Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
624 conjugacy classes of subgroups; only the 230 normal subgroups are shown.
This group has 624 conjugacy classes of subgroups — too many to draw. Only its 230 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×C5×#239 | C2 | semidirect |
| 2. C3×C4×C5×Q8 | C2 | semidirect |
| 3. C5×#895 | C2 | semidirect |
| 4. C5×#874 | C2 | semidirect |
| 5. C4×C5×D12 | C2 | semidirect |
| 17. #5577 | C5 | direct (N × H) |
| 21. C4×C5×Q8 | D3 | semidirect |
| 24. C3×C5×Q8 | D4 | semidirect |
| 33. C2×#239 | C2×C5 | semidirect |
| 34. C3×C4×Q8 | C2×C5 | semidirect |
| 35. #895 | C2×C5 | semidirect |
| 36. #874 | C2×C5 | semidirect |
| 37. C4×D12 | C2×C5 | semidirect |
| 55. C3×C4×C5 | #41 | semidirect |
| 68. C5×Q8 | D12 | semidirect |
| 80. C4×Q8 | C5×D3 | semidirect |
| 87. C3×Q8 | C5×D4 | semidirect |
| 103. C4×C5 | #239 | semidirect |
| 114. C3×C5 | #550 | semidirect |
| 121. C3×C4 | C5×#41 | semidirect |
| 128. Q8 | C5×D12 | semidirect |
| 141. C5 | #5577 | direct (N × H) |
| 149. C4 | C5×#239 | semidirect |
| 150. C3 | C5×#550 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#239 | 2 |
| C3×C4×C5×Q8 | 2 |
| C5×#895 | 2 |
| C5×#874 | 2 |
| C4×C5×D12 | 2 |
| C5×#550 | 3 |
| #5577 | 5 |