Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
304 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 106 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 |
|---|---|---|
| 4. #11746474 | C2 | semidirect |
| 5. #11746472 | C2 | semidirect |
| 15. #91096 | C4 | semidirect |
| 16. C5×#812 | C4 | semidirect |
| 18. D5×C3⋊C16 | C4 | semidirect |
| 39. C3⋊#672 | C2×C4 | semidirect |
| 40. C5×C3⋊C16 | C2×C4 | semidirect |
| 84. #812 | AGL(1,𝔽5) | semidirect |
| 131. C3⋊C16 | C2×AGL(1,𝔽5) | semidirect |
| 162. C3×D5 | #365 | semidirect |
| 203. C3×C5 | C2×#365 | semidirect |
| 216. D5 | #4487 | semidirect |
| 236. C5 | C2×#4487 | semidirect |
| 246. C3 | D5⋊#365 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D5⋊#819 | 2 |
| C2×C3×#3993 | 2 |
| D5×#812 | 2 |
| #11746474 | 2 |
| #11746472 | 2 |
| D5⋊#365 | 3 |
| C2×#4487 | 5 |