Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
1848 conjugacy classes of subgroups; only the 318 normal subgroups are shown.
This group has 1848 conjugacy classes of subgroups — too many to draw. Only its 318 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. C2×AGL(1,𝔽5)×D12 | C2 | semidirect |
| 3. #11752347 | C2 | semidirect |
| 4. C3×C42×AGL(1,𝔽5) | C2 | semidirect |
| 5. #11751850 | C2 | semidirect |
| 14. #91763 | C4 | semidirect |
| 15. C5×#874 | C4 | semidirect |
| 17. #91451 | C4 | semidirect |
| 23. C42×AGL(1,𝔽5) | D3 | semidirect |
| 29. C2×D60 | C2×C4 | semidirect |
| 30. C2×C5×D12 | C2×C4 | semidirect |
| 32. C2×#1203 | C2×C4 | semidirect |
| 37. C3×C4×AGL(1,𝔽5) | D4 | semidirect |
| 39. C3×C42×C5 | C2×C4 | semidirect |
| 40. C3×C4×Dic5 | C2×C4 | semidirect |
| 84. #874 | AGL(1,𝔽5) | direct (N × H) |
| 100. C4×AGL(1,𝔽5) | D12 | semidirect |
| 101. C42×C5 | C4×D3 | semidirect |
| 102. C4×Dic5 | C4×D3 | semidirect |
| 117. C3×AGL(1,𝔽5) | #127 | semidirect |
| 118. C3×C4×C5 | C4×D4 | semidirect |
| 119. C3×Dic5 | C4×D4 | semidirect |
| 129. C2×D12 | C2×AGL(1,𝔽5) | semidirect |
| 134. C3×C42 | C2×AGL(1,𝔽5) | semidirect |
| 196. AGL(1,𝔽5) | #874 | direct (N × H) |
| 197. C4×C5 | C4×D12 | semidirect |
| 198. Dic5 | C4×D12 | semidirect |
| 215. C42 | D3×AGL(1,𝔽5) | semidirect |
| 216. C3×C5 | C4×#127 | semidirect |
| 227. C3×C4 | D4×AGL(1,𝔽5) | semidirect |
| 256. C5 | C4×#874 | semidirect |
| 268. C4 | AGL(1,𝔽5)×D12 | semidirect |
| 269. C3 | AGL(1,𝔽5)×#127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×AGL(1,𝔽5)×D12 | 2 |
| D5×#874 | 2 |
| #11752347 | 2 |
| C3×C42×AGL(1,𝔽5) | 2 |
| #11751850 | 2 |
| AGL(1,𝔽5)×#127 | 3 |
| C4×#874 | 5 |