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. C5×#5195 | C2 | semidirect |
| 3. C5×#4909 | C2 | semidirect |
| 4. C5×#4867 | C2 | semidirect |
| 5. C3×C5×#360 | C2 | semidirect |
| 6. C5×#4514 | C2 | semidirect |
| 7. C5×#4488 | C2 | semidirect |
| 16. C2×C5×Dic12 | C22 | semidirect |
| 20. C3×C5×M32 | C22 | semidirect |
| 21. C3×C5×#106 | C22 | semidirect |
| 24. C5×#812 | C22 | semidirect |
| 28. #69253 | C5 | direct (N × H) |
| 34. C5×#360 | D3 | semidirect |
| 70. #5195 | C2×C5 | semidirect |
| 71. #4909 | C2×C5 | semidirect |
| 72. #4867 | C2×C5 | semidirect |
| 73. C3×#360 | C2×C5 | semidirect |
| 74. #4514 | C2×C5 | semidirect |
| 75. #4488 | C2×C5 | semidirect |
| 92. C5×M32 | C2×D3 | semidirect |
| 93. C5×#106 | C2×D3 | semidirect |
| 131. C2×Dic12 | C22×C5 | semidirect |
| 135. C3×M32 | C22×C5 | semidirect |
| 136. C3×#106 | C22×C5 | semidirect |
| 139. #812 | C22×C5 | semidirect |
| 181. #360 | C5×D3 | semidirect |
| 273. M32 | C2×C5×D3 | semidirect |
| 274. #106 | C2×C5×D3 | semidirect |
| 355. C3×C5 | #2191 | semidirect |
| 407. C5 | #69253 | direct (N × H) |
| 421. C3 | C5×#2191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#5768 | 2 |
| C5×#5195 | 2 |
| C5×#4909 | 2 |
| C5×#4867 | 2 |
| C3×C5×#360 | 2 |
| C5×#4514 | 2 |
| C5×#4488 | 2 |
| C5×#2191 | 3 |
| #69253 | 5 |