Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
720 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 720 conjugacy classes of subgroups — too many to draw. Only its 114 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 |
|---|---|---|
| 2. C2×#91237 | C2 | semidirect |
| 3. C2×C3×#4008 | C2 | semidirect |
| 4. C4×Dic3×AGL(1,𝔽5) | C2 | semidirect |
| 5. #11751824 | C2 | semidirect |
| 6. C2×#91156 | C2 | semidirect |
| 7. C2×#91155 | C2 | semidirect |
| 16. #91825 | C4 | semidirect |
| 17. C5×#940 | C4 | semidirect |
| 21. #91389 | C4 | semidirect |
| 22. #91370 | C4 | semidirect |
| 33. C2×#4008 | D3 | semidirect |
| 59. C4×ΓL(1,𝔽16) | D4 | semidirect |
| 64. C3×C4×AGL(1,𝔽5) | D4 | semidirect |
| 144. #940 | AGL(1,𝔽5) | semidirect |
| 184. C4×AGL(1,𝔽5) | #67 | semidirect |
| 219. C5×Dic3 | #104 | semidirect |
| 413. C3×C5 | #1962 | semidirect |
| 431. Dic3 | #4008 | semidirect |
| 481. C5 | #70356 | semidirect |
| 500. C3 | #10604611 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11754793 | 2 |
| C2×#91237 | 2 |
| C2×C3×#4008 | 2 |
| C4×Dic3×AGL(1,𝔽5) | 2 |
| #11751824 | 2 |
| C2×#91156 | 2 |
| C2×#91155 | 2 |
| #10604611 | 3 |
| #70356 | 5 |