Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
392 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 110 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C59 | #1519 |
| commutator | C2×C8 | C22×C4×C59 |
| Frattini, cosocle | C2×M16 | C23×C59 |
| prime radical | C59×#3058 | C2 |
| LCS | G ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C59 ◁ C2×C4×C59 ◁ C2×#131×C59 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C59×#2115 | C2 | semidirect |
| 3. C59×#1813 | C2 | semidirect |
| 4. C59×#1341 | C2 | semidirect |
| 18. C59×#349 | C22 | semidirect |
| 19. C59×#338 | C22 | semidirect |
| 126. #11870 | C59 | direct (N × H) |
| 145. #2115 | C2×C59 | semidirect |
| 146. #1813 | C2×C59 | semidirect |
| 147. #1341 | C2×C59 | semidirect |
| 167. #349 | C22×C59 | semidirect |
| 168. #338 | C22×C59 | semidirect |
| 169. C59 | #11870 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C59×#3058 | 2 |
| C59×#2115 | 2 |
| C59×#1813 | 2 |
| C59×#1341 | 2 |
| #11870 | 59 |