Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
660 conjugacy classes of subgroups; only the 168 normal subgroups are shown.
This group has 660 conjugacy classes of subgroups — too many to draw. Only its 168 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. C22×#1204 | C2 | semidirect |
| 3. C2×C5×#217 | C2 | semidirect |
| 4. C2×C3×C22⋊Dic5 | C2 | semidirect |
| 5. C2×#6667 | C2 | semidirect |
| 6. C2×#6667 | C2 | semidirect |
| 7. C2×Dic3×Dic5 | C2 | semidirect |
| 8. #91526 | C2 | direct (N × H) |
| 20. C2×#1204 | C22 | semidirect |
| 21. C5×#217 | C22 | semidirect |
| 22. C3×C22⋊Dic5 | C22 | semidirect |
| 23. #6667 | C22 | semidirect |
| 24. #6667 | C22 | semidirect |
| 25. Dic3×Dic5 | C22 | semidirect |
| 30. C2×C22⋊Dic5 | D3 | semidirect |
| 59. C2×#217 | D5 | semidirect |
| 76. C22⋊Dic5 | C2×D3 | semidirect |
| 110. #217 | C2×D5 | semidirect |
| 144. C2×C3×C5 | #124 | semidirect |
| 203. C3×C5 | C2×#124 | semidirect |
| 222. C2×C5 | #885 | semidirect |
| 249. C2×C3 | #4031 | semidirect |
| 254. C5 | C2×#885 | semidirect |
| 272. C3 | C2×#4031 | semidirect |
| 275. C2 | #91526 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#1220 | 2 |
| C22×#1204 | 2 |
| C2×C5×#217 | 2 |
| C2×C3×C22⋊Dic5 | 2 |
| C2×#6667 | 2 |
| C2×Dic3×Dic5 | 2 |
| #91526 | 2 |
| C2×#4031 | 3 |
| C2×#885 | 5 |