Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
402 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 104 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×C3×D3×AGL(1,𝔽5) | C2 | semidirect |
| 3. C3×C4×ΓL(1,𝔽16) | C2 | semidirect |
| 4. C32×C4⋊AGL(1,𝔽5) | C2 | semidirect |
| 5. C3×(C2×D3)⋊AGL(1,𝔽5) | C2 | semidirect |
| 7. #91921 | C3 | direct (N × H) |
| 13. C3×D60 | C4 | semidirect |
| 14. C3×C5×D12 | C4 | semidirect |
| 16. C3×#1203 | C4 | semidirect |
| 19. C2×D3×AGL(1,𝔽5) | C2×C3 | semidirect |
| 22. C4×ΓL(1,𝔽16) | C2×C3 | semidirect |
| 25. C3×C4⋊AGL(1,𝔽5) | D3 | semidirect |
| 26. C3×C4⋊AGL(1,𝔽5) | C2×C3 | semidirect |
| 28. (C2×D3)⋊AGL(1,𝔽5) | C2×C3 | semidirect |
| 29. C2×C3×D15 | C2×C4 | semidirect |
| 30. C2×C3×C5×D3 | C2×C4 | semidirect |
| 35. C3×ΓL(1,𝔽16) | D4 | semidirect |
| 37. C32×C4×C5 | C2×C4 | semidirect |
| 38. C32×Dic5 | C2×C4 | semidirect |
| 57. D60 | C3×C4 | semidirect |
| 58. C5×D12 | C3×C4 | semidirect |
| 64. #1203 | C3×C4 | semidirect |
| 75. C4⋊AGL(1,𝔽5) | C3×D3 | semidirect |
| 84. C3×D12 | AGL(1,𝔽5) | semidirect |
| 87. C2×D15 | C2×C3×C4 | semidirect |
| 88. C2×C5×D3 | C2×C3×C4 | semidirect |
| 98. ΓL(1,𝔽16) | C3×D4 | semidirect |
| 105. C3×C4×C5 | C4×D3 | semidirect |
| 106. C3×C4×C5 | C2×C3×C4 | semidirect |
| 108. C3×Dic5 | C4×D3 | semidirect |
| 109. C3×Dic5 | C2×C3×C4 | semidirect |
| 121. C32×C5 | C4×D4 | semidirect |
| 135. C2×C3×D3 | C2×AGL(1,𝔽5) | semidirect |
| 138. C32×C4 | C2×AGL(1,𝔽5) | semidirect |
| 173. D12 | C3×AGL(1,𝔽5) | semidirect |
| 183. C4×C5 | C3×C4×D3 | semidirect |
| 184. Dic5 | C3×C4×D3 | semidirect |
| 196. C3×C5 | #893 | semidirect |
| 197. C3×C5 | C3×C4×D4 | semidirect |
| 208. C2×D3 | C2×C3×AGL(1,𝔽5) | semidirect |
| 218. C3×C4 | D3×AGL(1,𝔽5) | semidirect |
| 219. C3×C4 | C2×C3×AGL(1,𝔽5) | semidirect |
| 227. C32 | D4×AGL(1,𝔽5) | semidirect |
| 250. C5 | C3×#893 | semidirect |
| 260. C4 | C3×D3×AGL(1,𝔽5) | semidirect |
| 262. C3 | #91921 | direct (N × H) |
| 263. C3 | C3×D4×AGL(1,𝔽5) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×D3×AGL(1,𝔽5) | 2 |
| C3×D5×D12 | 2 |
| C3×C4×ΓL(1,𝔽16) | 2 |
| C32×C4⋊AGL(1,𝔽5) | 2 |
| C3×(C2×D3)⋊AGL(1,𝔽5) | 2 |
| C3×D4×AGL(1,𝔽5) | 3 |
| #91921 | 3 |
| C3×#893 | 5 |