Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
324 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 102 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. C2×C5×#798 | C2 | semidirect |
| 3. C2×#90934 | C2 | semidirect |
| 4. #11746322 | C2 | semidirect |
| 5. C3×#64727 | C2 | semidirect |
| 6. (C2×D3)⋊#672 | C2 | semidirect |
| 7. #11745872 | C2 | semidirect |
| 27. #64727 | D3 | semidirect |
| 48. C5×C3⋊C16 | D4 | semidirect |
| 51. C2×#798 | D5 | semidirect |
| 136. Dic15 | M32 | semidirect |
| 157. C3⋊C16 | C22⋊D5 | semidirect |
| 242. C3×C5 | #2169 | semidirect |
| 283. C5 | #69104 | semidirect |
| 297. C3 | #10602223 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#798 | 2 |
| C8×#1201 | 2 |
| C2×#90934 | 2 |
| #11746322 | 2 |
| C3×#64727 | 2 |
| (C2×D3)⋊#672 | 2 |
| #11745872 | 2 |
| #10602223 | 3 |
| #69104 | 5 |