Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
616 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 616 conjugacy classes of subgroups — too many to draw. Only its 101 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. C3×C5×#474 | C2 | semidirect |
| 3. #11751189 | C2 | semidirect |
| 4. #11751184 | C2 | semidirect |
| 5. D4⋊(C3⋊#168) | C2 | semidirect |
| 6. #11746306 | C2 | semidirect |
| 7. #11746304 | C2 | semidirect |
| 11. C3×C5×C4⋊Q8 | C22 | semidirect |
| 20. C3×C5×C4⋊C8 | C22 | semidirect |
| 24. C4⋊(C3⋊#168) | C22 | semidirect |
| 25. C4×C3⋊#168 | C22 | semidirect |
| 28. C5×#474 | D3 | semidirect |
| 62. C3×#474 | D5 | semidirect |
| 70. C5×C4⋊Q8 | C2×D3 | semidirect |
| 79. C5×C4⋊C8 | C2×D3 | semidirect |
| 95. C3×C5×D4 | SD16 | semidirect |
| 120. C3×C4⋊Q8 | C2×D5 | semidirect |
| 129. C3×C4⋊C8 | C2×D5 | semidirect |
| 164. #474 | D15 | semidirect |
| 224. C5×D4 | #215 | semidirect |
| 250. C4⋊Q8 | C2×D15 | semidirect |
| 259. C4⋊C8 | C2×D15 | semidirect |
| 279. C3×D4 | #688 | semidirect |
| 348. C3×C5 | #1639 | semidirect |
| 392. D4 | #6717 | semidirect |
| 412. C5 | #71108 | semidirect |
| 432. C3 | #10601901 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×D60 | 2 |
| C3×C5×#474 | 2 |
| #11751189 | 2 |
| #11751184 | 2 |
| D4⋊(C3⋊#168) | 2 |
| #11746306 | 2 |
| #11746304 | 2 |
| #10601901 | 3 |
| #71108 | 5 |