Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
516 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 82 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 |
|---|---|---|
| 1. C5×#5587 | C2 | semidirect |
| 3. C5×#4746 | C2 | semidirect |
| 4. C5×#4742 | C2 | semidirect |
| 5. C3×C5×AΣL(1,𝔽16) | C2 | semidirect |
| 6. C5×#4476 | C2 | semidirect |
| 7. C5×#4473 | C2 | semidirect |
| 28. #69132 | C5 | direct (N × H) |
| 35. C5×AΣL(1,𝔽16) | D3 | semidirect |
| 44. C22×C5×Dic3 | D4 | semidirect |
| 48. C2×C5×Dic6 | D4 | semidirect |
| 60. C5×#217 | D4 | semidirect |
| 68. C4×C5×Dic3 | D4 | semidirect |
| 71. #5587 | C2×C5 | semidirect |
| 73. #4746 | C2×C5 | semidirect |
| 74. #4742 | C2×C5 | semidirect |
| 75. C3×AΣL(1,𝔽16) | C2×C5 | semidirect |
| 76. #4476 | C2×C5 | semidirect |
| 77. #4473 | C2×C5 | semidirect |
| 189. AΣL(1,𝔽16) | C5×D3 | semidirect |
| 220. C22×Dic3 | C5×D4 | semidirect |
| 224. C2×Dic6 | C5×D4 | semidirect |
| 236. #217 | C5×D4 | semidirect |
| 244. C4×Dic3 | C5×D4 | semidirect |
| 391. C3×C5 | #2197 | semidirect |
| 457. C5 | #69132 | direct (N × H) |
| 480. C3 | C5×#2197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#5587 | 2 |
| C5×#5032 | 2 |
| C5×#4746 | 2 |
| C5×#4742 | 2 |
| C3×C5×AΣL(1,𝔽16) | 2 |
| C5×#4476 | 2 |
| C5×#4473 | 2 |
| C5×#2197 | 3 |
| #69132 | 5 |