Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
504 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 131 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 | C3×C5×#127 | C2 |
| hypercenter | #127 | D15 |
| hypocenter | C3×C5 | #560 |
| LCS | G ▷ C22×C3×C5 ▷ C3×C5 | |
| UCS | C1 ◁ C22 ◁ #127 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×C5×#127 | C2 | semidirect |
| 2. #91828 | C2 | semidirect |
| 3. #91826 | C2 | semidirect |
| 4. #91824 | C2 | semidirect |
| 5. #91765 | C2 | semidirect |
| 9. C2×C3×C5×D4 | C22 | semidirect |
| 11. C22×Dic15 | C22 | semidirect |
| 12. C3×C42×C5 | C22 | semidirect |
| 14. #6719 | C22 | semidirect |
| 16. #6712 | C22 | semidirect |
| 18. C5×#127 | D3 | semidirect |
| 33. C3×#127 | D5 | semidirect |
| 40. C2×C5×D4 | C2×D3 | semidirect |
| 43. C42×C5 | C2×D3 | semidirect |
| 59. C2×C3×D4 | C2×D5 | semidirect |
| 62. C3×C42 | C2×D5 | semidirect |
| 77. #127 | D15 | semidirect |
| 107. C2×D4 | C2×D15 | semidirect |
| 113. C42 | C2×D15 | semidirect |
| 114. C3×C5 | #560 | semidirect |
| 141. C5 | #5720 | semidirect |
| 150. C3 | #66054 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#127 | 2 |
| #91828 | 2 |
| #91826 | 2 |
| #91824 | 2 |
| #91765 | 2 |
| #66054 | 3 |
| #5720 | 5 |