Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
308 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 75 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. #11752392 | C2 | semidirect |
| 2. #11752390 | C2 | semidirect |
| 4. #11746777 | C2 | semidirect |
| 5. #11746774 | C2 | semidirect |
| 6. #11746718 | C2 | semidirect |
| 7. #11746717 | C2 | semidirect |
| 19. C3×C5×D16 | C4 | semidirect |
| 20. C3×#3959 | C4 | semidirect |
| 21. C3×#3958 | C4 | semidirect |
| 22. C3×#3932 | C4 | semidirect |
| 43. C3×C5×D8 | C2×C4 | semidirect |
| 46. C3×Dic20 | C2×C4 | semidirect |
| 50. C3×C5×C16 | C2×C4 | semidirect |
| 51. C3×#672 | C2×C4 | semidirect |
| 69. C5×D16 | Dic3 | semidirect |
| 70. #3959 | Dic3 | semidirect |
| 71. #3958 | Dic3 | semidirect |
| 72. #3932 | Dic3 | semidirect |
| 98. C3×D16 | AGL(1,𝔽5) | semidirect |
| 117. C5×D8 | C2×Dic3 | semidirect |
| 120. Dic20 | C2×Dic3 | semidirect |
| 124. C5×C16 | C2×Dic3 | semidirect |
| 125. #672 | C2×Dic3 | semidirect |
| 152. C3×D8 | C2×AGL(1,𝔽5) | semidirect |
| 162. C3×C16 | C2×AGL(1,𝔽5) | semidirect |
| 187. D16 | ΓL(1,𝔽16) | semidirect |
| 235. D8 | C2×ΓL(1,𝔽16) | semidirect |
| 246. C16 | C2×ΓL(1,𝔽16) | semidirect |
| 247. C3×C5 | AGL(1,ℤ/16) | semidirect |
| 285. C5 | #71515 | semidirect |
| 297. C3 | #10604124 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11752392 | 2 |
| #11752390 | 2 |
| C3×#65200 | 2 |
| #11746777 | 2 |
| #11746774 | 2 |
| #11746718 | 2 |
| #11746717 | 2 |
| #10604124 | 3 |
| #71515 | 5 |