Finite Group DatabasebetaFinite Group DatabasebetaOrder 5280.
656 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 197 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. Q8×C3⋊AGL(1,𝔽11) | C2 | semidirect |
| 2. #239×C11⋊C5 | C2 | semidirect |
| 3. #72216857 | C2 | semidirect |
| 4. #72216851 | C2 | semidirect |
| 5. C3×#4343⋊C5 | C2 | semidirect |
| 6. #72216746 | C2 | semidirect |
| 7. C4×D3×AGL(1,𝔽11) | C2 | semidirect |
| 10. C3×Q8×C11⋊C5 | C22 | semidirect |
| 12. Dic66⋊C5 | C22 | semidirect |
| 13. D12×C11⋊C5 | C22 | semidirect |
| 14. C4×D3×C11⋊C5 | C22 | semidirect |
| 15. C3×C4⋊AGL(1,𝔽11) | C22 | semidirect |
| 16. C3×C4×AGL(1,𝔽11) | C22 | semidirect |
| 17. #63140⋊C5 | C22 | semidirect |
| 19. D3×Dic11⋊C5 | C22 | semidirect |
| 20. Dic3×AGL(1,𝔽11) | C22 | semidirect |
| 21. #11761402 | C5 | semidirect |
| 23. #4343⋊C5 | D3 | semidirect |
| 37. Q8×D33 | C2×C5 | semidirect |
| 38. C11×#239 | C2×C5 | semidirect |
| 39. C3×#4343 | C2×C5 | semidirect |
| 40. #10587239 | C2×C5 | semidirect |
| 41. C4×D3×D11 | C2×C5 | semidirect |
| 42. #10587234 | C2×C5 | semidirect |
| 43. #10587227 | C2×C5 | semidirect |
| 46. Q8×C11⋊C5 | C2×D3 | semidirect |
| 51. C4⋊AGL(1,𝔽11) | C2×D3 | semidirect |
| 55. C4×AGL(1,𝔽11) | C2×D3 | semidirect |
| 59. C3⋊AGL(1,𝔽11) | #41 | semidirect |
| 63. C3×Q8×C11 | C22×C5 | semidirect |
| 65. Dic66 | C22×C5 | semidirect |
| 66. C11×D12 | C22×C5 | semidirect |
| 67. C4×D3×C11 | C22×C5 | semidirect |
| 68. C3×D44 | C22×C5 | semidirect |
| 69. C3×C4×D11 | C22×C5 | semidirect |
| 70. #63140 | C22×C5 | semidirect |
| 72. D3×Dic11 | C22×C5 | semidirect |
| 73. Dic3×D11 | C22×C5 | semidirect |
| 90. #4343 | C5×D3 | semidirect |
| 96. C3×C11⋊C5 | C2×#41 | semidirect |
| 124. Q8×C11 | C2×C5×D3 | semidirect |
| 129. D44 | C2×C5×D3 | semidirect |
| 133. C4×D11 | C2×C5×D3 | semidirect |
| 143. D33 | C5×#41 | semidirect |
| 154. C11⋊C5 | D3×#41 | semidirect |
| 156. #239 | AGL(1,𝔽11) | semidirect |
| 182. C3×C11 | C2×C5×#41 | semidirect |
| 189. C3×Q8 | C2×AGL(1,𝔽11) | semidirect |
| 194. D12 | C2×AGL(1,𝔽11) | semidirect |
| 198. C4×D3 | C2×AGL(1,𝔽11) | semidirect |
| 228. C11 | C5×D3×#41 | 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 |
|---|---|
| Q8×C3⋊AGL(1,𝔽11) | 2 |
| #239×C11⋊C5 | 2 |
| #72216857 | 2 |
| #72216851 | 2 |
| C3×#4343⋊C5 | 2 |
| #72216746 | 2 |
| C4×D3×AGL(1,𝔽11) | 2 |
| #41×AGL(1,𝔽11) | 3 |
| #11761402 | 5 |
| C5×D3×#41 | 11 |