Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
676 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 676 conjugacy classes of subgroups — too many to draw. Only its 200 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×C5×#217 | C2 | semidirect |
| 3. C2×C3×C22⋊Dic5 | C2 | semidirect |
| 4. #91561 | C2 | semidirect |
| 5. #91556 | C2 | semidirect |
| 6. #91552 | C2 | semidirect |
| 7. #91532 | C2 | semidirect |
| 11. C2×#1220 | C4 | semidirect |
| 15. C22×C5×Dic3 | C22 | semidirect |
| 16. C22×C3×Dic5 | C22 | semidirect |
| 17. C2×#1200 | C22 | semidirect |
| 19. C5×#217 | C22 | semidirect |
| 21. C3×C22⋊Dic5 | C22 | semidirect |
| 22. #6669 | C22 | semidirect |
| 23. #6667 | C22 | semidirect |
| 24. Dic3×Dic5 | C22 | semidirect |
| 28. C2×C22⋊Dic5 | D3 | semidirect |
| 34. C23×C3×C5 | C2×C4 | semidirect |
| 39. C22×D15 | C2×C4 | semidirect |
| 41. #1220 | C2×C4 | semidirect |
| 42. #1220 | C2×C4 | semidirect |
| 43. C2×Dic15 | C2×C4 | semidirect |
| 52. C2×#217 | D5 | semidirect |
| 64. C22×Dic5 | C2×D3 | semidirect |
| 69. C22⋊Dic5 | C2×D3 | semidirect |
| 95. C22×Dic3 | C2×D5 | semidirect |
| 100. #217 | C2×D5 | semidirect |
| 105. C23×C5 | C4×D3 | semidirect |
| 135. C23×C3 | C4×D5 | semidirect |
| 181. C3×C5 | #518 | semidirect |
| 206. C23 | #1200 | semidirect |
| 225. C5 | #5486 | semidirect |
| 240. C3 | #65820 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#1220 | 2 |
| C2×C5×#217 | 2 |
| C2×C3×C22⋊Dic5 | 2 |
| #91561 | 2 |
| #91556 | 2 |
| #91552 | 2 |
| #91532 | 2 |
| #65820 | 3 |
| #5486 | 5 |