Finite Group DatabasebetaFinite Group DatabasebetaOrder 1760.
148 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 148 conjugacy classes of subgroups — too many to draw. Only its 70 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×C5×Q8×C11 | C2 | semidirect |
| 4. C5×C4⋊Dic11 | C2 | semidirect |
| 5. C5×Dic11⋊C4 | C2 | semidirect |
| 13. #66999 | C5 | direct (N × H) |
| 17. C2×C5×D11 | Q8 | semidirect |
| 22. C2×Q8×C11 | C2×C5 | semidirect |
| 25. C4⋊Dic11 | C2×C5 | semidirect |
| 26. Dic11⋊C4 | C2×C5 | semidirect |
| 39. C2×C5×Q8 | D11 | semidirect |
| 44. C5×C11 | C22⋊Q8 | semidirect |
| 48. C2×D11 | C5×Q8 | semidirect |
| 73. C2×Q8 | C5×D11 | semidirect |
| 78. C11 | C5×C22⋊Q8 | semidirect |
| 90. C5 | #66999 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×Q8×C11 | 2 |
| C2×C4×C5×D11 | 2 |
| C5×(C2×D11)⋊C4 | 2 |
| C5×C4⋊Dic11 | 2 |
| C5×Dic11⋊C4 | 2 |
| #66999 | 5 |
| C5×C22⋊Q8 | 11 |