Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
294 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 120 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. C2×C3×C5×C3⋊C8 | C2 | semidirect |
| 3. C2×C32×#168 | C2 | semidirect |
| 4. C3×#6651 | C2 | direct (N × H) |
| 6. C2×#6651 | C3 | direct (N × H) |
| 12. C3×C5×C3⋊C8 | C22 | semidirect |
| 13. C32×#168 | C22 | semidirect |
| 18. C2×C5×C3⋊C8 | C2×C3 | semidirect |
| 20. C2×C3×#168 | D3 | semidirect |
| 21. C2×C3×#168 | C2×C3 | semidirect |
| 23. #6651 | C2×C3 | direct (N × H) |
| 33. C2×C3×C3⋊C8 | D5 | semidirect |
| 48. C3×#168 | C2×D3 | semidirect |
| 49. C3×#168 | C22×C3 | semidirect |
| 50. C5×C3⋊C8 | C22×C3 | semidirect |
| 53. C2×C32×C5 | M16 | semidirect |
| 58. C2×#168 | C3×D3 | semidirect |
| 66. C3×C3⋊C8 | C2×D5 | semidirect |
| 89. C2×C3⋊C8 | C3×D5 | semidirect |
| 91. C32×C5 | C2×M16 | semidirect |
| 98. #168 | C2×C3×D3 | semidirect |
| 108. C2×C3×C5 | ΓL(1,𝔽25) | semidirect |
| 109. C2×C3×C5 | C3×M16 | semidirect |
| 129. C3⋊C8 | C2×C3×D5 | semidirect |
| 136. C2×C32 | #676 | semidirect |
| 144. C3×C5 | C2×ΓL(1,𝔽25) | semidirect |
| 145. C3×C5 | C2×C3×M16 | semidirect |
| 161. C2×C5 | C3×ΓL(1,𝔽25) | semidirect |
| 164. C32 | C2×#676 | semidirect |
| 175. C2×C3 | #6651 | direct (N × H) |
| 176. C2×C3 | C3×#676 | semidirect |
| 180. C5 | C2×C3×ΓL(1,𝔽25) | semidirect |
| 188. C3 | C2×#6651 | direct (N × H) |
| 189. C3 | C2×C3×#676 | semidirect |
| 191. C2 | C3×#6651 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C4×D15 | 2 |
| C2×C3×C5×C3⋊C8 | 2 |
| C2×C32×#168 | 2 |
| C3×#6651 | 2 |
| C2×C3×#676 | 3 |
| C2×#6651 | 3 |
| C2×C3×ΓL(1,𝔽25) | 5 |