Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
332 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 110 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. C3×C5×#494 | C2 | semidirect |
| 4. C5×#4564 | C2 | semidirect |
| 5. C5×C4⋊(C3⋊C16) | C2 | semidirect |
| 17. #71315 | C5 | direct (N × H) |
| 19. C5×#494 | D3 | semidirect |
| 39. C3×#494 | C2×C5 | semidirect |
| 42. #4564 | C2×C5 | semidirect |
| 43. C4⋊(C3⋊C16) | C2×C5 | semidirect |
| 96. #494 | C5×D3 | semidirect |
| 106. C3×C4×C5 | SD32 | semidirect |
| 175. C4×C5 | #828 | semidirect |
| 194. C3×C5 | #2208 | semidirect |
| 201. C3×C4 | C5×SD32 | semidirect |
| 227. C5 | #71315 | direct (N × H) |
| 235. C4 | C5×#828 | semidirect |
| 238. C3 | C5×#2208 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#494 | 2 |
| C2×C5×#828 | 2 |
| C4×C5×D24 | 2 |
| C5×#4564 | 2 |
| C5×C4⋊(C3⋊C16) | 2 |
| C5×#2208 | 3 |
| #71315 | 5 |