Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
1538 conjugacy classes of subgroups; only the 287 normal subgroups are shown.
This group has 1538 conjugacy classes of subgroups — too many to draw. Only its 287 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. C4×#14273708 | C2 | semidirect |
| 3. #21424509 | C2 | semidirect |
| 4. #21424377 | C2 | semidirect |
| 6. C4×#14273642 | C2 | semidirect |
| 9. C22×C4×Dic59 | C22 | semidirect |
| 10. #16837592 | C4 | direct (N × H) |
| 16. #16837274 | C22 | semidirect |
| 17. #16837263 | C22 | semidirect |
| 20. C4×C22⋊Dic59 | C22 | semidirect |
| 21. #16837169 | C22 | semidirect |
| 32. #14273708 | C2×C4 | semidirect |
| 43. #14273642 | C2×C4 | semidirect |
| 108. C22×Dic59 | C22×C4 | semidirect |
| 122. C22⋊Dic59 | C22×C4 | semidirect |
| 191. C4×C59 | #458 | semidirect |
| 230. C59 | C4×#458 | semidirect |
| 396. C4 | #16837592 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837592 | 2 |
| C4×#14273708 | 2 |
| #21424509 | 2 |
| #21424377 | 2 |
| #21424044 | 2 |
| C4×#14273642 | 2 |
| C4×H(5,𝔽2)×C59 | 2 |
| C4×#458 | 59 |