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. #69293 | C5 | direct (N × H) |
| 101. C3×C4×C5 | Q32 | semidirect |
| 167. C4×C5 | Dic24 | semidirect |
| 186. C3×C5 | #2209 | semidirect |
| 189. C3×C4 | C5×Q32 | semidirect |
| 214. C5 | #69293 | direct (N × H) |
| 220. C4 | C5×Dic24 | 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 |
|---|---|
| C2×C5×Dic24 | 2 |
| C5×#4699 | 2 |
| C4×C5×Dic12 | 2 |
| C3×C5×C4⋊C16 | 2 |
| C5×#4503 | 2 |
| C5×#2209 | 3 |
| #69293 | 5 |