Finite Group DatabasebetaFinite Group DatabasebetaOrder 1760.
152 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 61 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 | 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 |
| 38. C2×C4×C11 | AGL(1,𝔽5) | semidirect |
| 44. C5×C11 | #117 | semidirect |
| 56. C2×C4×C5 | Dic11 | semidirect |
| 57. C2×Dic5 | Dic11 | semidirect |
| 58. C4×D5 | Dic11 | semidirect |
| 59. C4×D5 | Dic11 | semidirect |
| 80. C11 | #4130 | semidirect |
| 92. C2×C4 | C11⋊AGL(1,𝔽5) | semidirect |
| 93. C5 | #66979 | 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 |
| C22⋊(C11⋊AGL(1,𝔽5)) | 2 |
| C4⋊(C11⋊AGL(1,𝔽5)) | 2 |
| C4×C11⋊AGL(1,𝔽5) | 2 |
| #66979 | 5 |
| #4130 | 11 |