Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
1348 conjugacy classes of subgroups; only the 432 normal subgroups are shown.
This group has 1348 conjugacy classes of subgroups — too many to draw. Only its 432 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. C23×Dic15 | C2 | semidirect |
| 3. C23×C5×Dic3 | C2 | semidirect |
| 4. C2×#6665 | C2 | direct (N × H) |
| 9. C23×C3×D5 | C4 | semidirect |
| 12. C22×Dic15 | C22 | semidirect |
| 14. C22×C5×Dic3 | C22 | semidirect |
| 15. #6665 | C22 | direct (N × H) |
| 28. C22×C3×D5 | C2×C4 | semidirect |
| 31. C2×Dic15 | C23 | semidirect |
| 33. C2×C5×Dic3 | C23 | semidirect |
| 36. C23×Dic3 | D5 | semidirect |
| 41. C23×D5 | Dic3 | semidirect |
| 49. C22×C3×C5 | C22⋊C4 | semidirect |
| 57. C2×C3×D5 | C22×C4 | semidirect |
| 68. C22×Dic3 | C2×D5 | semidirect |
| 77. C22×D5 | C2×Dic3 | semidirect |
| 87. C2×C3×C5 | C2×C22⋊C4 | semidirect |
| 104. C2×Dic3 | C22×D5 | semidirect |
| 105. C22×C5 | #217 | semidirect |
| 113. C2×D5 | C22×Dic3 | semidirect |
| 126. C3×C5 | C22×C22⋊C4 | semidirect |
| 131. C22×C3 | #685 | semidirect |
| 138. C2×C5 | C2×#217 | semidirect |
| 157. C2×C3 | C2×#685 | semidirect |
| 161. C5 | C22×#217 | semidirect |
| 166. C22 | #6665 | direct (N × H) |
| 173. C3 | C22×#685 | semidirect |
| 175. C2 | C2×#6665 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×C3×D5 | 2 |
| C23×Dic15 | 2 |
| C23×C5×Dic3 | 2 |
| C2×#6665 | 2 |
| C22×#685 | 3 |
| C22×#217 | 5 |