Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
520 conjugacy classes of subgroups; only the 182 normal subgroups are shown.
This group has 520 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.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×C5×#120 | C2 | semidirect |
| 2. C5×#953 | C2 | semidirect |
| 3. C5×#937 | C2 | semidirect |
| 4. C5×#936 | C2 | semidirect |
| 5. C5×#885 | C2 | semidirect |
| 7. C24×C3×C5 | C22 | semidirect |
| 8. C23×C5×D3 | C22 | semidirect |
| 11. C2×C5×Dic6 | C22 | semidirect |
| 12. C3×C5×C22⋊C4 | C22 | semidirect |
| 13. C5×#217 | C22 | semidirect |
| 14. C5×#217 | C22 | semidirect |
| 15. C5×(C2×D3)⋊C4 | C22 | semidirect |
| 16. C4×C5×Dic3 | C22 | semidirect |
| 17. #5594 | C5 | direct (N × H) |
| 22. C5×#120 | D3 | semidirect |
| 33. C3×#120 | C2×C5 | semidirect |
| 34. #953 | C2×C5 | semidirect |
| 35. #937 | C2×C5 | semidirect |
| 36. #936 | C2×C5 | semidirect |
| 37. #885 | C2×C5 | semidirect |
| 39. C24×C5 | C2×D3 | semidirect |
| 46. C5×C22⋊C4 | C2×D3 | semidirect |
| 58. C24×C3 | C22×C5 | semidirect |
| 59. C23×D3 | C22×C5 | semidirect |
| 62. C2×Dic6 | C22×C5 | semidirect |
| 63. C3×C22⋊C4 | C22×C5 | semidirect |
| 64. #217 | C22×C5 | semidirect |
| 65. #217 | C22×C5 | semidirect |
| 66. (C2×D3)⋊C4 | C22×C5 | semidirect |
| 67. C4×Dic3 | C22×C5 | semidirect |
| 82. #120 | C5×D3 | semidirect |
| 107. C24 | C2×C5×D3 | semidirect |
| 114. C22⋊C4 | C2×C5×D3 | semidirect |
| 116. C3×C5 | H(3,𝔽4) | semidirect |
| 144. C5 | #5594 | direct (N × H) |
| 154. C3 | C5×H(3,𝔽4) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#120 | 2 |
| C5×#953 | 2 |
| C5×#937 | 2 |
| C5×#936 | 2 |
| C5×#885 | 2 |
| C5×H(3,𝔽4) | 3 |
| #5594 | 5 |