Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
620 conjugacy classes of subgroups; only the 208 normal subgroups are shown.
This group has 620 conjugacy classes of subgroups — too many to draw. Only its 208 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×C4×C5×Dic3 | C2 | semidirect |
| 3. C3×#4072 | C2 | semidirect |
| 4. #91556 | C2 | semidirect |
| 5. #91428 | C2 | semidirect |
| 6. C4×#1200 | C2 | semidirect |
| 7. #91386 | C2 | semidirect |
| 8. #91340 | C2 | semidirect |
| 12. #6817 | C4 | semidirect |
| 31. #4072 | D3 | semidirect |
| 38. C2×C3×C4×C5 | C2×C4 | semidirect |
| 41. #1220 | C2×C4 | semidirect |
| 43. D60 | C2×C4 | semidirect |
| 44. C4×D15 | C2×C4 | semidirect |
| 45. Dic30 | C2×C4 | semidirect |
| 53. C2×C4×Dic3 | D5 | semidirect |
| 87. C5×Dic3 | #41 | semidirect |
| 110. C2×C4×C5 | C4×D3 | semidirect |
| 135. C2×C3×C4 | C4×D5 | semidirect |
| 175. C3×C5 | C4×#41 | semidirect |
| 186. Dic3 | #709 | semidirect |
| 203. C2×C4 | #1200 | semidirect |
| 210. C5 | #5522 | semidirect |
| 222. C3 | C4×#709 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#6817 | 2 |
| C2×C4×C5×Dic3 | 2 |
| C3×#4072 | 2 |
| #91556 | 2 |
| #91428 | 2 |
| C4×#1200 | 2 |
| #91386 | 2 |
| #91340 | 2 |
| C4×#709 | 3 |
| #5522 | 5 |