Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
720 conjugacy classes of subgroups; only the 207 normal subgroups are shown.
This group has 720 conjugacy classes of subgroups — too many to draw. Only its 207 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. C3×C5×#578 | C2 | semidirect |
| 2. #11756511 | C2 | semidirect |
| 3. #11751295 | C2 | semidirect |
| 4. #11751294 | C2 | semidirect |
| 5. #11751280 | C2 | semidirect |
| 6. C2×#91112 | C2 | semidirect |
| 7. #11751241 | C2 | semidirect |
| 12. C3×C5×#135 | C22 | semidirect |
| 13. C2×C3×C5×Q16 | C22 | semidirect |
| 18. #91113 | C22 | semidirect |
| 19. #91112 | C22 | semidirect |
| 20. #91112 | C22 | semidirect |
| 21. #91111 | C22 | semidirect |
| 22. #91110 | C22 | semidirect |
| 23. #91096 | C22 | semidirect |
| 24. C2×C3⋊#672 | C22 | semidirect |
| 26. C5×#578 | D3 | semidirect |
| 54. C3×#578 | D5 | semidirect |
| 64. C5×#135 | C2×D3 | semidirect |
| 65. C2×C5×Q16 | C2×D3 | semidirect |
| 98. C3×#135 | C2×D5 | semidirect |
| 99. C2×C3×Q16 | C2×D5 | semidirect |
| 132. #578 | D15 | semidirect |
| 190. #135 | C2×D15 | semidirect |
| 191. C2×Q16 | C2×D15 | semidirect |
| 251. C3×C5 | #3416 | semidirect |
| 285. C5 | #84016 | semidirect |
| 294. C3 | #10615747 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#578 | 2 |
| #11756511 | 2 |
| #11751295 | 2 |
| #11751294 | 2 |
| #11751280 | 2 |
| C2×#91112 | 2 |
| #11751241 | 2 |
| #10615747 | 3 |
| #84016 | 5 |