 72. D3×Dic11 | C22×C5 | semidirect |
| 91. Q8×D11 | C5×D3 | semidirect |
| 96. C3×C11⋊C5 | C2×#41 | semidirect |
| 121. AGL(1,𝔽11) | #239 | direct (N × H) |
| 124. Q8×C11 | C2×C5×D3 | semidirect |
| 134. Dic22 | C2×C5×D3 | semidirect |
| 144. C3×D11 | C5×#41 | semidirect |
| 154. C11⋊C5 | C2×#239 | semidirect |
| 159. #239 | AGL(1,𝔽11) | direct (N × H) |
| 182. C3×C11 | C2×C5×#41 | semidirect |
| 190. C3×Q8 | C2×AGL(1,𝔽11) | semidirect |
| 195. D12 | C2×AGL(1,𝔽11) | semidirect |
| 199. C4×D3 | C2×AGL(1,𝔽11) | semidirect |
| 203. D11 | C5×#239 | semidirect |
| 228. C11 | C2×C5×#239 | semidirect |
| 235. Q8 | D3×AGL(1,𝔽11) | semidirect |
| 258. C3 | #41×AGL(1,𝔽11) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×Q8×AGL(1,𝔽11) | 2 |
| #72216866 | 2 |
| #72216864 | 2 |
| #72216859 | 2 |
| #239×C11⋊C5 | 2 |
| D12×AGL(1,𝔽11) | 2 |
| C4×D3×AGL(1,𝔽11) | 2 |
| #41×AGL(1,𝔽11) | 3 |
| D11×#239 | 5 |
| C2×C5×#239 | 11 |