Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
372 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 372 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. #11750796 | C2 | semidirect |
| 2. C3×C4×D40 | C2 | semidirect |
| 3. C2×#90938 | C2 | semidirect |
| 4. C5×C4⋊(C3⋊C16) | C2 | semidirect |
| 5. #11745895 | C2 | semidirect |
| 20. C4×D40 | D3 | semidirect |
| 37. C3×D40 | D4 | semidirect |
| 43. C4⋊(C3⋊C16) | D5 | semidirect |
| 95. D40 | D12 | semidirect |
| 110. C3×C4×C5 | D16 | semidirect |
| 185. C4×C5 | #826 | semidirect |
| 205. C3×C5 | #2206 | semidirect |
| 215. C3×C4 | D80 | semidirect |
| 244. C5 | #70889 | semidirect |
| 254. C4 | #90938 | semidirect |
| 257. C3 | #10600079 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11750796 | 2 |
| C3×C4×D40 | 2 |
| C2×#90938 | 2 |
| C5×C4⋊(C3⋊C16) | 2 |
| #11745895 | 2 |
| #10600079 | 3 |
| #70889 | 5 |