Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
348 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 100 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. C3×D8×AGL(1,𝔽5) | C2 | semidirect |
| 3. C3×#64904 | C2 | semidirect |
| 4. C3×#64849 | C2 | semidirect |
| 5. C3×C16×AGL(1,𝔽5) | C2 | semidirect |
| 6. AGL(1,𝔽5)×D16 | C3 | direct (N × H) |
| 13. C3×C5×D16 | C4 | semidirect |
| 14. C3×#3958 | C4 | semidirect |
| 15. C3×D80 | C4 | semidirect |
| 18. D8×AGL(1,𝔽5) | C2×C3 | semidirect |
| 20. #64904 | C2×C3 | semidirect |
| 21. #64849 | C2×C3 | semidirect |
| 22. C16×AGL(1,𝔽5) | C2×C3 | semidirect |
| 29. C3×C5×D8 | C2×C4 | semidirect |
| 31. C3×D40 | C2×C4 | semidirect |
| 34. C3×C5×C16 | C2×C4 | semidirect |
| 35. C3×#672 | C2×C4 | semidirect |
| 47. C5×D16 | C3×C4 | semidirect |
| 48. #3958 | C3×C4 | semidirect |
| 49. D80 | C3×C4 | semidirect |
| 68. C3×D16 | AGL(1,𝔽5) | direct (N × H) |
| 80. C5×D8 | C2×C3×C4 | semidirect |
| 82. D40 | C2×C3×C4 | semidirect |
| 85. C5×C16 | C2×C3×C4 | semidirect |
| 86. #672 | C2×C3×C4 | semidirect |
| 99. C3×AGL(1,𝔽5) | D16 | direct (N × H) |
| 106. C3×D8 | C2×AGL(1,𝔽5) | semidirect |
| 114. C3×C16 | C2×AGL(1,𝔽5) | semidirect |
| 131. D16 | C3×AGL(1,𝔽5) | direct (N × H) |
| 161. AGL(1,𝔽5) | C3×D16 | direct (N × H) |
| 168. D8 | C2×C3×AGL(1,𝔽5) | semidirect |
| 176. C16 | C2×C3×AGL(1,𝔽5) | semidirect |
| 177. C3×C5 | C4×D16 | semidirect |
| 210. C5 | C3×C4×D16 | semidirect |
| 221. C3 | AGL(1,𝔽5)×D16 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×D8×AGL(1,𝔽5) | 2 |
| C3×D5×D16 | 2 |
| C3×#64904 | 2 |
| C3×#64849 | 2 |
| C3×C16×AGL(1,𝔽5) | 2 |
| AGL(1,𝔽5)×D16 | 3 |
| C3×C4×D16 | 5 |