Finite Group DatabasebetaFinite Group DatabasebetaOrder 1760.
188 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 63 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. C22×C11⋊AGL(1,𝔽5) | C2 | semidirect |
| 3. C22⋊(C11⋊AGL(1,𝔽5)) | C2 | semidirect |
| 4. C4⋊(C11⋊AGL(1,𝔽5)) | C2 | semidirect |
| 5. C4×C11⋊AGL(1,𝔽5) | C2 | semidirect |
| 11. C5×D4×C11 | C4 | semidirect |
| 12. C11×C22⋊D5 | C4 | semidirect |
| 13. C11×D20 | C4 | semidirect |
| 16. C22×C5×C11 | C2×C4 | semidirect |
| 19. C2×D5×C11 | C2×C4 | semidirect |
| 23. C11⋊AGL(1,𝔽5) | D4 | direct (N × H) |
| 24. C4×C5×C11 | C2×C4 | semidirect |
| 25. C11×Dic5 | C2×C4 | semidirect |
| 40. D4×C11 | AGL(1,𝔽5) | semidirect |
| 51. C5×C11 | C4×D4 | semidirect |
| 56. C22×C11 | C2×AGL(1,𝔽5) | semidirect |
| 58. C4×C11 | C2×AGL(1,𝔽5) | semidirect |
| 67. C5×D4 | Dic11 | semidirect |
| 68. C22⋊D5 | Dic11 | semidirect |
| 69. D20 | Dic11 | semidirect |
| 77. C22×C5 | C2×Dic11 | semidirect |
| 80. C2×D5 | C2×Dic11 | semidirect |
| 85. C4×C5 | C2×Dic11 | semidirect |
| 86. Dic5 | C2×Dic11 | semidirect |
| 92. C11 | D4×AGL(1,𝔽5) | semidirect |
| 101. D4 | C11⋊AGL(1,𝔽5) | direct (N × H) |
| 107. C5 | D4×Dic11 | semidirect |
| 112. C22 | C2×C11⋊AGL(1,𝔽5) | semidirect |
| 117. C4 | C2×C11⋊AGL(1,𝔽5) | semidirect |
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 |
| D4×D5×C11 | 2 |
| C22⋊(C11⋊AGL(1,𝔽5)) | 2 |
| C4⋊(C11⋊AGL(1,𝔽5)) | 2 |
| C4×C11⋊AGL(1,𝔽5) | 2 |
| D4×Dic11 | 5 |
| D4×AGL(1,𝔽5) | 11 |