Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
2942 conjugacy classes of subgroups.
The subgroup lattice has 512 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C25×C59 | C23 |
| commutator | C23 | C23×C4×C59 |
| Frattini, cosocle | C24 | C24×C59 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C25×C59 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 6. C59×#1442 | C2 | direct (N × H) |
| 18. C2×#95×C59 | C4 | semidirect |
| 64. #95×C59 | C2×C4 | semidirect |
| 204. C2×#1442 | C59 | direct (N × H) |
| 249. #1442 | C2×C59 | direct (N × H) |
| 250. C2×C59 | #1442 | direct (N × H) |
| 273. C2×#95 | C4×C59 | semidirect |
| 278. C59 | C2×#1442 | direct (N × H) |
| 320. #95 | C2×C4×C59 | semidirect |
| 499. C2 | C59×#1442 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C4⋊C4×C59 | 2 |
| C22×#95×C59 | 2 |
| C59×#1442 | 2 |
| C2×#1442 | 59 |