Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
422 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 3. C3×C4⋊ΓL(1,𝔽16) | C2 | semidirect |
| 4. #10623979 | C2 | semidirect |
| 9. C4×C3⋊D15 | C4 | semidirect |
| 10. C4×C5×C3⋊D3 | C4 | semidirect |
| 12. #67137 | C4 | semidirect |
| 13. C3⋊D3×Dic5 | C4 | semidirect |
| 19. C4⋊ΓL(1,𝔽16) | D3 | semidirect |
| 28. C32×C4×C5 | C2×C4 | semidirect |
| 29. C3⋊Dic15 | C2×C4 | semidirect |
| 30. C5×C3⋊Dic3 | C2×C4 | semidirect |
| 31. C32×Dic5 | C2×C4 | semidirect |
| 56. C3⋊D15 | C4⋊C4 | semidirect |
| 57. C5×C3⋊D3 | C4⋊C4 | semidirect |
| 70. C4×C3⋊D3 | AGL(1,𝔽5) | semidirect |
| 86. C3×C4×C5 | C4×D3 | semidirect |
| 90. C3×Dic5 | C4×D3 | semidirect |
| 99. C32×C5 | C2×C4⋊C4 | semidirect |
| 115. C32×C4 | C2×AGL(1,𝔽5) | semidirect |
| 117. C3⋊Dic3 | C2×AGL(1,𝔽5) | semidirect |
| 154. C4×C5 | #624 | semidirect |
| 156. Dic5 | #624 | semidirect |
| 161. C3⋊D3 | C4⋊AGL(1,𝔽5) | semidirect |
| 167. C3×C5 | D3×C4⋊C4 | semidirect |
| 182. C3×C4 | D3×AGL(1,𝔽5) | semidirect |
| 193. C32 | C2×C4⋊AGL(1,𝔽5) | semidirect |
| 213. C5 | #63900 | semidirect |
| 223. C4 | ΓL(1,𝔽16)⋊D3 | semidirect |
| 225. C3 | D3×C4⋊AGL(1,𝔽5) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×ΓL(1,𝔽16)⋊D3 | 2 |
| C4×D5×C3⋊D3 | 2 |
| C3×C4⋊ΓL(1,𝔽16) | 2 |
| #10623979 | 2 |
| D3×C4⋊AGL(1,𝔽5) | 3 |
| #63900 | 5 |