Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
422 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 115 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. #10623979 | C2 | direct (N × H) |
| 8. C2×C3⋊Dic15 | C4 | semidirect |
| 9. C2×C5×C3⋊Dic3 | C4 | semidirect |
| 10. D5×C3⋊Dic3 | C4 | semidirect |
| 24. C3⋊Dic15 | C2×C4 | semidirect |
| 25. C5×C3⋊Dic3 | C2×C4 | semidirect |
| 45. C2×C32×C5 | C4⋊C4 | semidirect |
| 47. C32×D5 | C4⋊C4 | semidirect |
| 57. C2×C3⋊Dic3 | AGL(1,𝔽5) | semidirect |
| 81. C32×C5 | C2×C4⋊C4 | semidirect |
| 95. C3⋊Dic3 | C2×AGL(1,𝔽5) | semidirect |
| 100. C2×C3×C5 | Dic3⋊C4 | semidirect |
| 105. C3×D5 | Dic3⋊C4 | semidirect |
| 133. C2×C32 | C4⋊AGL(1,𝔽5) | semidirect |
| 139. C3×C5 | C2×Dic3⋊C4 | semidirect |
| 156. C2×C5 | #3724 | semidirect |
| 158. D5 | #3724 | semidirect |
| 161. C32 | C2×C4⋊AGL(1,𝔽5) | semidirect |
| 177. C2×C3 | Dic3⋊AGL(1,𝔽5) | semidirect |
| 179. C5 | C2×#3724 | semidirect |
| 189. C3 | C2×Dic3⋊AGL(1,𝔽5) | semidirect |
| 193. C2 | #10623979 | 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 |
| C2×D5×C3⋊Dic3 | 2 |
| #10623979 | 2 |
| C2×Dic3⋊AGL(1,𝔽5) | 3 |
| C2×#3724 | 5 |