Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
180 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 78 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×Q16 | C2 | semidirect |
| 3. C5×#828 | C2 | direct (N × H) |
| 4. C2×C5×C3⋊C16 | C2 | semidirect |
| 9. C3×C5×Q16 | C22 | semidirect |
| 13. C5×C3⋊C16 | C22 | semidirect |
| 14. C2×#828 | C5 | direct (N × H) |
| 15. C2×C5×Q16 | D3 | semidirect |
| 28. C2×C3×Q16 | C2×C5 | semidirect |
| 30. #828 | C2×C5 | direct (N × H) |
| 31. C2×C3⋊C16 | C2×C5 | semidirect |
| 35. C5×Q16 | C2×D3 | semidirect |
| 50. C3×Q16 | C22×C5 | semidirect |
| 54. C3⋊C16 | C22×C5 | semidirect |
| 64. C2×Q16 | C5×D3 | semidirect |
| 68. C2×C3×C5 | SD32 | semidirect |
| 89. Q16 | C2×C5×D3 | semidirect |
| 94. C3×C5 | C2×SD32 | semidirect |
| 102. C2×C5 | #828 | direct (N × H) |
| 113. C2×C3 | C5×SD32 | semidirect |
| 116. C5 | C2×#828 | direct (N × H) |
| 123. C3 | C2×C5×SD32 | semidirect |
| 125. C2 | C5×#828 | 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×Q16 | 2 |
| C2×C5×D24 | 2 |
| C5×#828 | 2 |
| C2×C5×C3⋊C16 | 2 |
| C2×C5×SD32 | 3 |
| C2×#828 | 5 |