Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
316 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 98 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. C2×C3×C5×Q32 | C2 | semidirect |
| 3. C3×Q16×Dic5 | C2 | semidirect |
| 5. C3×#64784 | C2 | semidirect |
| 7. C3×#64721 | C2 | semidirect |
| 8. #10602291 | C3 | direct (N × H) |
| 23. C2×C5×Q32 | C2×C3 | semidirect |
| 25. Q16×Dic5 | C2×C3 | semidirect |
| 27. #64784 | C2×C3 | semidirect |
| 29. #64721 | C2×C3 | semidirect |
| 50. C2×C3×Q32 | D5 | semidirect |
| 120. C2×Q32 | C3×D5 | semidirect |
| 238. C3×C5 | #2211 | semidirect |
| 274. C5 | C3×#2211 | semidirect |
| 286. C3 | #10602291 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C5×Q32 | 2 |
| C3×#65480 | 2 |
| C3×Q16×Dic5 | 2 |
| C2×C3×#3960 | 2 |
| C3×#64784 | 2 |
| C3×#64729 | 2 |
| C3×#64721 | 2 |
| #10602291 | 3 |
| C3×#2211 | 5 |