Finite Group DatabasebetaFinite Group DatabasebetaOrder 1760.
112 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 112 conjugacy classes of subgroups — too many to draw. Only its 62 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 |
|---|---|---|
| 15. #66942 | C5 | direct (N × H) |
| 49. C5×C11 | #125 | semidirect |
| 84. C11 | C5×#125 | semidirect |
| 95. C5 | #66942 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×C11×C4⋊C4 | 2 |
| C5×C4⋊Dic11 | 2 |
| C5×Dic11⋊C4 | 2 |
| C4×C5×Dic11 | 2 |
| #66942 | 5 |
| C5×#125 | 11 |