Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
308 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 102 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 |
|---|---|---|
| 8. #10602290 | C3 | direct (N × H) |
| 135. C3×Dic5 | Q32 | semidirect |
| 212. Dic5 | C3×Q32 | semidirect |
| 233. C3×C5 | #2209 | semidirect |
| 265. C5 | C3×#2209 | semidirect |
| 275. C3 | #10602290 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C5×Q32 | 2 |
| C3×Q16×Dic5 | 2 |
| C3×#65470 | 2 |
| C2×C3×#3961 | 2 |
| C3×#64784 | 2 |
| C3×#64723 | 2 |
| C3×#64721 | 2 |
| #10602290 | 3 |
| C3×#2209 | 5 |