Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
616 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 616 conjugacy classes of subgroups — too many to draw. Only its 104 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. C5×#5007 | C2 | semidirect |
| 3. #11747059 | C2 | semidirect |
| 4. #11746895 | C2 | semidirect |
| 5. D4⋊(C3⋊#168) | C2 | semidirect |
| 6. #11745852 | C2 | semidirect |
| 7. #11745834 | C2 | semidirect |
| 12. C5×#869 | C22 | semidirect |
| 19. C4⋊(C3⋊#168) | C22 | semidirect |
| 20. C4×C3⋊#168 | C22 | semidirect |
| 23. C5×C4⋊(C3⋊C8) | C22 | semidirect |
| 64. #5007 | D5 | semidirect |
| 93. C3×C5×D4 | SD16 | semidirect |
| 127. #869 | C2×D5 | semidirect |
| 133. C4⋊(C3⋊C8) | C2×D5 | semidirect |
| 224. C5×D4 | #214 | semidirect |
| 286. C3×D4 | #688 | semidirect |
| 348. C3×C5 | #1639 | semidirect |
| 392. D4 | #6655 | semidirect |
| 412. C5 | #71908 | semidirect |
| 432. C3 | #10601901 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×D4×D20 | 2 |
| C5×#5007 | 2 |
| #11747059 | 2 |
| #11746895 | 2 |
| D4⋊(C3⋊#168) | 2 |
| #11745852 | 2 |
| #11745834 | 2 |
| #10601901 | 3 |
| #71908 | 5 |