Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
268 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 82 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×#65182 | C2 | semidirect |
| 3. C3×C5×#365 | C2 | semidirect |
| 4. C3×#64736 | C2 | semidirect |
| 5. C3×#64734 | C2 | semidirect |
| 6. C3×#64715 | C2 | semidirect |
| 7. C3×#64707 | C2 | semidirect |
| 8. #10600106 | C3 | direct (N × H) |
| 21. #65182 | C2×C3 | semidirect |
| 23. C5×#365 | C2×C3 | semidirect |
| 24. #64736 | C2×C3 | semidirect |
| 25. #64734 | C2×C3 | semidirect |
| 26. #64715 | C2×C3 | semidirect |
| 27. #64707 | C2×C3 | semidirect |
| 48. C3×#365 | D5 | semidirect |
| 110. #365 | C3×D5 | semidirect |
| 213. C3×C5 | #2238 | semidirect |
| 247. C5 | C3×#2238 | semidirect |
| 258. C3 | #10600106 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#65182 | 2 |
| C3×#65154 | 2 |
| C3×C5×#365 | 2 |
| C3×#64736 | 2 |
| C3×#64734 | 2 |
| C3×#64715 | 2 |
| C3×#64707 | 2 |
| #10600106 | 3 |
| C3×#2238 | 5 |