Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
536 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 106 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 | #392 |
| commutator, Frattini, cosocle | C23×C4 | C23×C59 |
| prime radical | C2×#121×C59 | C22 |
| LCS | G ▷ C23×C4 ▷ C22 ▷ 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×#484 | C2 | semidirect |
| 4. C59×#1821 | C2 | semidirect |
| 5. C59×#1472 | C2 | semidirect |
| 7. C59×#1298 | C2 | semidirect |
| 163. #9994 | C59 | direct (N × H) |
| 188. C2×#484 | C2×C59 | semidirect |
| 190. #1821 | C2×C59 | semidirect |
| 191. #1472 | C2×C59 | semidirect |
| 193. #1298 | C2×C59 | semidirect |
| 224. C59 | #9994 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C59×#3193 | 2 |
| C2×C59×#484 | 2 |
| C2×C59×#480 | 2 |
| C59×#1821 | 2 |
| C59×#1472 | 2 |
| C59×#1471 | 2 |
| C59×#1298 | 2 |
| #9994 | 59 |