Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
4032 conjugacy classes of subgroups; only the 370 normal subgroups are shown.
This group has 4032 conjugacy classes of subgroups — too many to draw. Only its 370 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 | C22×H(5,𝔽2)×C59 | C2 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C59 ◁ C25×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×#2405 | C2 | semidirect |
| 4. C59×#1790 | C2 | semidirect |
| 5. C59×#1781 | C2 | semidirect |
| 12. C2×#123×C59 | C22 | semidirect |
| 13. C22×C22⋊C4×C59 | C22 | semidirect |
| 15. C2×#99×C59 | C22 | semidirect |
| 17. C59×#386 | C22 | semidirect |
| 20. C59×#379 | C22 | semidirect |
| 43. C23×C4×C59 | C23 | semidirect |
| 44. C23×C4×C59 | C23 | semidirect |
| 53. C2×C22⋊C4×C59 | C23 | semidirect |
| 155. #32900 | C59 | direct (N × H) |
| 174. C22×C59 | #458 | semidirect |
| 182. C2×#458 | C2×C59 | semidirect |
| 183. #2405 | C2×C59 | semidirect |
| 184. #1790 | C2×C59 | semidirect |
| 185. #1781 | C2×C59 | semidirect |
| 199. C2×#123 | C22×C59 | semidirect |
| 200. C22×C22⋊C4 | C22×C59 | semidirect |
| 202. C2×#99 | C22×C59 | semidirect |
| 204. #386 | C22×C59 | semidirect |
| 207. #379 | C22×C59 | semidirect |
| 208. C59 | #32900 | direct (N × H) |
| 231. C23×C4 | C23×C59 | semidirect |
| 232. C23×C4 | C23×C59 | semidirect |
| 241. C2×C22⋊C4 | C23×C59 | semidirect |
| 361. C22 | C59×#458 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×H(5,𝔽2)×C59 | 2 |
| C2×C59×#458 | 2 |
| C59×#2405 | 2 |
| C59×#1790 | 2 |
| C59×#1781 | 2 |
| #32900 | 59 |