Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
456 conjugacy classes of subgroups; only the 216 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 216 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. C32×C4⋊AGL(1,𝔽5) | C2 | semidirect |
| 4. C32×C4×AGL(1,𝔽5) | C2 | semidirect |
| 5. C3×#4130 | C3 | direct (N × H) |
| 8. C2×C32×C4×C5 | C4 | semidirect |
| 9. C2×C32×Dic5 | C4 | semidirect |
| 10. C32×C4×D5 | C4 | semidirect |
| 11. C32×C4×D5 | C4 | semidirect |
| 17. C3×C4⋊AGL(1,𝔽5) | C2×C3 | semidirect |
| 18. C3×C4×AGL(1,𝔽5) | C2×C3 | semidirect |
| 28. #4130 | C32 | direct (N × H) |
| 35. C2×C3×C4×C5 | C3×C4 | semidirect |
| 36. C2×C3×Dic5 | C3×C4 | semidirect |
| 37. C3×C4×D5 | C3×C4 | semidirect |
| 38. C3×C4×D5 | C3×C4 | semidirect |
| 48. C4⋊AGL(1,𝔽5) | C2×C32 | semidirect |
| 49. C4×AGL(1,𝔽5) | C2×C32 | semidirect |
| 57. C2×C32×C4 | AGL(1,𝔽5) | semidirect |
| 71. C32×C5 | #117 | semidirect |
| 74. C2×C4×C5 | C32×C4 | semidirect |
| 75. C2×Dic5 | C32×C4 | semidirect |
| 76. C4×D5 | C32×C4 | semidirect |
| 77. C4×D5 | C32×C4 | semidirect |
| 101. C2×C3×C4 | C3×AGL(1,𝔽5) | semidirect |
| 119. C3×C5 | C3×#117 | semidirect |
| 133. C32 | #4130 | direct (N × H) |
| 141. C2×C4 | C32×AGL(1,𝔽5) | semidirect |
| 146. C5 | C32×#117 | semidirect |
| 156. C3 | C3×#4130 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×C4×D5 | 2 |
| C32×C22⋊AGL(1,𝔽5) | 2 |
| C32×C4⋊AGL(1,𝔽5) | 2 |
| C32×C4×AGL(1,𝔽5) | 2 |
| C3×#4130 | 3 |
| C32×#117 | 5 |