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×#126 | C2 |
| hypercenter | #126 | D15 |
| hypocenter | C3×C5 | #560 |
| LCS | G ▷ C22×C3×C5 ▷ C3×C5 | |
| UCS | C1 ◁ C22 ◁ #126 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×C5×#126 | C2 | semidirect |
| 2. #91784 | C2 | semidirect |
| 3. #91783 | C2 | semidirect |
| 4. #91773 | C2 | semidirect |
| 5. #91771 | C2 | semidirect |
| 6. #91765 | C2 | semidirect |
| 7. #91763 | C2 | semidirect |
| 13. C2×D60 | C22 | semidirect |
| 14. C2×C4×D15 | C22 | semidirect |
| 15. C3×C5×C4⋊C4 | C22 | semidirect |
| 17. C3×C42×C5 | C22 | semidirect |
| 20. #6714 | C22 | semidirect |
| 21. #6712 | C22 | semidirect |
| 23. C5×#126 | D3 | semidirect |
| 43. C3×#126 | D5 | semidirect |
| 56. C5×C4⋊C4 | C2×D3 | semidirect |
| 58. C42×C5 | C2×D3 | semidirect |
| 81. C3×C4⋊C4 | C2×D5 | semidirect |
| 83. C3×C42 | C2×D5 | semidirect |
| 103. #126 | D15 | semidirect |
| 144. C4⋊C4 | C2×D15 | semidirect |
| 149. C42 | C2×D15 | semidirect |
| 150. C3×C5 | #560 | semidirect |
| 185. C5 | #5711 | semidirect |
| 197. C3 | #66045 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#126 | 2 |
| #91784 | 2 |
| #91783 | 2 |
| #91773 | 2 |
| #91771 | 2 |
| #91765 | 2 |
| #91763 | 2 |
| #66045 | 3 |
| #5711 | 5 |