Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
1426 conjugacy classes of subgroups; only the 251 normal subgroups are shown.
This group has 1426 conjugacy classes of subgroups — too many to draw. Only its 251 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C24 | C23×D59 |
| commutator, socle, cosocle | C24×C59 | C24 |
| Fitting | C59×#1438 | C2 |
| prime radical | C23×D4×C59 | C22 |
| hypercenter | #1438 | D59 |
| hypocenter | C59 | #17273 |
| LCS | G ▷ C24×C59 ▷ C59 | |
| UCS | C1 ◁ C24 ◁ #1438 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #21422365 | C2 | semidirect |
| 2. #21422341 | C2 | semidirect |
| 137. C59 | #17273 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21422365 | 2 |
| #21422341 | 2 |
| #21422337 | 2 |
| C59×#1438 | 2 |
| #17273 | 59 |