Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
452 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 106 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×C3×D5×Q16 | C2 | semidirect |
| 2. C2×C3×#3960 | C2 | semidirect |
| 3. C2×C3×#3932 | C2 | semidirect |
| 5. C3×C5×#358 | C2 | semidirect |
| 6. C3×#64727 | C2 | semidirect |
| 7. C3×#64712 | C2 | semidirect |
| 8. #10600016 | C3 | direct (N × H) |
| 25. C2×D5×Q16 | C2×C3 | semidirect |
| 26. C2×#3960 | C2×C3 | semidirect |
| 27. C2×#3932 | C2×C3 | semidirect |
| 29. C5×#358 | C2×C3 | semidirect |
| 30. #64727 | C2×C3 | semidirect |
| 31. #64712 | C2×C3 | semidirect |
| 42. C3×C5×Q16 | D4 | semidirect |
| 49. C3×Dic20 | D4 | semidirect |
| 61. C3×#358 | D5 | semidirect |
| 125. C5×Q16 | C3×D4 | semidirect |
| 132. Dic20 | C3×D4 | semidirect |
| 144. #358 | C3×D5 | semidirect |
| 152. C2×C3×D5 | SD32 | semidirect |
| 172. C3×Q16 | D20 | semidirect |
| 251. C2×D5 | C3×SD32 | semidirect |
| 271. Q16 | C3×D20 | semidirect |
| 282. C3×C5 | #2185 | semidirect |
| 327. C5 | C3×#2185 | semidirect |
| 341. C3 | #10600016 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×D5×Q16 | 2 |
| C2×C3×#3960 | 2 |
| C2×C3×#3932 | 2 |
| C3×#65172 | 2 |
| C3×C5×#358 | 2 |
| C3×#64727 | 2 |
| C3×#64712 | 2 |
| #10600016 | 3 |
| C3×#2185 | 5 |