Finite Group DatabasebetaFinite Group DatabasebetaOrder 3520.
340 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 112 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×C4×Dic11⋊C5 | C2 | semidirect |
| 3. C2×#4318⋊C5 | C2 | semidirect |
| 4. #66901⋊C5 | C2 | direct (N × H) |
| 7. #41×C11⋊C5 | C4 | semidirect |
| 9. C2×Q8×C11⋊C5 | C4 | semidirect |
| 11. C2×D4×C11⋊C5 | C4 | semidirect |
| 16. C4×Dic11⋊C5 | C22 | semidirect |
| 18. #4318⋊C5 | C22 | semidirect |
| 20. C2×#66901 | C5 | semidirect |
| 24. Q8×C11⋊C5 | C2×C4 | semidirect |
| 28. D4×C11⋊C5 | C2×C4 | semidirect |
| 42. C2×C4×Dic11 | C2×C5 | semidirect |
| 43. C2×#4318 | C2×C5 | semidirect |
| 44. #66901 | C2×C5 | semidirect |
| 60. C11×#41 | C4×C5 | semidirect |
| 62. C2×Q8×C11 | C4×C5 | semidirect |
| 64. C2×D4×C11 | C4×C5 | semidirect |
| 69. C4×Dic11 | C22×C5 | semidirect |
| 71. #4318 | C22×C5 | semidirect |
| 80. C2×C11⋊C5 | #104 | semidirect |
| 85. Q8×C11 | C2×C4×C5 | semidirect |
| 89. D4×C11 | C2×C4×C5 | semidirect |
| 118. C11⋊C5 | C2×#104 | semidirect |
| 158. C2×C11 | C5×#104 | semidirect |
| 174. #41 | Dic11⋊C5 | semidirect |
| 176. C2×Q8 | Dic11⋊C5 | semidirect |
| 178. C2×D4 | Dic11⋊C5 | semidirect |
| 187. C11 | C2×C5×#104 | semidirect |
| 196. Q8 | C2×Dic11⋊C5 | semidirect |
| 200. D4 | C2×Dic11⋊C5 | semidirect |
| 229. C2 | #66901⋊C5 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#41×C11⋊C5 | 2 |
| C2×C4×Dic11⋊C5 | 2 |
| C2×#4318⋊C5 | 2 |
| #66901⋊C5 | 2 |
| C2×#66901 | 5 |
| C2×C5×#104 | 11 |