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. C5×#5189 | C2 | semidirect |
| 4. C5×#5179 | C2 | semidirect |
| 5. C5×#4566 | C2 | semidirect |
| 6. C5×#4518 | C2 | semidirect |
| 7. C5×#4514 | C2 | semidirect |
| 11. C2×C3×C5×Q16 | C22 | semidirect |
| 22. C3×C5×M32 | C22 | semidirect |
| 26. C5×#817 | C22 | semidirect |
| 27. C5×#812 | C22 | semidirect |
| 28. #71522 | C5 | direct (N × H) |
| 31. C5×#510 | D3 | semidirect |
| 70. C3×#510 | C2×C5 | semidirect |
| 71. #5189 | C2×C5 | semidirect |
| 72. #5179 | C2×C5 | semidirect |
| 73. #4566 | C2×C5 | semidirect |
| 74. #4518 | C2×C5 | semidirect |
| 75. #4514 | C2×C5 | semidirect |
| 84. C2×C5×Q16 | C2×D3 | semidirect |
| 92. C5×M32 | C2×D3 | semidirect |
| 126. C2×C3×Q16 | C22×C5 | semidirect |
| 137. C3×M32 | C22×C5 | semidirect |
| 141. #817 | C22×C5 | semidirect |
| 142. #812 | C22×C5 | semidirect |
| 178. #510 | C5×D3 | semidirect |
| 265. C2×Q16 | C2×C5×D3 | semidirect |
| 273. M32 | C2×C5×D3 | semidirect |
| 355. C3×C5 | #2191 | semidirect |
| 407. C5 | #71522 | 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 |
| C3×C5×#510 | 2 |
| C5×#5189 | 2 |
| C5×#5179 | 2 |
| C5×#4566 | 2 |
| C5×#4518 | 2 |
| C5×#4514 | 2 |
| C5×#2191 | 3 |
| #71522 | 5 |