Finite Group DatabasebetaFinite Group Databasebeta← C2×C4⋊(C11⋊AGL(1,𝔽5)) #13183348
Order 1760.
184 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 81 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 |
|---|---|---|
| 3. C4⋊(C11⋊AGL(1,𝔽5)) | C2 | direct (N × H) |
| 7. C2×C4×C5×C11 | C4 | semidirect |
| 8. C2×C11×Dic5 | C4 | semidirect |
| 9. C4×D5×C11 | C4 | semidirect |
| 18. C4×C5×C11 | C2×C4 | semidirect |
| 19. C11×Dic5 | C2×C4 | semidirect |
| 24. C2×C5×C11 | C4⋊C4 | semidirect |
| 26. D5×C11 | C4⋊C4 | semidirect |
| 33. C2×C4×C11 | AGL(1,𝔽5) | semidirect |
| 39. C5×C11 | C2×C4⋊C4 | semidirect |
| 46. C4×C11 | C2×AGL(1,𝔽5) | semidirect |
| 51. C2×C4×C5 | Dic11 | semidirect |
| 52. C2×Dic5 | Dic11 | semidirect |
| 53. C4×D5 | Dic11 | semidirect |
| 59. C2×C11 | C4⋊AGL(1,𝔽5) | semidirect |
| 67. C4×C5 | C2×Dic11 | semidirect |
| 68. Dic5 | C2×Dic11 | semidirect |
| 72. C11 | C2×C4⋊AGL(1,𝔽5) | semidirect |
| 73. C2×C5 | C4⋊Dic11 | semidirect |
| 75. D5 | C4⋊Dic11 | semidirect |
| 84. C2×C4 | C11⋊AGL(1,𝔽5) | semidirect |
| 85. C5 | C2×C4⋊Dic11 | semidirect |
| 93. C4 | C2×C11⋊AGL(1,𝔽5) | semidirect |
| 97. C2 | C4⋊(C11⋊AGL(1,𝔽5)) | 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 |
| C2×C4×D5×C11 | 2 |
| C4⋊(C11⋊AGL(1,𝔽5)) | 2 |
| C2×C4⋊Dic11 | 5 |
| C2×C4⋊AGL(1,𝔽5) | 11 |