Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
432 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 98 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×#5143 | C2 | semidirect |
| 3. C5×#4909 | C2 | semidirect |
| 4. C2×C5×#800 | C2 | semidirect |
| 5. C3×C5×#350 | C2 | semidirect |
| 6. C5×#4516 | C2 | semidirect |
| 7. C5×#4510 | C2 | semidirect |
| 14. C2×C5×Dic12 | C22 | semidirect |
| 19. C3×C5×M32 | C22 | semidirect |
| 20. C2×C3×C5×C16 | C22 | semidirect |
| 22. C5×#819 | C22 | semidirect |
| 26. #69128 | C5 | direct (N × H) |
| 33. C5×#350 | D3 | semidirect |
| 62. #5143 | C2×C5 | semidirect |
| 63. #4909 | C2×C5 | semidirect |
| 64. C2×#800 | C2×C5 | semidirect |
| 65. C3×#350 | C2×C5 | semidirect |
| 66. #4516 | C2×C5 | semidirect |
| 67. #4510 | C2×C5 | semidirect |
| 81. C5×M32 | C2×D3 | semidirect |
| 82. C2×C5×C16 | C2×D3 | semidirect |
| 114. C2×Dic12 | C22×C5 | semidirect |
| 119. C3×M32 | C22×C5 | semidirect |
| 120. C2×C3×C16 | C22×C5 | semidirect |
| 122. #819 | C22×C5 | semidirect |
| 159. #350 | C5×D3 | semidirect |
| 234. M32 | C2×C5×D3 | semidirect |
| 235. C2×C16 | C2×C5×D3 | semidirect |
| 304. C3×C5 | #2194 | semidirect |
| 349. C5 | #69128 | 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×#5752 | 2 |
| C5×#5143 | 2 |
| C5×#4909 | 2 |
| C2×C5×#800 | 2 |
| C3×C5×#350 | 2 |
| C5×#4516 | 2 |
| C5×#4510 | 2 |
| C5×#2194 | 3 |
| #69128 | 5 |