Finite Group DatabasebetaFinite Group DatabasebetaOrder 3520.
340 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 104 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 |
|---|---|---|
| 2. C2×C42×C11⋊C5 | C2 | semidirect |
| 3. C2×#4318⋊C5 | C2 | semidirect |
| 4. #66869⋊C5 | C2 | direct (N × H) |
| 10. #4339⋊C5 | C4 | semidirect |
| 12. C2×C4⋊AGL(1,𝔽11) | C4 | semidirect |
| 14. C2×(C11⋊C5)⋊Q8 | C4 | semidirect |
| 16. C42×C11⋊C5 | C22 | semidirect |
| 18. #4318⋊C5 | C22 | semidirect |
| 20. C2×#66869 | C5 | semidirect |
| 35. C4⋊AGL(1,𝔽11) | C2×C4 | semidirect |
| 39. (C11⋊C5)⋊Q8 | C2×C4 | semidirect |
| 42. C2×C42×C11 | C2×C5 | semidirect |
| 43. C2×#4318 | C2×C5 | semidirect |
| 44. #66869 | C2×C5 | semidirect |
| 63. #4339 | C4×C5 | semidirect |
| 65. C2×D44 | C4×C5 | semidirect |
| 67. C2×Dic22 | C4×C5 | semidirect |
| 69. C42×C11 | C22×C5 | semidirect |
| 71. #4318 | C22×C5 | semidirect |
| 79. C2×C11⋊C5 | #104 | semidirect |
| 96. D44 | C2×C4×C5 | semidirect |
| 100. Dic22 | C2×C4×C5 | semidirect |
| 118. C11⋊C5 | C2×#104 | semidirect |
| 153. C2×C42 | AGL(1,𝔽11) | semidirect |
| 157. C2×C11 | C5×#104 | semidirect |
| 186. C42 | C2×AGL(1,𝔽11) | semidirect |
| 187. C11 | C2×C5×#104 | semidirect |
| 229. C2 | #66869⋊C5 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4339⋊C5 | 2 |
| C2×C42×C11⋊C5 | 2 |
| C2×#4318⋊C5 | 2 |
| #66869⋊C5 | 2 |
| C2×#66869 | 5 |
| C2×C5×#104 | 11 |