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. C2×C3×C5×SD32 | C2 | semidirect |
| 3. C5×#5192 | C2 | semidirect |
| 4. C5×#5179 | C2 | semidirect |
| 5. C5×#4563 | C2 | semidirect |
| 6. C5×#4510 | C2 | semidirect |
| 7. C5×#4508 | C2 | semidirect |
| 10. C2×C3×C5×Q16 | C22 | semidirect |
| 20. C2×C3×C5×C16 | C22 | semidirect |
| 24. C5×#819 | C22 | semidirect |
| 25. C5×#812 | C22 | semidirect |
| 26. #71490 | C5 | direct (N × H) |
| 29. C2×C5×SD32 | D3 | semidirect |
| 62. C2×C3×SD32 | C2×C5 | semidirect |
| 63. #5192 | C2×C5 | semidirect |
| 64. #5179 | C2×C5 | semidirect |
| 65. #4563 | C2×C5 | semidirect |
| 66. #4510 | C2×C5 | semidirect |
| 67. #4508 | C2×C5 | semidirect |
| 74. C2×C5×Q16 | C2×D3 | semidirect |
| 82. C2×C5×C16 | C2×D3 | semidirect |
| 110. C2×C3×Q16 | C22×C5 | semidirect |
| 120. C2×C3×C16 | C22×C5 | semidirect |
| 124. #819 | C22×C5 | semidirect |
| 125. #812 | C22×C5 | semidirect |
| 155. C2×SD32 | C5×D3 | semidirect |
| 227. C2×Q16 | C2×C5×D3 | semidirect |
| 235. C2×C16 | C2×C5×D3 | semidirect |
| 304. C3×C5 | #2194 | semidirect |
| 349. C5 | #71490 | 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×#5757 | 2 |
| C2×C3×C5×SD32 | 2 |
| C5×#5192 | 2 |
| C5×#5179 | 2 |
| C5×#4563 | 2 |
| C5×#4510 | 2 |
| C5×#4508 | 2 |
| C5×#2194 | 3 |
| #71490 | 5 |