Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
172 conjugacy classes of subgroups; only the 33 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 33 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. #91228 | C2 | semidirect |
| 4. C2×C3×C5×D4 | C4 | semidirect |
| 8. C3×C4×Dic5 | C4 | semidirect |
| 22. C2×C5×D4 | Dic3 | semidirect |
| 26. C4×Dic5 | Dic3 | semidirect |
| 38. C2×C3×D4 | AGL(1,𝔽5) | semidirect |
| 73. C2×D4 | ΓL(1,𝔽16) | semidirect |
| 76. C3×C5 | #353 | semidirect |
| 101. C5 | #4545 | semidirect |
| 110. C3 | #64922 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4086 | 2 |
| #91228 | 2 |
| #64922 | 3 |
| #4545 | 5 |