Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
316 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 96 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 |
|---|---|---|
| 2. C3×#4130 | C2 | semidirect |
| 3. C3×#3999 | C2 | semidirect |
| 4. #65785 | C3 | direct (N × H) |
| 5. C2×C3×C5×Q8 | C4 | semidirect |
| 8. C2×C3×D20 | C4 | semidirect |
| 10. C2×C3×C4×D5 | C4 | semidirect |
| 17. #4130 | C2×C3 | semidirect |
| 18. #3999 | C2×C3 | semidirect |
| 35. C2×C5×Q8 | C3×C4 | semidirect |
| 38. C2×D20 | C3×C4 | semidirect |
| 40. C2×C4×D5 | C3×C4 | semidirect |
| 58. C2×C3×Q8 | AGL(1,𝔽5) | semidirect |
| 111. C2×Q8 | C3×AGL(1,𝔽5) | semidirect |
| 119. C3×C5 | #410 | semidirect |
| 151. C5 | C3×#410 | semidirect |
| 162. C3 | #65785 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#713 | 2 |
| C3×#4130 | 2 |
| C3×#3999 | 2 |
| #65785 | 3 |
| C3×#410 | 5 |