Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
386 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 77 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. #21424249 | C2 | semidirect |
| 3. #21422797 | C2 | semidirect |
| 5. #21422609 | C2 | semidirect |
| 7. C59×#1290 | C2 | semidirect |
| 159. #1290 | D59 | semidirect |
| 184. C59 | #10514 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21435413 | 2 |
| #21424249 | 2 |
| #21422797 | 2 |
| #21422792 | 2 |
| #21422609 | 2 |
| #21422605 | 2 |
| C59×#1290 | 2 |
| #10514 | 59 |