Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
324 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 83 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. Q16×ΓL(1,𝔽16) | C2 | semidirect |
| 4. #11746779 | C2 | semidirect |
| 6. #11746721 | C2 | semidirect |
| 7. C16×ΓL(1,𝔽16) | C2 | semidirect |
| 19. C3×C5×SD32 | C4 | semidirect |
| 20. C3×#3960 | C4 | semidirect |
| 21. C3×#3959 | C4 | semidirect |
| 22. C3×#3932 | C4 | semidirect |
| 42. C3×C5×Q16 | C2×C4 | semidirect |
| 46. C3×Dic20 | 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. #3959 | Dic3 | semidirect |
| 72. #3932 | Dic3 | semidirect |
| 99. C3×SD32 | AGL(1,𝔽5) | semidirect |
| 117. C5×Q16 | C2×Dic3 | semidirect |
| 121. Dic20 | C2×Dic3 | semidirect |
| 125. C5×C16 | C2×Dic3 | semidirect |
| 126. #672 | C2×Dic3 | semidirect |
| 142. ΓL(1,𝔽16) | SD32 | direct (N × H) |
| 152. C3×Q16 | C2×AGL(1,𝔽5) | semidirect |
| 165. C3×C16 | C2×AGL(1,𝔽5) | semidirect |
| 191. SD32 | ΓL(1,𝔽16) | direct (N × H) |
| 239. Q16 | C2×ΓL(1,𝔽16) | semidirect |
| 253. C16 | C2×ΓL(1,𝔽16) | semidirect |
| 254. C3×C5 | C4×SD32 | semidirect |
| 295. C5 | Dic3×SD32 | semidirect |
| 309. C3 | AGL(1,𝔽5)×SD32 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q16×ΓL(1,𝔽16) | 2 |
| D8×ΓL(1,𝔽16) | 2 |
| C3×D5×SD32 | 2 |
| #11746779 | 2 |
| #11746775 | 2 |
| #11746721 | 2 |
| C16×ΓL(1,𝔽16) | 2 |
| AGL(1,𝔽5)×SD32 | 3 |
| Dic3×SD32 | 5 |