Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
348 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 72 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. #11751664 | C2 | semidirect |
| 3. C16×ΓL(1,𝔽16) | C2 | semidirect |
| 4. C3×#64849 | C2 | semidirect |
| 5. #11746456 | C2 | semidirect |
| 13. D240 | C4 | semidirect |
| 14. C5×D48 | C4 | semidirect |
| 16. #90939 | C4 | semidirect |
| 21. #64849 | D3 | semidirect |
| 29. D120 | C2×C4 | semidirect |
| 30. C5×D24 | C2×C4 | semidirect |
| 34. C3×C5×C16 | C2×C4 | semidirect |
| 35. C3×#672 | C2×C4 | semidirect |
| 73. D48 | AGL(1,𝔽5) | semidirect |
| 85. C5×C16 | C4×D3 | semidirect |
| 86. #672 | C4×D3 | semidirect |
| 98. ΓL(1,𝔽16) | D16 | semidirect |
| 111. D24 | C2×AGL(1,𝔽5) | semidirect |
| 113. C3×C16 | C2×AGL(1,𝔽5) | semidirect |
| 176. C16 | D3×AGL(1,𝔽5) | semidirect |
| 177. C3×C5 | C4×D16 | semidirect |
| 210. C5 | #69317 | semidirect |
| 221. C3 | AGL(1,𝔽5)×D16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11751664 | 2 |
| D5×D48 | 2 |
| C16×ΓL(1,𝔽16) | 2 |
| C3×#64849 | 2 |
| #11746456 | 2 |
| AGL(1,𝔽5)×D16 | 3 |
| #69317 | 5 |