Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
532 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 114 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×#544 | C2 | semidirect |
| 4. C5×#4538 | C2 | semidirect |
| 5. C5×#4528 | C2 | semidirect |
| 20. #71902 | C5 | direct (N × H) |
| 21. C5×#544 | D3 | semidirect |
| 48. C3×#544 | C2×C5 | semidirect |
| 51. #4538 | C2×C5 | semidirect |
| 52. #4528 | C2×C5 | semidirect |
| 84. C2×C3×C4×C5 | SD16 | semidirect |
| 127. #544 | C5×D3 | semidirect |
| 194. C2×C4×C5 | #215 | semidirect |
| 233. C2×C3×C4 | C5×SD16 | semidirect |
| 281. C3×C5 | #1599 | semidirect |
| 328. C2×C4 | C5×#215 | semidirect |
| 337. C5 | #71902 | direct (N × H) |
| 356. C3 | C5×#1599 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#544 | 2 |
| C5×#5046 | 2 |
| C5×#4991 | 2 |
| C5×#4538 | 2 |
| C5×#4528 | 2 |
| C5×#1599 | 3 |
| #71902 | 5 |