Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
504 conjugacy classes of subgroups; only the 182 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 182 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22×C3 | C23×D5 |
| commutator, cosocle | C22×C5 | C24×C3 |
| Frattini | C22 | C23×C3×D5 |
| Fitting | C3×C5×#126 | C2 |
| socle | C22×C3×C5 | C24 |
| hypercenter | C3×#126 | D5 |
| hypocenter | C5 | C3×#560 |
| LCS | G ▷ C22×C5 ▷ C5 | |
| UCS | C1 ◁ C22×C3 ◁ C3×#126 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×C5×#126 | C2 | semidirect |
| 2. C3×#4041 | C2 | semidirect |
| 3. C3×#4040 | C2 | semidirect |
| 4. C3×#4030 | C2 | semidirect |
| 5. C3×#4028 | C2 | semidirect |
| 6. C3×#4022 | C2 | semidirect |
| 7. C3×#4020 | C2 | semidirect |
| 8. #66045 | C3 | direct (N × H) |
| 13. C2×C3×D20 | C22 | semidirect |
| 14. C2×C3×C4×D5 | C22 | semidirect |
| 15. C3×C5×C4⋊C4 | C22 | semidirect |
| 17. C3×C42×C5 | C22 | semidirect |
| 20. C3×#685 | C22 | semidirect |
| 21. C3×#683 | C22 | semidirect |
| 23. C5×#126 | C2×C3 | semidirect |
| 24. #4041 | C2×C3 | semidirect |
| 25. #4040 | C2×C3 | semidirect |
| 26. #4030 | C2×C3 | semidirect |
| 27. #4028 | C2×C3 | semidirect |
| 28. #4022 | C2×C3 | semidirect |
| 29. #4020 | C2×C3 | semidirect |
| 45. C3×#126 | D5 | semidirect |
| 54. C2×D20 | C22×C3 | semidirect |
| 55. C2×C4×D5 | C22×C3 | semidirect |
| 56. C5×C4⋊C4 | C22×C3 | semidirect |
| 58. C42×C5 | C22×C3 | semidirect |
| 61. #685 | C22×C3 | semidirect |
| 62. #683 | C22×C3 | semidirect |
| 82. C3×C4⋊C4 | C2×D5 | semidirect |
| 87. C3×C42 | C2×D5 | semidirect |
| 103. #126 | C3×D5 | semidirect |
| 144. C4⋊C4 | C2×C3×D5 | semidirect |
| 149. C42 | C2×C3×D5 | semidirect |
| 150. C3×C5 | #560 | semidirect |
| 185. C5 | C3×#560 | semidirect |
| 197. C3 | #66045 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#126 | 2 |
| C3×#4041 | 2 |
| C3×#4040 | 2 |
| C3×#4030 | 2 |
| C3×#4028 | 2 |
| C3×#4022 | 2 |
| C3×#4020 | 2 |
| #66045 | 3 |
| C3×#560 | 5 |