Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
196 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 67 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. C2×C3×C5×D8 | C2 | semidirect |
| 2. C2×D120 | C2 | semidirect |
| 3. #91110 | C2 | direct (N × H) |
| 4. C2×C3⋊#672 | C2 | semidirect |
| 9. C3×C5×D8 | C22 | semidirect |
| 12. D120 | C22 | semidirect |
| 13. C3⋊#672 | C22 | semidirect |
| 15. C2×C5×D8 | D3 | semidirect |
| 28. C2×C3×D8 | D5 | semidirect |
| 35. C5×D8 | C2×D3 | semidirect |
| 51. C3×D8 | C2×D5 | semidirect |
| 66. C2×D8 | D15 | semidirect |
| 70. C2×C3×C5 | D16 | semidirect |
| 94. D8 | C2×D15 | semidirect |
| 97. C3×C5 | C2×D16 | semidirect |
| 106. C2×C5 | #826 | semidirect |
| 119. C2×C3 | #3958 | semidirect |
| 122. C5 | C2×#826 | semidirect |
| 130. C3 | C2×#3958 | semidirect |
| 133. C2 | #91110 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C5×D8 | 2 |
| C2×D120 | 2 |
| #91110 | 2 |
| C2×C3⋊#672 | 2 |
| C2×#3958 | 3 |
| C2×#826 | 5 |