Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
664 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 664 conjugacy classes of subgroups — too many to draw. Only its 98 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. AGL(1,𝔽5)×#235 | C2 | semidirect |
| 3. #11751817 | C2 | semidirect |
| 4. C2×#91158 | C2 | semidirect |
| 5. #11751720 | C2 | semidirect |
| 6. #11746773 | C2 | semidirect |
| 7. C3×#64900 | C2 | semidirect |
| 20. #91797 | C4 | semidirect |
| 21. C5×#909 | C4 | semidirect |
| 23. #91321 | C4 | semidirect |
| 24. #91305 | C4 | semidirect |
| 41. #64900 | D3 | semidirect |
| 45. C2×D60 | C2×C4 | semidirect |
| 47. C2×C5×Dic6 | C2×C4 | semidirect |
| 78. C3×C5×M16 | C2×C4 | semidirect |
| 83. C3×#681 | C2×C4 | semidirect |
| 175. #909 | AGL(1,𝔽5) | semidirect |
| 228. C5×M16 | C4×D3 | semidirect |
| 233. #681 | C4×D3 | semidirect |
| 285. C2×Dic6 | C2×AGL(1,𝔽5) | semidirect |
| 288. C3×M16 | C2×AGL(1,𝔽5) | semidirect |
| 482. M16 | D3×AGL(1,𝔽5) | semidirect |
| 497. C3×C5 | #1906 | semidirect |
| 574. C5 | #68778 | semidirect |
| 595. C3 | #10604868 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| AGL(1,𝔽5)×#235 | 2 |
| #11754021 | 2 |
| #11751817 | 2 |
| C2×#91158 | 2 |
| #11751720 | 2 |
| #11746773 | 2 |
| C3×#64900 | 2 |
| #10604868 | 3 |
| #68778 | 5 |