Finite Group DatabasebetaFinite Group DatabasebetaOrder 1760.
152 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 50 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 |
|---|---|---|
| 4. Dic11⋊AGL(1,𝔽5) | C2 | semidirect |
| 5. AGL(1,𝔽5)×Dic11 | C2 | semidirect |
| 9. C2×Dic55 | C4 | semidirect |
| 10. C2×C5×Dic11 | C4 | semidirect |
| 11. D5×Dic11 | C4 | semidirect |
| 12. D5×Dic11 | C4 | semidirect |
| 44. C2×Dic11 | AGL(1,𝔽5) | semidirect |
| 50. C5×C11 | #117 | semidirect |
| 90. C11 | #4130 | semidirect |
| 104. C5 | #66930 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D5×Dic11 | 2 |
| C22⋊(C11⋊AGL(1,𝔽5)) | 2 |
| C11×C22⋊AGL(1,𝔽5) | 2 |
| Dic11⋊AGL(1,𝔽5) | 2 |
| AGL(1,𝔽5)×Dic11 | 2 |
| #66930 | 5 |
| #4130 | 11 |