Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
3706 conjugacy classes of subgroups; only the 366 normal subgroups are shown.
This group has 3706 conjugacy classes of subgroups — too many to draw. Only its 366 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C59 | C2×#120 |
| commutator, Frattini, cosocle | C24 | C24×C59 |
| prime radical | C2×C59×#585 | C2 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C59 ◁ C23×C4×C59 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C59×#458 | C2 | semidirect |
| 3. C59×#2406 | C2 | semidirect |
| 4. C59×#1790 | C2 | semidirect |
| 5. C59×#1782 | C2 | semidirect |
| 12. C2×#123×C59 | C22 | semidirect |
| 13. C22×C4⋊C4×C59 | C22 | semidirect |
| 15. C2×#99×C59 | C22 | semidirect |
| 18. C59×#386 | C22 | semidirect |
| 20. C59×#381 | C22 | semidirect |
| 133. #32901 | C59 | direct (N × H) |
| 152. C2×#458 | C2×C59 | semidirect |
| 153. #2406 | C2×C59 | semidirect |
| 154. #1790 | C2×C59 | semidirect |
| 155. #1782 | C2×C59 | semidirect |
| 167. C2×#123 | C22×C59 | semidirect |
| 168. C22×C4⋊C4 | C22×C59 | semidirect |
| 170. C2×#99 | C22×C59 | semidirect |
| 173. #386 | C22×C59 | semidirect |
| 175. #381 | C22×C59 | semidirect |
| 176. C59 | #32901 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C59×#585 | 2 |
| C2×C59×#458 | 2 |
| C59×#2406 | 2 |
| C59×#1790 | 2 |
| C59×#1782 | 2 |
| #32901 | 59 |