Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
300 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 300 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 |
|---|---|---|
| 19. #91113 | C4 | semidirect |
| 20. C5×#829 | C4 | semidirect |
| 21. #90947 | C4 | semidirect |
| 22. #90946 | C4 | semidirect |
| 101. #829 | AGL(1,𝔽5) | semidirect |
| 136. ΓL(1,𝔽16) | Q32 | semidirect |
| 245. C3×C5 | C4×Q32 | semidirect |
| 279. C5 | #69207 | semidirect |
| 291. C3 | AGL(1,𝔽5)×Q32 | 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 |
| #11751669 | 2 |
| D5×#829 | 2 |
| C3×#64908 | 2 |
| #11746476 | 2 |
| #11746459 | 2 |
| ΓL(1,𝔽16)⋊C16 | 2 |
| AGL(1,𝔽5)×Q32 | 3 |
| #69207 | 5 |