Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
256 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 256 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. C3×C4×C5×Q8 | C2 | semidirect |
| 2. C2×C5×#215 | C2 | semidirect |
| 4. C5×#809 | C2 | semidirect |
| 5. C5×C4⋊(C3⋊C8) | C2 | semidirect |
| 17. #5027 | C5 | direct (N × H) |
| 20. C4×C5×Q8 | D3 | semidirect |
| 25. C3×C5×Q8 | D4 | semidirect |
| 36. C3×C4×Q8 | C2×C5 | semidirect |
| 37. C2×#215 | C2×C5 | semidirect |
| 39. #809 | C2×C5 | semidirect |
| 40. C4⋊(C3⋊C8) | C2×C5 | semidirect |
| 59. C3×C4×C5 | SD16 | semidirect |
| 74. C5×Q8 | D12 | semidirect |
| 87. C4×Q8 | C5×D3 | semidirect |
| 96. C3×Q8 | C5×D4 | semidirect |
| 114. C4×C5 | #215 | semidirect |
| 127. C3×C5 | #460 | semidirect |
| 135. C3×C4 | C5×SD16 | semidirect |
| 144. Q8 | C5×D12 | semidirect |
| 159. C5 | #5027 | direct (N × H) |
| 167. C4 | C5×#215 | semidirect |
| 170. C3 | C5×#460 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×C5×Q8 | 2 |
| C2×C5×#215 | 2 |
| C5×#874 | 2 |
| C5×#809 | 2 |
| C5×C4⋊(C3⋊C8) | 2 |
| C5×#460 | 3 |
| #5027 | 5 |