Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
702 conjugacy classes of subgroups; only the 235 normal subgroups are shown.
This group has 702 conjugacy classes of subgroups — too many to draw. Only its 235 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 |
|---|---|---|
| 3. #21424660 | C2 | semidirect |
| 4. #21424241 | C2 | semidirect |
| 5. C8×Dic59⋊C4 | C2 | semidirect |
| 7. C59×#1726 | C2 | semidirect |
| 119. #1726 | D59 | semidirect |
| 141. C59 | #21668 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21427394 | 2 |
| #21424709 | 2 |
| #21424660 | 2 |
| #21424241 | 2 |
| C8×Dic59⋊C4 | 2 |
| C8×(C2×D59)⋊C4 | 2 |
| C59×#1726 | 2 |
| #21668 | 59 |