Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
2774 conjugacy classes of subgroups; only the 291 normal subgroups are shown.
This group has 2774 conjugacy classes of subgroups — too many to draw. Only its 291 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. C22×#14273642 | C2 | semidirect |
| 3. C2×#16837190 | C2 | direct (N × H) |
| 4. C22×#100×C59 | C2 | semidirect |
| 5. C25×D59 | C4 | semidirect |
| 9. C2×#14273695 | C4 | semidirect |
| 12. C22×C22⋊Dic59 | C4 | semidirect |
| 15. C2×#14273642 | C22 | semidirect |
| 16. #16837190 | C22 | direct (N × H) |
| 20. C2×#100×C59 | C22 | semidirect |
| 26. C24×D59 | C2×C4 | semidirect |
| 35. #14273695 | C2×C4 | semidirect |
| 40. C2×C22⋊Dic59 | C2×C4 | semidirect |
| 44. #14273642 | C23 | semidirect |
| 58. #100×C59 | C23 | semidirect |
| 85. C23×D59 | C22×C4 | semidirect |
| 117. C22⋊Dic59 | C22×C4 | semidirect |
| 197. C22×C59 | AΣL(1,𝔽16) | semidirect |
| 214. C22×#100 | D59 | semidirect |
| 223. C2×C59 | C2×AΣL(1,𝔽16) | semidirect |
| 238. C2×#100 | C2×D59 | semidirect |
| 242. C59 | C22×AΣL(1,𝔽16) | semidirect |
| 278. #100 | C22×D59 | semidirect |
| 426. C22 | #16837190 | direct (N × H) |
| 441. C2 | C2×#16837190 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14273695 | 2 |
| C22×#14273642 | 2 |
| C2×#16837190 | 2 |
| C22×#100×C59 | 2 |
| C22×AΣL(1,𝔽16) | 59 |