Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
432 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 94 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. C3×C5×#510 | C2 | semidirect |
| 3. C3×#65481 | C2 | semidirect |
| 4. C2×C3×#3960 | C2 | semidirect |
| 5. C3×#64787 | C2 | semidirect |
| 6. C3×#64736 | C2 | semidirect |
| 7. C3×#64735 | C2 | semidirect |
| 8. #10602316 | C3 | direct (N × H) |
| 11. C2×C3×C5×Q16 | C22 | semidirect |
| 21. C3×C5×M32 | C22 | semidirect |
| 24. C3×#3951 | C22 | semidirect |
| 25. C2×C3×#672 | C22 | semidirect |
| 28. C5×#510 | C2×C3 | semidirect |
| 29. #65481 | C2×C3 | semidirect |
| 30. C2×#3960 | C2×C3 | semidirect |
| 31. #64787 | C2×C3 | semidirect |
| 32. #64736 | C2×C3 | semidirect |
| 33. #64735 | C2×C3 | semidirect |
| 62. C3×#510 | D5 | semidirect |
| 70. C2×C5×Q16 | C22×C3 | semidirect |
| 80. C5×M32 | C22×C3 | semidirect |
| 83. #3951 | C22×C3 | semidirect |
| 84. C2×#672 | C22×C3 | semidirect |
| 115. C2×C3×Q16 | C2×D5 | semidirect |
| 122. C3×M32 | C2×D5 | semidirect |
| 154. #510 | C3×D5 | semidirect |
| 227. C2×Q16 | C2×C3×D5 | semidirect |
| 234. M32 | C2×C3×D5 | semidirect |
| 304. C3×C5 | #2194 | semidirect |
| 349. C5 | C3×#2194 | semidirect |
| 361. C3 | #10602316 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#66103 | 2 |
| C3×C5×#510 | 2 |
| C3×#65481 | 2 |
| C2×C3×#3960 | 2 |
| C3×#64787 | 2 |
| C3×#64736 | 2 |
| C3×#64735 | 2 |
| #10602316 | 3 |
| C3×#2194 | 5 |