Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
656 conjugacy classes of subgroups; only the 238 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 238 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C59 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C59 |
| prime radical | C22×D4×C59 | C23 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C59 ◁ C59×#376 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C59×#2645 | C2 | semidirect |
| 4. C59×#1941 | C2 | semidirect |
| 6. C59×#1935 | C2 | semidirect |
| 7. C59×#1726 | C2 | semidirect |
| 98. #33271 | C59 | direct (N × H) |
| 112. #2645 | C2×C59 | semidirect |
| 115. #1941 | C2×C59 | semidirect |
| 117. #1935 | C2×C59 | semidirect |
| 118. #1726 | C2×C59 | semidirect |
| 139. C59 | #33271 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C59×#2645 | 2 |
| C59×#2644 | 2 |
| C59×#1968 | 2 |
| C59×#1941 | 2 |
| C59×#1936 | 2 |
| C59×#1935 | 2 |
| C59×#1726 | 2 |
| #33271 | 59 |