Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
532 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 86 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×D3×D40 | C2 | semidirect |
| 2. C2×D240 | C2 | semidirect |
| 3. #11747917 | C2 | semidirect |
| 4. C2×#90938 | C2 | semidirect |
| 5. C5×(C2×D3)⋊C16 | C2 | semidirect |
| 6. C3×#64729 | C2 | semidirect |
| 7. #11745895 | C2 | semidirect |
| 11. C2×D120 | C22 | semidirect |
| 18. C2×C3×C5×C16 | C22 | semidirect |
| 20. C2×C5×C3⋊C16 | C22 | semidirect |
| 21. C3×#3950 | C22 | semidirect |
| 31. #64729 | D3 | semidirect |
| 45. D120 | D4 | semidirect |
| 51. C3×D40 | D4 | semidirect |
| 61. (C2×D3)⋊C16 | D5 | semidirect |
| 73. C2×C5×C16 | C2×D3 | semidirect |
| 75. #3950 | C2×D3 | semidirect |
| 111. C2×C3×C16 | C2×D5 | semidirect |
| 114. C2×C3⋊C16 | C2×D5 | semidirect |
| 138. D40 | D12 | semidirect |
| 157. C2×C5×D3 | D16 | semidirect |
| 225. C2×C16 | D3×D5 | semidirect |
| 300. C3×C5 | #2184 | semidirect |
| 314. C2×D3 | D80 | semidirect |
| 356. C5 | #69191 | semidirect |
| 375. C3 | #10599901 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D3×D40 | 2 |
| C2×D240 | 2 |
| #11747917 | 2 |
| C2×#90938 | 2 |
| C5×(C2×D3)⋊C16 | 2 |
| C3×#64729 | 2 |
| #11745895 | 2 |
| #10599901 | 3 |
| #69191 | 5 |