Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
240 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 94 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×#499 | C2 | semidirect |
| 4. C3×#64707 | C2 | semidirect |
| 5. C3×#64683 | C2 | semidirect |
| 6. #10602151 | C3 | direct (N × H) |
| 17. C5×#499 | C2×C3 | semidirect |
| 20. #64707 | C2×C3 | semidirect |
| 21. #64683 | C2×C3 | semidirect |
| 35. C3×#499 | D5 | semidirect |
| 84. #499 | C3×D5 | semidirect |
| 165. C3×C5 | #2231 | semidirect |
| 191. C5 | C3×#2231 | semidirect |
| 199. C3 | #10602151 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#499 | 2 |
| C3×#64989 | 2 |
| C3×#64708 | 2 |
| C3×#64707 | 2 |
| C3×#64683 | 2 |
| #10602151 | 3 |
| C3×#2231 | 5 |