Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
256 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 90 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×#677 | C2 | semidirect |
| 3. C3×C4×Dic10 | C2 | semidirect |
| 4. C3×C5×C4⋊C8 | C2 | semidirect |
| 5. C3×#3953 | C2 | semidirect |
| 6. #65137 | C3 | direct (N × H) |
| 18. C2×#677 | C2×C3 | semidirect |
| 20. C4×Dic10 | C2×C3 | semidirect |
| 21. C5×C4⋊C8 | C2×C3 | semidirect |
| 22. #3953 | C2×C3 | semidirect |
| 34. C3×Dic10 | D4 | semidirect |
| 39. C3×C4⋊C8 | D5 | semidirect |
| 57. C3×C4×C5 | SD16 | semidirect |
| 83. Dic10 | C3×D4 | semidirect |
| 88. C4⋊C8 | C3×D5 | semidirect |
| 112. C4×C5 | C3×SD16 | semidirect |
| 127. C3×C5 | #460 | semidirect |
| 135. C3×C4 | #677 | semidirect |
| 159. C5 | C3×#460 | semidirect |
| 167. C4 | C3×#677 | semidirect |
| 170. C3 | #65137 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#677 | 2 |
| C3×#4020 | 2 |
| C3×C4×Dic10 | 2 |
| C3×C5×C4⋊C8 | 2 |
| C3×#3953 | 2 |
| #65137 | 3 |
| C3×#460 | 5 |