Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
720 conjugacy classes of subgroups; only the 134 normal subgroups are shown.
This group has 720 conjugacy classes of subgroups — too many to draw. Only its 134 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 |
|---|---|---|
| 2. #11752340 | C2 | semidirect |
| 3. C3×C42×AGL(1,𝔽5) | C2 | semidirect |
| 4. C2×#91156 | C2 | semidirect |
| 10. #91758 | C4 | semidirect |
| 11. C5×#874 | C4 | semidirect |
| 15. #91373 | C4 | semidirect |
| 21. C42×AGL(1,𝔽5) | D3 | semidirect |
| 37. C3×C4×AGL(1,𝔽5) | D4 | semidirect |
| 86. #874 | AGL(1,𝔽5) | semidirect |
| 104. C4×AGL(1,𝔽5) | D12 | semidirect |
| 121. C3×C4×C5 | #104 | semidirect |
| 207. C4×C5 | #805 | semidirect |
| 233. C3×C5 | #1962 | semidirect |
| 243. C3×C4 | #4008 | semidirect |
| 273. C5 | #69395 | semidirect |
| 284. C4 | #91156 | semidirect |
| 286. C3 | #10604611 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11752672 | 2 |
| #11752340 | 2 |
| C3×C42×AGL(1,𝔽5) | 2 |
| C2×#91156 | 2 |
| #10604611 | 3 |
| #69395 | 5 |