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. #11752400 | C2 | semidirect |
| 2. #11752390 | C2 | semidirect |
| 4. #11746778 | C2 | semidirect |
| 5. #11746777 | C2 | semidirect |
| 6. #11746718 | C2 | semidirect |
| 7. #11746716 | C2 | semidirect |
| 19. C3×C5×SD32 | C4 | semidirect |
| 20. C3×#3960 | C4 | semidirect |
| 21. C3×#3958 | C4 | semidirect |
| 22. C3×D80 | C4 | semidirect |
| 42. C3×C5×Q16 | C2×C4 | semidirect |
| 47. C3×D40 | C2×C4 | semidirect |
| 50. C3×C5×C16 | C2×C4 | semidirect |
| 51. C3×#672 | C2×C4 | semidirect |
| 69. C5×SD32 | Dic3 | semidirect |
| 70. #3960 | Dic3 | semidirect |
| 71. #3958 | Dic3 | semidirect |
| 72. D80 | Dic3 | semidirect |
| 96. C3×SD32 | AGL(1,𝔽5) | semidirect |
| 116. C5×Q16 | C2×Dic3 | semidirect |
| 121. D40 | C2×Dic3 | semidirect |
| 124. C5×C16 | C2×Dic3 | semidirect |
| 125. #672 | C2×Dic3 | semidirect |
| 147. C3×Q16 | C2×AGL(1,𝔽5) | semidirect |
| 162. C3×C16 | C2×AGL(1,𝔽5) | semidirect |
| 185. SD32 | ΓL(1,𝔽16) | semidirect |
| 230. Q16 | 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 | #10604133 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11752400 | 2 |
| #11752390 | 2 |
| C3×#65203 | 2 |
| #11746778 | 2 |
| #11746777 | 2 |
| #11746718 | 2 |
| #11746716 | 2 |
| #10604133 | 3 |
| #71515 | 5 |