Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
240 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 240 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 |
|---|---|---|
| 1. C5×Q8×Dic3 | C2 | semidirect |
| 4. C3×C5×#103 | C2 | semidirect |
| 6. C5×#815 | C2 | semidirect |
| 7. C5×#807 | C2 | semidirect |
| 14. C5×#215 | C4 | semidirect |
| 21. #4817 | C5 | direct (N × H) |
| 26. C5×#103 | D3 | semidirect |
| 31. C3×C5×Q8 | C2×C4 | semidirect |
| 42. C5×C3⋊C8 | C2×C4 | semidirect |
| 43. Q8×Dic3 | C2×C5 | semidirect |
| 46. C3×#103 | C2×C5 | semidirect |
| 48. #815 | C2×C5 | semidirect |
| 49. #807 | C2×C5 | semidirect |
| 79. #215 | C4×C5 | semidirect |
| 88. C5×Q8 | C4×D3 | semidirect |
| 104. #103 | C5×D3 | semidirect |
| 113. C3×Q8 | C2×C4×C5 | semidirect |
| 124. C3⋊C8 | C2×C4×C5 | semidirect |
| 148. C3×C5 | #440 | semidirect |
| 166. Q8 | C4×C5×D3 | semidirect |
| 182. C5 | #4817 | direct (N × H) |
| 194. C3 | C5×#440 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×Q8×Dic3 | 2 |
| C2×C5×#215 | 2 |
| C5×#893 | 2 |
| C3×C5×#103 | 2 |
| C5×#821 | 2 |
| C5×#815 | 2 |
| C5×#807 | 2 |
| C5×#440 | 3 |
| #4817 | 5 |