Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
332 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 96 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. #11750800 | C2 | semidirect |
| 4. C3×C4⋊#672 | C2 | semidirect |
| 5. #11745902 | C2 | semidirect |
| 22. C4⋊#672 | D3 | semidirect |
| 105. C3×C4×C5 | SD32 | semidirect |
| 174. C4×C5 | #800 | semidirect |
| 194. C3×C5 | #2208 | semidirect |
| 200. C3×C4 | #3959 | semidirect |
| 227. C5 | #69287 | semidirect |
| 235. C4 | #90944 | semidirect |
| 238. C3 | #10601685 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11750800 | 2 |
| C4×C5×D24 | 2 |
| C2×#90944 | 2 |
| C3×C4⋊#672 | 2 |
| #11745902 | 2 |
| #10601685 | 3 |
| #69287 | 5 |