Finite Group DatabasebetaFinite Group Databasebeta← C2×AGL(1,𝔽5)×Dic11 #13183308
Order 1760.
216 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 94 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 |
|---|---|---|
| 4. AGL(1,𝔽5)×Dic11 | C2 | direct (N × H) |
| 6. C2×C11⋊AGL(1,𝔽5) | C4 | semidirect |
| 8. C2×C11×AGL(1,𝔽5) | C4 | semidirect |
| 10. C2×Dic55 | C4 | semidirect |
| 11. C2×C5×Dic11 | C4 | semidirect |
| 12. D5×Dic11 | C4 | semidirect |
| 20. C11⋊AGL(1,𝔽5) | C2×C4 | semidirect |
| 21. C11×AGL(1,𝔽5) | C2×C4 | semidirect |
| 22. Dic55 | C2×C4 | semidirect |
| 23. C5×Dic11 | C2×C4 | semidirect |
| 29. C2×C5×C11 | C42 | semidirect |
| 31. D5×C11 | C42 | semidirect |
| 42. C2×Dic11 | AGL(1,𝔽5) | direct (N × H) |
| 47. C5×C11 | C2×C42 | semidirect |
| 56. Dic11 | C2×AGL(1,𝔽5) | direct (N × H) |
| 60. C2×AGL(1,𝔽5) | Dic11 | direct (N × H) |
| 70. C2×C11 | C4×AGL(1,𝔽5) | semidirect |
| 78. AGL(1,𝔽5) | C2×Dic11 | direct (N × H) |
| 85. C11 | C2×C4×AGL(1,𝔽5) | semidirect |
| 86. C2×C5 | C4×Dic11 | semidirect |
| 88. D5 | C4×Dic11 | semidirect |
| 100. C5 | C2×C4×Dic11 | semidirect |
| 113. C2 | AGL(1,𝔽5)×Dic11 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C11⋊AGL(1,𝔽5) | 2 |
| C22×C11×AGL(1,𝔽5) | 2 |
| C2×D5×Dic11 | 2 |
| AGL(1,𝔽5)×Dic11 | 2 |
| C2×C4×Dic11 | 5 |
| C2×C4×AGL(1,𝔽5) | 11 |