Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
422 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 126 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 |
|---|---|---|
| 4. Dic3⋊ΓL(1,𝔽16) | C2 | direct (N × H) |
| 12. C2×C3×Dic15 | C4 | semidirect |
| 13. C2×C3×C5×Dic3 | C4 | semidirect |
| 14. C3×D5×Dic3 | C4 | semidirect |
| 33. C3×Dic15 | C2×C4 | semidirect |
| 34. C3×C5×Dic3 | C2×C4 | semidirect |
| 54. C2×Dic15 | Dic3 | semidirect |
| 55. C2×C5×Dic3 | Dic3 | semidirect |
| 59. D5×Dic3 | Dic3 | semidirect |
| 63. C2×C32×C5 | C4⋊C4 | semidirect |
| 65. C32×D5 | C4⋊C4 | semidirect |
| 80. C2×C3×Dic3 | AGL(1,𝔽5) | semidirect |
| 102. Dic15 | C2×Dic3 | semidirect |
| 104. C5×Dic3 | C2×Dic3 | semidirect |
| 114. C32×C5 | C2×C4⋊C4 | semidirect |
| 132. C3×Dic3 | C2×AGL(1,𝔽5) | semidirect |
| 136. C2×C3×C5 | Dic3⋊C4 | semidirect |
| 137. C2×C3×C5 | C4⋊Dic3 | semidirect |
| 143. C3×D5 | Dic3⋊C4 | semidirect |
| 144. C3×D5 | C4⋊Dic3 | semidirect |
| 169. C2×Dic3 | ΓL(1,𝔽16) | semidirect |
| 182. C2×C32 | C4⋊AGL(1,𝔽5) | semidirect |
| 189. C3×C5 | C2×Dic3⋊C4 | semidirect |
| 190. C3×C5 | C2×C4⋊Dic3 | semidirect |
| 214. Dic3 | C2×ΓL(1,𝔽16) | semidirect |
| 215. C2×C5 | Dic3⋊Dic3 | semidirect |
| 217. D5 | Dic3⋊Dic3 | semidirect |
| 220. C32 | C2×C4⋊AGL(1,𝔽5) | semidirect |
| 241. C2×C3 | Dic3⋊AGL(1,𝔽5) | semidirect |
| 242. C2×C3 | C4⋊ΓL(1,𝔽16) | semidirect |
| 245. C5 | C2×Dic3⋊Dic3 | semidirect |
| 256. C3 | C2×Dic3⋊AGL(1,𝔽5) | semidirect |
| 257. C3 | C2×C4⋊ΓL(1,𝔽16) | semidirect |
| 261. C2 | Dic3⋊ΓL(1,𝔽16) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3⋊ΓL(1,𝔽16) | 2 |
| C22×C3×ΓL(1,𝔽16) | 2 |
| C2×C3×D5×Dic3 | 2 |
| Dic3⋊ΓL(1,𝔽16) | 2 |
| C2×C4⋊ΓL(1,𝔽16) | 3 |
| C2×Dic3⋊AGL(1,𝔽5) | 3 |
| C2×Dic3⋊Dic3 | 5 |