Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
492 conjugacy classes of subgroups; only the 160 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 160 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×C4×Dic15 | C2 | semidirect |
| 3. C2×C3×#683 | C2 | semidirect |
| 4. C2×Dic3⋊Dic5 | C2 | semidirect |
| 5. C2×#6668 | C2 | semidirect |
| 8. #91367 | C2 | direct (N × H) |
| 17. C4×Dic15 | C22 | semidirect |
| 19. C3×#683 | C22 | semidirect |
| 20. Dic3⋊Dic5 | C22 | semidirect |
| 21. #6668 | C22 | semidirect |
| 30. C2×#683 | D3 | semidirect |
| 70. #683 | C2×D3 | semidirect |
| 126. C2×C3×C5 | #126 | semidirect |
| 176. C3×C5 | C2×#126 | semidirect |
| 192. C2×C5 | #898 | semidirect |
| 213. C2×C3 | #4025 | semidirect |
| 218. C5 | C2×#898 | semidirect |
| 233. C3 | C2×#4025 | semidirect |
| 235. C2 | #91367 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×Dic15 | 2 |
| C2×C5×(C2×D3)⋊C4 | 2 |
| C2×C3×#683 | 2 |
| C2×Dic3⋊Dic5 | 2 |
| C2×#6668 | 2 |
| C2×(C2×D3)⋊Dic5 | 2 |
| #91367 | 2 |
| C2×#4025 | 3 |
| C2×#898 | 5 |