Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
164 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 70 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×#829 | C2 | semidirect |
| 4. C5×#828 | C2 | semidirect |
| 5. C5×#812 | C2 | semidirect |
| 16. #5179 | C5 | direct (N × H) |
| 18. C2×C5×Q16 | D3 | semidirect |
| 32. C2×C3×Q16 | C2×C5 | semidirect |
| 34. #829 | C2×C5 | semidirect |
| 35. #828 | C2×C5 | semidirect |
| 36. #812 | C2×C5 | semidirect |
| 73. C2×Q16 | C5×D3 | semidirect |
| 105. C3×C5 | #510 | semidirect |
| 128. C5 | #5179 | direct (N × H) |
| 135. C3 | C5×#510 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C5×Q16 | 2 |
| C5×#904 | 2 |
| C5×#829 | 2 |
| C5×#828 | 2 |
| C5×#812 | 2 |
| C5×#510 | 3 |
| #5179 | 5 |