Finite Group DatabasebetaFinite Group DatabasebetaOrder 5280.
656 conjugacy classes of subgroups; only the 199 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 199 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. D3×Q8×C11⋊C5 | C2 | semidirect |
| 2. #72216866 | C2 | semidirect |
| 3. #72216862 | C2 | semidirect |
| 4. #72216853 | C2 | semidirect |
| 5. C3×#4343⋊C5 | C2 | semidirect |
| 6. D3×C4⋊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 |
| 14. Dic6×C11⋊C5 | C22 | semidirect |
| 15. C3×C4⋊AGL(1,𝔽11) | C22 | semidirect |
| 16. C3×C4×AGL(1,𝔽11) | C22 | semidirect |
| 17. #63141⋊C5 | C22 | semidirect |
| 18. (D33⋊C4)⋊C5 | C22 | semidirect |
| 20. Dic3×AGL(1,𝔽11) | C22 | semidirect |
| 21. D3×#4343 | C5 | semidirect |
| 26. #4343⋊C5 | D3 | direct (N × H) |
| 37. #10587283 | C2×C5 | semidirect |
| 38. D3×Q8×C11 | C2×C5 | semidirect |
| 39. C3×#4343 | C2×C5 | semidirect |
| 40. D3×D44 | C2×C5 | semidirect |
| 41. C4×D3×D11 | C2×C5 | semidirect |
| 42. #10587235 | C2×C5 | semidirect |
| 43. #10587228 | C2×C5 | semidirect |
| 47. Q8×C11⋊C5 | C2×D3 | semidirect |
| 52. C4⋊AGL(1,𝔽11) | C2×D3 | semidirect |
| 56. C4×AGL(1,𝔽11) | C2×D3 | semidirect |
| 60. D3×C11⋊C5 | #41 | semidirect |
| 63. C3×Q8×C11 | C22×C5 | semidirect |
| 64. D132 | C22×C5 | semidirect |
| 65. C4×D33 | C22×C5 | semidirect |
| 67. C11×Dic6 | C22×C5 | semidirect |
| 68. C3×D44 | C22×C5 | semidirect |
| 69. C3×C4×D11 | C22×C5 | semidirect |
| 70. #63141 | C22×C5 | semidirect |
| 71. D33⋊C4 | C22×C5 | semidirect |
| 73. Dic3×D11 | C22×C5 | semidirect |
| 93. #4343 | C5×D3 | semidirect |
| 96. C3×C11⋊C5 | C2×#41 | semidirect |
| 125. Q8×C11 | C2×C5×D3 | semidirect |
| 130. D44 | C2×C5×D3 | semidirect |
| 134. C4×D11 | C2×C5×D3 | semidirect |
| 145. D3×C11 | C5×#41 | semidirect |
| 154. C11⋊C5 | D3×#41 | semidirect |
| 157. D3×Q8 | AGL(1,𝔽11) | semidirect |
| 182. C3×C11 | C2×C5×#41 | semidirect |
| 189. C3×Q8 | C2×AGL(1,𝔽11) | semidirect |
| 199. Dic6 | C2×AGL(1,𝔽11) | semidirect |
| 228. C11 | C5×D3×#41 | semidirect |
| 235. Q8 | D3×AGL(1,𝔽11) | semidirect |
| 248. D3 | #4343⋊C5 | direct (N × H) |
| 258. C3 | C2×#4343⋊C5 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D3×Q8×C11⋊C5 | 2 |
| #72216866 | 2 |
| #72216862 | 2 |
| #72216853 | 2 |
| C3×#4343⋊C5 | 2 |
| D3×C4⋊AGL(1,𝔽11) | 2 |
| C4×D3×AGL(1,𝔽11) | 2 |
| C2×#4343⋊C5 | 3 |
| D3×#4343 | 5 |
| C5×D3×#41 | 11 |