Finite Group DatabasebetaFinite Group DatabasebetaOrder 1760.
188 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 52 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. C2×AGL(1,𝔽5)×D11 | C2 | semidirect |
| 3. C4×C11⋊AGL(1,𝔽5) | C2 | semidirect |
| 4. C11×C4⋊AGL(1,𝔽5) | C2 | semidirect |
| 5. (C2×AGL(1,𝔽5))⋊D11 | C2 | semidirect |
| 11. D220 | C4 | semidirect |
| 13. C5×D44 | C4 | semidirect |
| 14. #89168 | C4 | semidirect |
| 16. C2×D55 | C2×C4 | semidirect |
| 18. C2×C5×D11 | C2×C4 | semidirect |
| 22. C11⋊AGL(1,𝔽5) | D4 | semidirect |
| 24. C4×C5×C11 | C2×C4 | semidirect |
| 25. C11×Dic5 | C2×C4 | semidirect |
| 44. D44 | AGL(1,𝔽5) | semidirect |
| 49. C4⋊AGL(1,𝔽5) | D11 | semidirect |
| 51. C5×C11 | C4×D4 | semidirect |
| 56. C2×D11 | C2×AGL(1,𝔽5) | semidirect |
| 59. C4×C11 | C2×AGL(1,𝔽5) | semidirect |
| 85. C4×C5 | C4×D11 | semidirect |
| 86. Dic5 | C4×D11 | semidirect |
| 92. C11 | D4×AGL(1,𝔽5) | semidirect |
| 107. C5 | #66946 | semidirect |
| 117. C4 | AGL(1,𝔽5)×D11 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×AGL(1,𝔽5)×D11 | 2 |
| D5×D44 | 2 |
| C4×C11⋊AGL(1,𝔽5) | 2 |
| C11×C4⋊AGL(1,𝔽5) | 2 |
| (C2×AGL(1,𝔽5))⋊D11 | 2 |
| #66946 | 5 |
| D4×AGL(1,𝔽5) | 11 |