Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
602 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 602 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. C2×C5×C8×A4 | C2 | semidirect |
| 3. C2×C5×A4⋊C8 | C2 | semidirect |
| 4. C5×#5400 | C2 | direct (N × H) |
| 12. C5×C8×A4 | C22 | semidirect |
| 13. C5×A4⋊C8 | C22 | semidirect |
| 14. C2×#5400 | C5 | direct (N × H) |
| 16. C23×C5×C8 | D3 | semidirect |
| 35. C2×C8×A4 | C2×C5 | semidirect |
| 36. C2×A4⋊C8 | C2×C5 | semidirect |
| 37. #5400 | C2×C5 | direct (N × H) |
| 50. C22×C5×C8 | C2×D3 | semidirect |
| 66. C2×C5×A4 | M16 | semidirect |
| 81. C8×A4 | C22×C5 | semidirect |
| 82. A4⋊C8 | C22×C5 | semidirect |
| 117. C2×C5×C8 | S4 | semidirect |
| 127. C23×C8 | C5×D3 | semidirect |
| 138. C5×A4 | C2×M16 | semidirect |
| 160. C23×C5 | ΓL(1,𝔽25) | semidirect |
| 188. C5×C8 | C2×S4 | semidirect |
| 201. C22×C8 | C2×C5×D3 | semidirect |
| 219. C2×A4 | C5×M16 | semidirect |
| 240. C22×C5 | C2×ΓL(1,𝔽25) | semidirect |
| 283. C2×C8 | C5×S4 | semidirect |
| 296. A4 | C2×C5×M16 | semidirect |
| 304. C2×C5 | #5400 | direct (N × H) |
| 314. C23 | C5×ΓL(1,𝔽25) | semidirect |
| 342. C8 | C2×C5×S4 | semidirect |
| 346. C5 | C2×#5400 | direct (N × H) |
| 359. C22 | C2×C5×ΓL(1,𝔽25) | semidirect |
| 373. C2 | C5×#5400 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C5×S4 | 2 |
| C2×C5×C8×A4 | 2 |
| C2×C5×A4⋊C8 | 2 |
| C5×#5400 | 2 |
| C2×C5×#435 | 3 |
| C2×C5×ΓL(1,𝔽25) | 4 |
| C2×#5400 | 5 |