Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
680 conjugacy classes of subgroups; only the 134 normal subgroups are shown.
This group has 680 conjugacy classes of subgroups — too many to draw. Only its 134 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×#99 |
| commutator | C22×C4 | C22×C4×C59 |
| Frattini, cosocle | C22×D4 | C23×C59 |
| prime radical | C2×#127×C59 | C22 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C59 ◁ C22×C4×C59 ◁ C2×C4×D4×C59 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C59×#1799 | C2 | semidirect |
| 4. C59×#1393 | C2 | semidirect |
| 7. C2×C4×D4×C59 | C4 | semidirect |
| 11. C59×#390 | C4 | semidirect |
| 13. C59×#384 | C4 | semidirect |
| 15. C43×C59 | C4 | semidirect |
| 59. C2×D4×C59 | C4⋊C4 | semidirect |
| 93. C42×C59 | C4⋊C4 | semidirect |
| 139. #12797 | C59 | direct (N × H) |
| 166. C4×C59 | #353 | semidirect |
| 169. #1799 | C2×C59 | semidirect |
| 170. #1393 | C2×C59 | semidirect |
| 181. C2×C4×D4 | C4×C59 | semidirect |
| 185. #390 | C4×C59 | semidirect |
| 187. #384 | C4×C59 | semidirect |
| 189. C43 | C4×C59 | semidirect |
| 192. C59 | #12797 | direct (N × H) |
| 234. C2×D4 | C4⋊C4×C59 | semidirect |
| 268. C42 | C4⋊C4×C59 | semidirect |
| 340. C4 | C59×#353 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#127×C59 | 2 |
| C2×C59×#353 | 2 |
| C59×#1799 | 2 |
| C59×#1393 | 2 |
| #12797 | 59 |