Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
308 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 110 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 |
|---|---|---|
| 17. #71316 | C5 | direct (N × H) |
| 102. C3×C4×C5 | Q32 | semidirect |
| 167. C4×C5 | #829 | semidirect |
| 186. C3×C5 | #2209 | semidirect |
| 190. C3×C4 | C5×Q32 | semidirect |
| 214. C5 | #71316 | direct (N × H) |
| 220. C4 | C5×#829 | semidirect |
| 223. C3 | C5×#2209 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#494 | 2 |
| C2×C5×#829 | 2 |
| C4×C5×Dic12 | 2 |
| C5×#4564 | 2 |
| C5×C4⋊(C3⋊C16) | 2 |
| C5×#2209 | 3 |
| #71316 | 5 |