Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
884 conjugacy classes of subgroups; only the 230 normal subgroups are shown.
This group has 884 conjugacy classes of subgroups — too many to draw. Only its 230 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 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C59 |
| prime radical | C2×#127×C59 | C22 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C59 ◁ C2×C42×C59 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C59×#3556 | C2 | semidirect |
| 4. C59×#1626 | C2 | semidirect |
| 5. C59×#1544 | C2 | semidirect |
| 6. C59×#1485 | C2 | semidirect |
| 10. C59×#557 | C22 | semidirect |
| 25. C59×#332 | C22 | semidirect |
| 26. C59×Q8⋊C8 | C22 | semidirect |
| 124. #18731 | C59 | direct (N × H) |
| 138. #3556 | C2×C59 | semidirect |
| 141. #1626 | C2×C59 | semidirect |
| 142. #1544 | C2×C59 | semidirect |
| 143. #1485 | C2×C59 | semidirect |
| 151. #557 | C22×C59 | semidirect |
| 166. #332 | C22×C59 | semidirect |
| 167. Q8⋊C8 | C22×C59 | semidirect |
| 168. C59 | #18731 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C59×#3556 | 2 |
| C59×#3208 | 2 |
| C59×#3138 | 2 |
| C59×#1626 | 2 |
| C59×#1544 | 2 |
| C59×#1485 | 2 |
| #18731 | 59 |