Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
524 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 84 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. C2×C5×C8×A4 | C2 | semidirect |
| 3. C5×A4×C4⋊C4 | C2 | semidirect |
| 4. C22×C5×#102 | C3 | semidirect |
| 7. C5×D4×A4 | C4 | semidirect |
| 12. A4×#102 | C5 | direct (N × H) |
| 14. C23×C5×C8 | C2×C3 | semidirect |
| 15. C22×C5×C4⋊C4 | C2×C3 | semidirect |
| 31. C2×C8×A4 | C2×C5 | semidirect |
| 32. A4×C4⋊C4 | C2×C5 | semidirect |
| 40. C22×C5×D4 | C3×C4 | semidirect |
| 54. C5×#102 | A4 | direct (N × H) |
| 55. C22×#102 | C3×C5 | semidirect |
| 68. D4×A4 | C4×C5 | semidirect |
| 112. C2×C5×C8 | C2×A4 | semidirect |
| 116. C5×C4⋊C4 | C2×A4 | semidirect |
| 118. C23×C8 | C2×C3×C5 | semidirect |
| 119. C22×C4⋊C4 | C2×C3×C5 | semidirect |
| 128. C5×A4 | #102 | direct (N × H) |
| 175. C5×D4 | C4×A4 | semidirect |
| 200. C22×D4 | C3×C4×C5 | semidirect |
| 214. #102 | C5×A4 | direct (N × H) |
| 253. C22×C5 | C3×#102 | semidirect |
| 300. C2×C8 | C2×C5×A4 | semidirect |
| 304. C4⋊C4 | C2×C5×A4 | semidirect |
| 310. A4 | C5×#102 | direct (N × H) |
| 356. D4 | C4×C5×A4 | semidirect |
| 378. C5 | A4×#102 | direct (N × H) |
| 403. C22 | C3×C5×#102 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×D4×A4 | 2 |
| C2×C5×C8×A4 | 2 |
| C5×A4×C4⋊C4 | 2 |
| C22×C5×#102 | 3 |
| C3×C5×#102 | 4 |
| A4×#102 | 5 |