Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
852 conjugacy classes of subgroups; only the 288 normal subgroups are shown.
This group has 852 conjugacy classes of subgroups — too many to draw. Only its 288 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. C22×D5×Dic3 | C2 | semidirect |
| 3. C2×C4⋊Dic15 | C2 | semidirect |
| 4. C2×C4×C5×Dic3 | C2 | semidirect |
| 5. C2×#6665 | C2 | semidirect |
| 6. Dic3×D20 | C2 | direct (N × H) |
| 13. C2×C3×D20 | C4 | semidirect |
| 16. C2×D5×Dic3 | C22 | semidirect |
| 17. C4⋊Dic15 | C22 | semidirect |
| 18. C4×C5×Dic3 | C22 | semidirect |
| 19. #6665 | C22 | semidirect |
| 30. C22×C3×D5 | C2×C4 | semidirect |
| 32. C2×C3×C4×C5 | C2×C4 | semidirect |
| 37. C2×C5×Dic3 | D4 | semidirect |
| 40. C3×D20 | C2×C4 | semidirect |
| 47. C2×C4×Dic3 | D5 | semidirect |
| 53. C2×D20 | Dic3 | direct (N × H) |
| 68. C2×C3×D5 | C22×C4 | semidirect |
| 69. C3×C4×C5 | C22×C4 | semidirect |
| 72. C5×Dic3 | C2×D4 | semidirect |
| 84. C4×Dic3 | C2×D5 | semidirect |
| 88. C22×D5 | C2×Dic3 | semidirect |
| 94. C2×C4×C5 | C2×Dic3 | semidirect |
| 98. D20 | C2×Dic3 | direct (N × H) |
| 106. C2×C3×C5 | C4×D4 | semidirect |
| 117. C2×C3×C4 | C4×D5 | semidirect |
| 123. C2×Dic3 | D20 | direct (N × H) |
| 133. C2×D5 | C22×Dic3 | semidirect |
| 136. C4×C5 | C22×Dic3 | semidirect |
| 150. C3×C5 | C2×C4×D4 | semidirect |
| 159. C3×C4 | C2×C4×D5 | semidirect |
| 162. Dic3 | C2×D20 | direct (N × H) |
| 163. C2×C5 | D4×Dic3 | semidirect |
| 181. C2×C4 | D5×Dic3 | semidirect |
| 184. C2×C3 | C4×D20 | semidirect |
| 188. C5 | C2×D4×Dic3 | semidirect |
| 200. C4 | C2×D5×Dic3 | semidirect |
| 201. C3 | C2×C4×D20 | semidirect |
| 203. C2 | Dic3×D20 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×D20 | 2 |
| C22×D5×Dic3 | 2 |
| C2×C4⋊Dic15 | 2 |
| C2×C4×C5×Dic3 | 2 |
| C2×#6665 | 2 |
| Dic3×D20 | 2 |
| C2×C4×D20 | 3 |
| C2×D4×Dic3 | 5 |