Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
456 conjugacy classes of subgroups; only the 186 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 186 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×C32×Dic10 | C2 | semidirect |
| 3. C32×C5×C22⋊C4 | C2 | semidirect |
| 4. C32×C22⋊Dic5 | C2 | semidirect |
| 5. C32×#685 | C2 | semidirect |
| 6. C32×#685 | C2 | semidirect |
| 7. C32×C4×Dic5 | C2 | semidirect |
| 8. C3×#4031 | C3 | direct (N × H) |
| 20. C2×C3×Dic10 | C2×C3 | semidirect |
| 21. C3×C5×C22⋊C4 | C2×C3 | semidirect |
| 22. C3×C22⋊Dic5 | C2×C3 | semidirect |
| 23. C3×#685 | C2×C3 | semidirect |
| 24. C3×#685 | C2×C3 | semidirect |
| 25. C3×C4×Dic5 | C2×C3 | semidirect |
| 38. #4031 | C32 | direct (N × H) |
| 44. C32×C22⋊C4 | D5 | semidirect |
| 62. C2×Dic10 | C2×C32 | semidirect |
| 63. C5×C22⋊C4 | C2×C32 | semidirect |
| 64. C22⋊Dic5 | C2×C32 | semidirect |
| 65. #685 | C2×C32 | semidirect |
| 66. #685 | C2×C32 | semidirect |
| 67. C4×Dic5 | C2×C32 | semidirect |
| 94. C3×C22⋊C4 | C3×D5 | semidirect |
| 96. C32×C5 | #124 | semidirect |
| 155. C22⋊C4 | C32×D5 | semidirect |
| 157. C3×C5 | C3×#124 | semidirect |
| 175. C32 | #4031 | direct (N × H) |
| 190. C5 | C32×#124 | semidirect |
| 203. C3 | C3×#4031 | 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 |
| C2×C32×Dic10 | 2 |
| C32×C5×C22⋊C4 | 2 |
| C32×C22⋊Dic5 | 2 |
| C32×#685 | 2 |
| C32×C4×Dic5 | 2 |
| C3×#4031 | 3 |
| C32×#124 | 5 |