Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
502 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 502 conjugacy classes of subgroups — too many to draw. Only its 99 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. #21425850 | C2 | semidirect |
| 3. #21422843 | C2 | semidirect |
| 4. #21422143 | C2 | semidirect |
| 5. #21422142 | C2 | semidirect |
| 6. #21422141 | C2 | semidirect |
| 7. C59×#1361 | C2 | semidirect |
| 18. C4⋊(C59⋊C16) | C22 | semidirect |
| 20. #16837155 | C22 | semidirect |
| 23. C59×C4⋊C16 | C22 | semidirect |
| 24. C59×#335 | C22 | semidirect |
| 160. #1361 | D59 | semidirect |
| 180. C4⋊C16 | C2×D59 | semidirect |
| 182. #335 | C2×D59 | semidirect |
| 184. C59 | #11931 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #493×D59 | 2 |
| #21425850 | 2 |
| #21422843 | 2 |
| #21422143 | 2 |
| #21422142 | 2 |
| #21422141 | 2 |
| C59×#1361 | 2 |
| #11931 | 59 |