Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
348 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 102 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×SD32 | C2 | semidirect |
| 2. C3×Q16×Dic5 | C2 | semidirect |
| 3. C2×C3×#3960 | C2 | semidirect |
| 5. C3×#64782 | C2 | semidirect |
| 6. C3×#64729 | C2 | semidirect |
| 7. C3×#64721 | C2 | semidirect |
| 8. #10602268 | C3 | direct (N × H) |
| 23. C2×C5×SD32 | C2×C3 | semidirect |
| 24. Q16×Dic5 | C2×C3 | semidirect |
| 25. C2×#3960 | C2×C3 | semidirect |
| 27. #64782 | C2×C3 | semidirect |
| 28. #64729 | C2×C3 | semidirect |
| 29. #64721 | C2×C3 | semidirect |
| 36. C3×C5×Q16 | D4 | semidirect |
| 51. C2×C3×SD32 | D5 | semidirect |
| 108. C5×Q16 | C3×D4 | semidirect |
| 123. C2×SD32 | C3×D5 | semidirect |
| 141. C3×Dic5 | SD32 | semidirect |
| 148. C3×Q16 | C22⋊D5 | semidirect |
| 228. Dic5 | C3×SD32 | semidirect |
| 235. Q16 | C3×C22⋊D5 | semidirect |
| 249. C3×C5 | #2207 | semidirect |
| 291. C5 | C3×#2207 | semidirect |
| 305. C3 | #10602268 | 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×SD32 | 2 |
| C3×Q16×Dic5 | 2 |
| C2×C3×#3960 | 2 |
| C3×#65440 | 2 |
| C3×#64782 | 2 |
| C3×#64729 | 2 |
| C3×#64721 | 2 |
| #10602268 | 3 |
| C3×#2207 | 5 |