Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
260 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 98 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 |
|---|---|---|
| 4. #91160 | C2 | direct (N × H) |
| 13. C2×C3⋊#168 | C4 | semidirect |
| 14. C2×C5×C3⋊C8 | C4 | semidirect |
| 15. D5×C3⋊C8 | C4 | semidirect |
| 33. C3⋊#168 | C2×C4 | semidirect |
| 34. C5×C3⋊C8 | C2×C4 | semidirect |
| 72. C2×C3⋊C8 | AGL(1,𝔽5) | semidirect |
| 90. C2×C3×C5 | #107 | semidirect |
| 92. C3×D5 | #107 | semidirect |
| 107. C3⋊C8 | C2×AGL(1,𝔽5) | semidirect |
| 130. C3×C5 | C2×#107 | semidirect |
| 142. C2×C5 | #807 | semidirect |
| 144. D5 | #807 | semidirect |
| 163. C2×C3 | #3994 | semidirect |
| 165. C5 | C2×#807 | semidirect |
| 177. C3 | C2×#3994 | semidirect |
| 181. C2 | #91160 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊ΓL(1,𝔽16) | 2 |
| C2×C3×C4⋊AGL(1,𝔽5) | 2 |
| C2×D5×C3⋊C8 | 2 |
| #91160 | 2 |
| C2×#3994 | 3 |
| C2×#807 | 5 |