Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
262 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 58 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 |
|---|---|---|
| 2. C3×#6763 | C2 | semidirect |
| 3. #91240 | C3 | direct (N × H) |
| 5. C23×C32×C5 | C4 | semidirect |
| 9. C2×C32×Dic5 | C4 | semidirect |
| 14. #6763 | C2×C3 | semidirect |
| 27. C23×C3×C5 | Dic3 | semidirect |
| 28. C23×C3×C5 | C3×C4 | semidirect |
| 38. C2×C3×Dic5 | Dic3 | semidirect |
| 39. C2×C3×Dic5 | C3×C4 | semidirect |
| 49. C23×C32 | AGL(1,𝔽5) | semidirect |
| 78. C32×C5 | #99 | semidirect |
| 79. C23×C5 | C3×Dic3 | semidirect |
| 83. C2×Dic5 | C3×Dic3 | semidirect |
| 108. C23×C3 | C3×AGL(1,𝔽5) | semidirect |
| 109. C23×C3 | ΓL(1,𝔽16) | semidirect |
| 132. C3×C5 | #834 | semidirect |
| 133. C3×C5 | C3×#99 | semidirect |
| 158. C32 | #4011 | semidirect |
| 160. C23 | C3×ΓL(1,𝔽16) | semidirect |
| 176. C5 | C3×#834 | semidirect |
| 185. C3 | C3×#4011 | semidirect |
| 186. C3 | #91240 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×C22⋊D5 | 2 |
| C3×#6763 | 2 |
| #91240 | 3 |
| C3×#4011 | 3 |
| C3×#834 | 5 |