Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
478 conjugacy classes of subgroups; only the 134 normal subgroups are shown.
This group has 478 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 | #390 |
| commutator | C42 | C22×C4×C59 |
| Frattini, cosocle | C2×C42 | C23×C59 |
| prime radical | C59×#3147 | C2 |
| 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 |
|---|---|---|
| 2. C59×#1835 | C2 | semidirect |
| 3. C59×#1517 | C2 | semidirect |
| 4. C59×#1452 | C2 | semidirect |
| 8. C59×#494 | C4 | semidirect |
| 9. C59×#493 | C4 | semidirect |
| 10. C59×#492 | C4 | semidirect |
| 78. #9760 | C59 | direct (N × H) |
| 91. #1835 | C2×C59 | semidirect |
| 92. #1517 | C2×C59 | semidirect |
| 93. #1452 | C2×C59 | semidirect |
| 101. #494 | C4×C59 | semidirect |
| 102. #493 | C4×C59 | semidirect |
| 103. #492 | C4×C59 | semidirect |
| 110. C59 | #9760 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C59×#3147 | 2 |
| C59×#1835 | 2 |
| C59×#1517 | 2 |
| C59×#1452 | 2 |
| #9760 | 59 |