Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
420 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 93 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. C2×#6763 | C2 | semidirect |
| 3. #91240 | C2 | direct (N × H) |
| 5. C24×C3×C5 | C4 | semidirect |
| 10. C2×C3×C22⋊D5 | C4 | semidirect |
| 12. C22×C3×Dic5 | C4 | semidirect |
| 14. #6763 | C22 | semidirect |
| 23. C23×C3×C5 | C2×C4 | semidirect |
| 35. C2×C3×Dic5 | C2×C4 | semidirect |
| 39. C24×C5 | Dic3 | semidirect |
| 44. C2×C22⋊D5 | Dic3 | semidirect |
| 46. C22×Dic5 | Dic3 | semidirect |
| 67. C24×C3 | AGL(1,𝔽5) | semidirect |
| 80. C23×C5 | C2×Dic3 | semidirect |
| 92. C2×Dic5 | C2×Dic3 | semidirect |
| 99. C2×C3×C5 | #99 | semidirect |
| 112. C23×C3 | C2×AGL(1,𝔽5) | semidirect |
| 137. C24 | ΓL(1,𝔽16) | semidirect |
| 146. C3×C5 | C2×#99 | semidirect |
| 166. C2×C5 | #834 | semidirect |
| 179. C23 | C2×ΓL(1,𝔽16) | semidirect |
| 192. C2×C3 | #4011 | semidirect |
| 194. C5 | C2×#834 | semidirect |
| 211. C3 | C2×#4011 | semidirect |
| 217. C2 | #91240 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×C22⋊D5 | 2 |
| C2×#6763 | 2 |
| #91240 | 2 |
| C2×#4011 | 3 |
| C2×#834 | 5 |