Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
288 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 288 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. #71378 | C5 | direct (N × H) |
| 176. C3×C5 | #1676 | semidirect |
| 205. C5 | #71378 | direct (N × H) |
| 215. C3 | C5×#1676 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#500 | 2 |
| C5×#5091 | 2 |
| C5×C8×Dic6 | 2 |
| C5×#4546 | 2 |
| C5×#4458 | 2 |
| C5×#1676 | 3 |
| #71378 | 5 |