Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
520 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 86 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. #11751658 | C2 | semidirect |
| 3. D5⋊#798 | C2 | semidirect |
| 4. #11746775 | C2 | semidirect |
| 5. C3×#64904 | C2 | semidirect |
| 6. #11746457 | C2 | semidirect |
| 7. #11746456 | C2 | semidirect |
| 11. D8×D15 | C4 | semidirect |
| 12. C5×D3×D8 | C4 | semidirect |
| 17. #91256 | C4 | semidirect |
| 18. D3×D40 | C4 | semidirect |
| 21. #91223 | C22 | semidirect |
| 22. D5⋊(C3⋊C16) | C22 | semidirect |
| 23. C3×#3994 | C22 | semidirect |
| 24. C3×D5⋊C16 | C22 | semidirect |
| 35. #64904 | D3 | semidirect |
| 90. #3994 | C2×D3 | semidirect |
| 94. D5⋊C16 | C2×D3 | semidirect |
| 135. D3×D8 | AGL(1,𝔽5) | semidirect |
| 388. C3×C5 | #2140 | semidirect |
| 461. C5 | #69190 | semidirect |
| 485. C3 | #10604786 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D3×D5×D8 | 2 |
| #11751658 | 2 |
| D5⋊#798 | 2 |
| #11746775 | 2 |
| C3×#64904 | 2 |
| #11746457 | 2 |
| #11746456 | 2 |
| #10604786 | 3 |
| #69190 | 5 |