Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
414 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 119 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×#16837153 | C2 | semidirect |
| 4. #21421970 | C2 | semidirect |
| 5. C59×#1837 | C2 | semidirect |
| 130. #1837 | D59 | semidirect |
| 156. C59 | #8686 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21432809 | 2 |
| C2×#16837153 | 2 |
| #21422774 | 2 |
| #21421970 | 2 |
| C59×#1837 | 2 |
| #8686 | 59 |