Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
420 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 118 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 |
|---|---|---|
| 10. #67180 | C4 | semidirect |
| 11. C5×#634 | C4 | semidirect |
| 13. #67141 | C4 | semidirect |
| 24. C32×AGL(1,𝔽5) | Q8 | semidirect |
| 59. #634 | AGL(1,𝔽5) | direct (N × H) |
| 63. C3×AGL(1,𝔽5) | Dic6 | semidirect |
| 73. C32×C5 | C4×Q8 | semidirect |
| 105. AGL(1,𝔽5) | #634 | direct (N × H) |
| 118. C3×C5 | C4×Dic6 | semidirect |
| 130. C32 | Q8×AGL(1,𝔽5) | semidirect |
| 142. C5 | C4×#634 | semidirect |
| 151. C3 | AGL(1,𝔽5)×Dic6 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D5×#634 | 2 |
| C4⋊(C3⋊ΓL(1,𝔽16)) | 2 |
| C32×C4×AGL(1,𝔽5) | 2 |
| #10623965 | 2 |
| AGL(1,𝔽5)×C3⋊Dic3 | 2 |
| AGL(1,𝔽5)×Dic6 | 3 |
| C4×#634 | 5 |