Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
608 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 608 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 |
|---|---|---|
| 4. D5⋊#824 | C2 | semidirect |
| 5. #11751712 | C2 | semidirect |
| 6. #11746539 | C2 | semidirect |
| 7. #11746521 | C2 | semidirect |
| 18. C2×#6718 | C4 | semidirect |
| 19. C2×C5×#216 | C4 | semidirect |
| 22. C2×#6657 | C4 | semidirect |
| 23. C2×#6655 | C4 | semidirect |
| 145. C2×#216 | AGL(1,𝔽5) | semidirect |
| 396. C3×C5 | #1902 | semidirect |
| 454. C5 | #72022 | semidirect |
| 469. C3 | #10604851 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#66260 | 2 |
| C2×#91508 | 2 |
| #11752443 | 2 |
| D5⋊#824 | 2 |
| #11751712 | 2 |
| #11746539 | 2 |
| #11746521 | 2 |
| #10604851 | 3 |
| #72022 | 5 |