Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
376 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 376 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 |
|---|---|---|
| 2. C3×C5×C22⋊Q8 | C2 | semidirect |
| 3. C2×C5×#215 | C2 | semidirect |
| 4. C5×#830 | C2 | semidirect |
| 5. C5×#809 | C2 | semidirect |
| 8. C2×C3×C5×Q8 | C22 | semidirect |
| 14. C3×C5×C4⋊C4 | C22 | semidirect |
| 17. C2×C5×C3⋊C8 | C22 | semidirect |
| 18. #5046 | C5 | direct (N × H) |
| 21. C5×C22⋊Q8 | D3 | semidirect |
| 40. C3×C22⋊Q8 | C2×C5 | semidirect |
| 41. C2×#215 | C2×C5 | semidirect |
| 42. #830 | C2×C5 | semidirect |
| 43. #809 | C2×C5 | semidirect |
| 45. C2×C5×Q8 | C2×D3 | semidirect |
| 53. C5×C4⋊C4 | C2×D3 | semidirect |
| 58. C22×C3×C5 | SD16 | semidirect |
| 69. C2×C3×Q8 | C22×C5 | semidirect |
| 75. C3×C4⋊C4 | C22×C5 | semidirect |
| 78. C2×C3⋊C8 | C22×C5 | semidirect |
| 96. C22⋊Q8 | C5×D3 | semidirect |
| 125. C22×C5 | #215 | semidirect |
| 132. C2×Q8 | C2×C5×D3 | semidirect |
| 140. C4⋊C4 | C2×C5×D3 | semidirect |
| 142. C3×C5 | #450 | semidirect |
| 145. C22×C3 | C5×SD16 | semidirect |
| 180. C5 | #5046 | direct (N × H) |
| 187. C22 | C5×#215 | semidirect |
| 193. C3 | C5×#450 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×D12 | 2 |
| C3×C5×C22⋊Q8 | 2 |
| C2×C5×#215 | 2 |
| C5×#830 | 2 |
| C5×#809 | 2 |
| C5×#450 | 3 |
| #5046 | 5 |