Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
668 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 668 conjugacy classes of subgroups — too many to draw. Only its 171 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D15 |
| commutator, socle, cosocle | C22×C3×C5 | C24 |
| Fitting | C2×C3×C5×#41 | C2 |
| hypercenter | C2×#41 | D15 |
| hypocenter | C3×C5 | #535 |
| LCS | G ▷ C22×C3×C5 ▷ C3×C5 | |
| UCS | C1 ◁ C22 ◁ C2×#41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C3×C5×#41 | C2 | semidirect |
| 2. C22×D60 | C2 | semidirect |
| 3. #91836 | C2 | semidirect |
| 4. #91829 | C2 | semidirect |
| 5. #91826 | C2 | semidirect |
| 6. #91819 | C2 | semidirect |
| 7. #91815 | C2 | semidirect |
| 11. C2×C3×C5×Q8 | C22 | semidirect |
| 13. C2×C3×C5×D4 | C22 | semidirect |
| 15. C22×C3×C4×C5 | C22 | semidirect |
| 16. C2×#1220 | C22 | semidirect |
| 21. #6714 | C22 | semidirect |
| 22. C4⋊Dic15 | C22 | semidirect |
| 23. C4×Dic15 | C22 | semidirect |
| 25. C2×C5×#41 | D3 | semidirect |
| 41. C2×C3×C4×C5 | D4 | semidirect |
| 49. C2×C3×#41 | D5 | semidirect |
| 58. C2×C5×Q8 | C2×D3 | semidirect |
| 60. C2×C5×D4 | C2×D3 | semidirect |
| 62. C22×C4×C5 | C2×D3 | semidirect |
| 86. C2×C3×Q8 | C2×D5 | semidirect |
| 88. C2×C3×D4 | C2×D5 | semidirect |
| 90. C22×C3×C4 | C2×D5 | semidirect |
| 108. C2×C4×C5 | #67 | semidirect |
| 116. C2×#41 | D15 | semidirect |
| 137. C2×C3×C4 | C22⋊D5 | semidirect |
| 159. C2×Q8 | C2×D15 | semidirect |
| 165. C2×D4 | C2×D15 | semidirect |
| 167. C22×C4 | C2×D15 | semidirect |
| 172. C3×C5 | #535 | semidirect |
| 203. C2×C4 | #1220 | semidirect |
| 212. C5 | #5830 | semidirect |
| 225. C3 | #66164 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C5×#41 | 2 |
| C22×D60 | 2 |
| #91836 | 2 |
| #91829 | 2 |
| #91826 | 2 |
| #91819 | 2 |
| #91815 | 2 |
| #66164 | 3 |
| #5830 | 5 |