Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
724 conjugacy classes of subgroups; only the 156 normal subgroups are shown.
This group has 724 conjugacy classes of subgroups — too many to draw. Only its 156 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. C5×#5798 | C2 | semidirect |
| 3. C2×#91117 | C2 | semidirect |
| 4. #11748421 | C2 | semidirect |
| 5. #11745969 | C2 | semidirect |
| 14. C3×#4086 | C4 | semidirect |
| 16. C3×#4082 | C4 | semidirect |
| 37. C2×C3×D20 | C2×C4 | semidirect |
| 39. C2×C3×Dic10 | C2×C4 | semidirect |
| 46. C4×C5×Dic3 | D4 | semidirect |
| 50. C3×C4×Dic5 | C2×C4 | semidirect |
| 52. #5798 | D5 | semidirect |
| 62. #4086 | Dic3 | semidirect |
| 64. #4082 | Dic3 | semidirect |
| 117. C2×D20 | C2×Dic3 | semidirect |
| 119. C2×Dic10 | C2×Dic3 | semidirect |
| 127. C4×Dic5 | C2×Dic3 | semidirect |
| 172. C4×Dic3 | C22⋊D5 | semidirect |
| 281. C3×C5 | #1911 | semidirect |
| 332. C5 | #71853 | semidirect |
| 348. C3 | #10602445 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#5798 | 2 |
| C3×#66139 | 2 |
| C2×#91117 | 2 |
| #11748421 | 2 |
| #11745969 | 2 |
| #10602445 | 3 |
| #71853 | 5 |