Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
248 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 94 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 |
|---|---|---|
| 1. C22×C3×C5×C8 | C2 | semidirect |
| 3. C5×#924 | C2 | semidirect |
| 4. C2×C5×#204 | C2 | semidirect |
| 5. C5×#821 | C2 | semidirect |
| 6. C5×#817 | C2 | semidirect |
| 7. C5×#816 | C2 | semidirect |
| 22. #5114 | C5 | direct (N × H) |
| 24. C22×C5×C8 | D3 | semidirect |
| 45. C3×C5×C8 | D4 | semidirect |
| 46. C22×C3×C8 | C2×C5 | semidirect |
| 48. #924 | C2×C5 | semidirect |
| 49. C2×#204 | C2×C5 | semidirect |
| 50. #821 | C2×C5 | semidirect |
| 51. #817 | C2×C5 | semidirect |
| 52. #816 | C2×C5 | semidirect |
| 69. C22×C3×C5 | SD16 | semidirect |
| 108. C5×C8 | #67 | semidirect |
| 110. C22×C8 | C5×D3 | semidirect |
| 136. C3×C8 | C5×D4 | semidirect |
| 142. C22×C5 | #204 | semidirect |
| 163. C3×C5 | #465 | semidirect |
| 166. C22×C3 | C5×SD16 | semidirect |
| 197. C8 | C5×#67 | semidirect |
| 203. C5 | #5114 | direct (N × H) |
| 209. C22 | C5×#204 | semidirect |
| 217. C3 | C5×#465 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×C5×C8 | 2 |
| C5×#930 | 2 |
| C5×#924 | 2 |
| C2×C5×#204 | 2 |
| C5×#821 | 2 |
| C5×#817 | 2 |
| C5×#816 | 2 |
| C5×#465 | 3 |
| #5114 | 5 |