Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
340 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 104 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×C3×C4×AGL(1,𝔽5) | C2 | semidirect |
| 3. C2×C3×#700 | C2 | semidirect |
| 4. C3×#4008 | C2 | direct (N × H) |
| 5. C2×#4008 | C3 | direct (N × H) |
| 7. C2×C3×C5×D4 | C4 | semidirect |
| 12. C3×#711 | C4 | semidirect |
| 15. C2×C3×Dic10 | C4 | semidirect |
| 18. C3×C4×AGL(1,𝔽5) | C22 | semidirect |
| 20. C3×#700 | C22 | semidirect |
| 23. C2×C4×AGL(1,𝔽5) | C2×C3 | semidirect |
| 24. C2×#700 | C2×C3 | semidirect |
| 25. #4008 | C2×C3 | direct (N × H) |
| 31. C3×C5×D4 | C2×C4 | semidirect |
| 44. C3×Dic10 | C2×C4 | semidirect |
| 51. C2×C5×D4 | C3×C4 | semidirect |
| 56. #711 | C3×C4 | semidirect |
| 59. C2×Dic10 | C3×C4 | semidirect |
| 62. C4×AGL(1,𝔽5) | C22×C3 | semidirect |
| 64. #700 | C22×C3 | semidirect |
| 84. C2×C3×D4 | AGL(1,𝔽5) | semidirect |
| 98. C5×D4 | C2×C3×C4 | semidirect |
| 111. Dic10 | C2×C3×C4 | semidirect |
| 118. C2×C3×C5 | #104 | semidirect |
| 129. C3×D4 | C2×AGL(1,𝔽5) | semidirect |
| 160. C2×D4 | C3×AGL(1,𝔽5) | semidirect |
| 169. C3×C5 | C2×#104 | semidirect |
| 183. C2×C5 | C3×#104 | semidirect |
| 194. D4 | C2×C3×AGL(1,𝔽5) | semidirect |
| 210. C2×C3 | #4008 | direct (N × H) |
| 212. C5 | C2×C3×#104 | semidirect |
| 225. C3 | C2×#4008 | direct (N × H) |
| 229. C2 | C3×#4008 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#711 | 2 |
| C2×C3×C4×AGL(1,𝔽5) | 2 |
| C2×C3×#700 | 2 |
| C3×#4008 | 2 |
| C2×#4008 | 3 |
| C2×C3×#104 | 5 |