Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
312 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 103 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. C3×C5×#367 | C2 | semidirect |
| 5. #11746325 | C2 | semidirect |
| 6. #11746311 | C2 | semidirect |
| 7. #11746310 | C2 | semidirect |
| 20. #91082 | C4 | semidirect |
| 25. C5×#367 | D3 | semidirect |
| 42. C3×C5×C16 | C2×C4 | semidirect |
| 43. C3⋊#672 | C2×C4 | semidirect |
| 47. C3×#367 | D5 | semidirect |
| 102. C5×C16 | C4×D3 | semidirect |
| 108. #367 | D15 | semidirect |
| 135. C3×C16 | C4×D5 | semidirect |
| 204. C16 | C4×D15 | semidirect |
| 205. C3×C5 | #2159 | semidirect |
| 238. C5 | #69346 | semidirect |
| 250. C3 | #10600139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#91082 | 2 |
| #11750981 | 2 |
| D15×#107 | 2 |
| C3×C5×#367 | 2 |
| #11746325 | 2 |
| #11746311 | 2 |
| #11746310 | 2 |
| #10600139 | 3 |
| #69346 | 5 |