Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
520 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 106 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. D5⋊#812 | C2 | semidirect |
| 3. C3×#65721 | C2 | semidirect |
| 4. #11746456 | C2 | semidirect |
| 8. C2×D120 | C4 | semidirect |
| 9. C2×C5×D24 | C4 | semidirect |
| 14. D5×D24 | C4 | semidirect |
| 18. D5⋊(C3⋊C16) | C22 | semidirect |
| 19. C3×#3994 | C22 | semidirect |
| 23. #65721 | D3 | semidirect |
| 66. #3994 | C2×D3 | semidirect |
| 103. C2×D24 | AGL(1,𝔽5) | semidirect |
| 285. C3×C5 | #2140 | semidirect |
| 336. C5 | #70652 | semidirect |
| 352. C3 | #10604786 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D5×D24 | 2 |
| D5⋊#812 | 2 |
| C3×#65721 | 2 |
| #11746456 | 2 |
| #10604786 | 3 |
| #70652 | 5 |