Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
312 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 312 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 |
|---|---|---|
| 4. #11746311 | C2 | semidirect |
| 5. C5×#4489 | C2 | semidirect |
| 6. #11745944 | C2 | semidirect |
| 7. #11745940 | C2 | semidirect |
| 20. #90934 | C4 | semidirect |
| 42. C3⋊#672 | C2×C4 | semidirect |
| 43. C5×C3⋊C16 | C2×C4 | semidirect |
| 50. #4489 | D5 | semidirect |
| 136. C3⋊C16 | C4×D5 | semidirect |
| 205. C3×C5 | #2159 | semidirect |
| 238. C5 | #70596 | semidirect |
| 250. C3 | #10600119 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×D5×#107 | 2 |
| #11747672 | 2 |
| C2×#90934 | 2 |
| #11746311 | 2 |
| C5×#4489 | 2 |
| #11745944 | 2 |
| #11745940 | 2 |
| #10600119 | 3 |
| #70596 | 5 |