Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
660 conjugacy classes of subgroups; only the 194 normal subgroups are shown.
This group has 660 conjugacy classes of subgroups — too many to draw. Only its 194 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. C2×Dic3⋊AGL(1,𝔽5) | C2 | semidirect |
| 5. #91923 | C2 | direct (N × H) |
| 6. C2×Dic3×AGL(1,𝔽5) | C2 | semidirect |
| 11. C22×Dic15 | C4 | semidirect |
| 12. C22×C5×Dic3 | C4 | semidirect |
| 13. C2×D5×Dic3 | C4 | semidirect |
| 14. C2×D5×Dic3 | C4 | semidirect |
| 15. C2×D5×Dic3 | C4 | semidirect |
| 21. Dic3⋊AGL(1,𝔽5) | C22 | semidirect |
| 22. Dic3×AGL(1,𝔽5) | C22 | semidirect |
| 42. C2×Dic15 | C2×C4 | semidirect |
| 45. C2×C5×Dic3 | C2×C4 | semidirect |
| 48. D5×Dic3 | C2×C4 | semidirect |
| 49. D5×Dic3 | C2×C4 | semidirect |
| 100. C22×Dic3 | AGL(1,𝔽5) | semidirect |
| 134. C2×C3×C5 | #117 | semidirect |
| 137. C3×D5 | #117 | semidirect |
| 160. C2×Dic3 | C2×AGL(1,𝔽5) | semidirect |
| 192. C3×C5 | C2×#117 | semidirect |
| 210. C2×C5 | #877 | semidirect |
| 213. D5 | #877 | semidirect |
| 241. C2×C3 | #4130 | semidirect |
| 243. C5 | C2×#877 | semidirect |
| 260. C3 | C2×#4130 | semidirect |
| 265. C2 | #91923 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D5×Dic3 | 2 |
| C2×#6763 | 2 |
| C2×C3×C22⋊AGL(1,𝔽5) | 2 |
| C2×Dic3⋊AGL(1,𝔽5) | 2 |
| #91923 | 2 |
| C2×Dic3×AGL(1,𝔽5) | 2 |
| C2×#4130 | 3 |
| C2×#877 | 5 |