Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
906 conjugacy classes of subgroups; only the 206 normal subgroups are shown.
This group has 906 conjugacy classes of subgroups — too many to draw. Only its 206 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 | C59×#2615 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C59 ◁ C22×#41×C59 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C59×#2616 | C2 | semidirect |
| 3. C59×#2077 | C2 | semidirect |
| 4. C59×#2035 | C2 | semidirect |
| 5. C59×#2034 | C2 | semidirect |
| 6. C59×#2000 | C2 | semidirect |
| 7. C59×#1780 | C2 | semidirect |
| 130. #32716 | C59 | direct (N × H) |
| 150. #2616 | C2×C59 | semidirect |
| 152. #2077 | C2×C59 | semidirect |
| 153. #2035 | C2×C59 | semidirect |
| 154. #2034 | C2×C59 | semidirect |
| 155. #2000 | C2×C59 | semidirect |
| 156. #1780 | C2×C59 | semidirect |
| 179. C59 | #32716 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C59×#2616 | 2 |
| C59×#2615 | 2 |
| C59×#2077 | 2 |
| C59×#2035 | 2 |
| C59×#2034 | 2 |
| C59×#2000 | 2 |
| C59×#1780 | 2 |
| #32716 | 59 |