Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
1848 conjugacy classes of subgroups; only the 341 normal subgroups are shown.
This group has 1848 conjugacy classes of subgroups — too many to draw. Only its 341 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×D4×ΓL(1,𝔽16) | C2 | semidirect |
| 3. #11752439 | C2 | semidirect |
| 4. #11752347 | C2 | semidirect |
| 5. C42×ΓL(1,𝔽16) | C2 | semidirect |
| 14. C3×C5×#127 | C4 | semidirect |
| 15. C3×#4086 | C4 | semidirect |
| 16. C3×#4020 | C4 | semidirect |
| 29. C2×C3×C5×D4 | C2×C4 | semidirect |
| 30. C2×C3×C22⋊D5 | C2×C4 | semidirect |
| 33. C2×C3×D20 | C2×C4 | semidirect |
| 38. C4×ΓL(1,𝔽16) | D4 | semidirect |
| 39. C3×C42×C5 | C2×C4 | semidirect |
| 40. C3×C4×Dic5 | C2×C4 | semidirect |
| 53. C5×#127 | Dic3 | semidirect |
| 54. #4086 | Dic3 | semidirect |
| 55. #4020 | Dic3 | semidirect |
| 79. C3×#127 | AGL(1,𝔽5) | semidirect |
| 91. C2×C5×D4 | C2×Dic3 | semidirect |
| 92. C2×C22⋊D5 | C2×Dic3 | semidirect |
| 95. C2×D20 | C2×Dic3 | semidirect |
| 101. C42×C5 | C2×Dic3 | semidirect |
| 102. C4×Dic5 | C2×Dic3 | semidirect |
| 117. ΓL(1,𝔽16) | #127 | direct (N × H) |
| 118. C3×C4×C5 | C4×D4 | semidirect |
| 119. C3×Dic5 | C4×D4 | semidirect |
| 125. C2×C3×D4 | C2×AGL(1,𝔽5) | semidirect |
| 132. C3×C42 | C2×AGL(1,𝔽5) | semidirect |
| 158. #127 | ΓL(1,𝔽16) | direct (N × H) |
| 197. C4×C5 | D4×Dic3 | semidirect |
| 198. Dic5 | D4×Dic3 | semidirect |
| 204. C2×D4 | C2×ΓL(1,𝔽16) | semidirect |
| 215. C42 | C2×ΓL(1,𝔽16) | semidirect |
| 216. C3×C5 | C4×#127 | semidirect |
| 225. C3×C4 | D4×AGL(1,𝔽5) | semidirect |
| 256. C5 | Dic3×#127 | semidirect |
| 268. C4 | D4×ΓL(1,𝔽16) | semidirect |
| 269. C3 | AGL(1,𝔽5)×#127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×ΓL(1,𝔽16) | 2 |
| C3×D5×#127 | 2 |
| #11752439 | 2 |
| #11752347 | 2 |
| C42×ΓL(1,𝔽16) | 2 |
| AGL(1,𝔽5)×#127 | 3 |
| Dic3×#127 | 5 |