Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
420 conjugacy classes of subgroups; only the 142 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 142 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×C22⋊Dic5 | C2 | semidirect |
| 3. C3×#3966 | C2 | direct (N × H) |
| 4. C2×#3966 | C3 | direct (N × H) |
| 5. C24×C3×C5 | C4 | semidirect |
| 9. C2×C3×C5×D4 | C4 | semidirect |
| 11. C22×C3×C4×C5 | C4 | semidirect |
| 14. C3×C22⋊Dic5 | C22 | semidirect |
| 17. C2×C22⋊Dic5 | C2×C3 | semidirect |
| 18. #3966 | C2×C3 | direct (N × H) |
| 25. C23×C3×C5 | C2×C4 | semidirect |
| 33. C2×C3×C4×C5 | C2×C4 | semidirect |
| 39. C24×C5 | C3×C4 | semidirect |
| 43. C2×C5×D4 | C3×C4 | semidirect |
| 45. C22×C4×C5 | C3×C4 | semidirect |
| 48. C22⋊Dic5 | C22×C3 | semidirect |
| 66. C24×C3 | Dic5 | semidirect |
| 70. C2×C3×D4 | Dic5 | semidirect |
| 73. C22×C3×C4 | Dic5 | semidirect |
| 82. C23×C5 | C2×C3×C4 | semidirect |
| 90. C2×C4×C5 | C2×C3×C4 | semidirect |
| 101. C2×C3×C5 | #99 | semidirect |
| 109. C23×C3 | C2×Dic5 | semidirect |
| 119. C2×C3×C4 | C2×Dic5 | semidirect |
| 136. C24 | C3×Dic5 | semidirect |
| 140. C2×D4 | C3×Dic5 | semidirect |
| 143. C22×C4 | C3×Dic5 | semidirect |
| 146. C3×C5 | C2×#99 | semidirect |
| 168. C2×C5 | C3×#99 | semidirect |
| 176. C23 | C2×C3×Dic5 | semidirect |
| 186. C2×C4 | C2×C3×Dic5 | semidirect |
| 192. C2×C3 | #3966 | direct (N × H) |
| 194. C5 | C2×C3×#99 | semidirect |
| 211. C3 | C2×#3966 | direct (N × H) |
| 217. C2 | C3×#3966 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×C5×D4 | 2 |
| C2×C3×C22⋊Dic5 | 2 |
| C3×#3966 | 2 |
| C2×#3966 | 3 |
| C2×C3×#99 | 5 |