Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
312 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 114 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 |
|---|---|---|
| 18. #68587 | C5 | direct (N × H) |
| 64. C5×Dic6 | Q16 | semidirect |
| 159. Dic6 | C5×Q16 | semidirect |
| 187. C3×C5 | #1670 | semidirect |
| 217. C5 | #68587 | direct (N × H) |
| 227. C3 | C5×#1670 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4851 | 2 |
| C5×#4699 | 2 |
| C5×C8×Dic6 | 2 |
| C3×C5×#335 | 2 |
| C5×#4486 | 2 |
| C5×#1670 | 3 |
| #68587 | 5 |