Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
456 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 90 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×#5055 | C2 | semidirect |
| 3. C5×#4715 | C2 | semidirect |
| 4. C5×#4714 | C2 | semidirect |
| 5. C3×C5×#329 | C2 | semidirect |
| 6. C5×#4464 | C2 | semidirect |
| 7. C5×#4464 | C2 | semidirect |
| 20. C5×#869 | C22 | semidirect |
| 21. C3×C5×#97 | C22 | semidirect |
| 22. C3×C5×#97 | C22 | semidirect |
| 27. C5×#803 | C22 | semidirect |
| 28. #68352 | C5 | direct (N × H) |
| 35. C5×#329 | D3 | semidirect |
| 66. #5055 | C2×C5 | semidirect |
| 67. #4715 | C2×C5 | semidirect |
| 68. #4714 | C2×C5 | semidirect |
| 69. C3×#329 | C2×C5 | semidirect |
| 70. #4464 | C2×C5 | semidirect |
| 71. #4464 | C2×C5 | semidirect |
| 89. C5×#97 | C2×D3 | semidirect |
| 90. C5×#97 | C2×D3 | semidirect |
| 130. #869 | C22×C5 | semidirect |
| 131. C3×#97 | C22×C5 | semidirect |
| 132. C3×#97 | C22×C5 | semidirect |
| 137. #803 | C22×C5 | semidirect |
| 173. #329 | C5×D3 | semidirect |
| 265. #97 | C2×C5×D3 | semidirect |
| 266. #97 | C2×C5×D3 | semidirect |
| 347. C3×C5 | #1659 | semidirect |
| 405. C5 | #68352 | direct (N × H) |
| 424. C3 | C5×#1659 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#5683 | 2 |
| C5×#5055 | 2 |
| C5×#4715 | 2 |
| C5×#4714 | 2 |
| C3×C5×#329 | 2 |
| C5×#4464 | 2 |
| C5×#1659 | 3 |
| #68352 | 5 |