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×#5192 | C2 | semidirect |
| 4. C2×C5×#828 | C2 | semidirect |
| 5. C5×#4567 | C2 | semidirect |
| 6. C5×#4516 | C2 | semidirect |
| 7. C5×#4515 | C2 | semidirect |
| 11. C2×C3×C5×Q16 | C22 | semidirect |
| 21. C3×C5×M32 | C22 | semidirect |
| 24. C5×#819 | C22 | semidirect |
| 25. C2×C5×C3⋊C16 | C22 | semidirect |
| 26. #71523 | C5 | direct (N × H) |
| 28. C5×#510 | D3 | semidirect |
| 62. C3×#510 | C2×C5 | semidirect |
| 63. #5192 | C2×C5 | semidirect |
| 64. C2×#828 | C2×C5 | semidirect |
| 65. #4567 | C2×C5 | semidirect |
| 66. #4516 | C2×C5 | semidirect |
| 67. #4515 | C2×C5 | semidirect |
| 74. C2×C5×Q16 | C2×D3 | semidirect |
| 81. C5×M32 | C2×D3 | semidirect |
| 111. C2×C3×Q16 | C22×C5 | semidirect |
| 121. C3×M32 | C22×C5 | semidirect |
| 124. #819 | C22×C5 | semidirect |
| 125. C2×C3⋊C16 | C22×C5 | semidirect |
| 154. #510 | C5×D3 | semidirect |
| 227. C2×Q16 | C2×C5×D3 | semidirect |
| 234. M32 | C2×C5×D3 | semidirect |
| 304. C3×C5 | #2194 | semidirect |
| 349. C5 | #71523 | direct (N × H) |
| 361. C3 | C5×#2194 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#5769 | 2 |
| C3×C5×#510 | 2 |
| C5×#5192 | 2 |
| C2×C5×#828 | 2 |
| C5×#4567 | 2 |
| C5×#4516 | 2 |
| C5×#4515 | 2 |
| C5×#2194 | 3 |
| #71523 | 5 |