Finite Group DatabasebetaFinite Group DatabasebetaOrder 1760.
152 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 72 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. C11×C4⋊AGL(1,𝔽5) | C2 | semidirect |
| 4. C4×C11×AGL(1,𝔽5) | C2 | semidirect |
| 7. C2×C4×C5×C11 | C4 | semidirect |
| 8. C2×C11×Dic5 | C4 | semidirect |
| 9. C4×D5×C11 | C4 | semidirect |
| 10. C4×D5×C11 | C4 | semidirect |
| 27. #4130 | C11 | direct (N × H) |
| 39. C2×C4×C11 | AGL(1,𝔽5) | semidirect |
| 42. C4⋊AGL(1,𝔽5) | C2×C11 | semidirect |
| 43. C4×AGL(1,𝔽5) | C2×C11 | semidirect |
| 44. C5×C11 | #117 | semidirect |
| 56. C2×C4×C5 | C4×C11 | semidirect |
| 57. C2×Dic5 | C4×C11 | semidirect |
| 58. C4×D5 | C4×C11 | semidirect |
| 59. C4×D5 | C4×C11 | semidirect |
| 80. C11 | #4130 | direct (N × H) |
| 92. C2×C4 | C11×AGL(1,𝔽5) | semidirect |
| 93. C5 | C11×#117 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D5×C11 | 2 |
| C11×C22⋊AGL(1,𝔽5) | 2 |
| C11×C4⋊AGL(1,𝔽5) | 2 |
| C4×C11×AGL(1,𝔽5) | 2 |
| C11×#117 | 5 |
| #4130 | 11 |