Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
452 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 1. C22×Dic60 | C2 | semidirect |
| 3. C2×#91111 | C2 | semidirect |
| 4. #11746370 | C2 | semidirect |
| 5. #11746313 | C2 | semidirect |
| 40. Dic60 | D4 | semidirect |
| 115. C22×C3×C5 | SD32 | semidirect |
| 195. C22×C5 | #827 | semidirect |
| 220. C3×C5 | #2185 | semidirect |
| 226. C22×C3 | #3959 | semidirect |
| 260. C5 | #71077 | semidirect |
| 266. C22 | #91111 | semidirect |
| 273. C3 | #10601870 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic60 | 2 |
| C3×C5×#466 | 2 |
| C2×#91111 | 2 |
| #11746370 | 2 |
| #11746313 | 2 |
| #10601870 | 3 |
| #71077 | 5 |