Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
440 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 95 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 |
|---|---|---|
| 2. C2×#91082 | C2 | semidirect |
| 3. D15×#108 | C2 | semidirect |
| 4. C3×C5×#359 | C2 | semidirect |
| 5. #11746388 | C2 | semidirect |
| 6. #11746331 | C2 | semidirect |
| 7. #11746318 | C2 | semidirect |
| 21. C2×C3×C5×C16 | C22 | semidirect |
| 22. C3×C5×#108 | C22 | semidirect |
| 24. #91103 | C22 | semidirect |
| 25. C2×C3⋊#672 | C22 | semidirect |
| 32. C5×#359 | D3 | semidirect |
| 72. C3×#359 | D5 | semidirect |
| 88. C2×C5×C16 | C2×D3 | semidirect |
| 89. C5×#108 | C2×D3 | semidirect |
| 137. C2×C3×C16 | C2×D5 | semidirect |
| 138. C3×#108 | C2×D5 | semidirect |
| 183. #359 | D15 | semidirect |
| 274. C2×C16 | C2×D15 | semidirect |
| 277. #108 | C2×D15 | semidirect |
| 359. C3×C5 | #2143 | semidirect |
| 414. C5 | #69241 | semidirect |
| 428. C3 | #10600034 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D15×#135 | 2 |
| C2×#91082 | 2 |
| D15×#108 | 2 |
| C3×C5×#359 | 2 |
| #11746388 | 2 |
| #11746331 | 2 |
| #11746318 | 2 |
| #10600034 | 3 |
| #69241 | 5 |