Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
428 conjugacy classes of subgroups; only the 142 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 142 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C59 | #127 |
| commutator | C42 | C22×C4×C59 |
| Frattini, cosocle | C2×C42 | C23×C59 |
| socle | C22×C59 | #390 |
| prime radical | C59×#532 | C22 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C59 ◁ C2×C42×C59 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C59×#1837 | C2 | semidirect |
| 3. C59×#1493 | C2 | semidirect |
| 5. C2×C82×C59 | C2 | semidirect |
| 86. #9857 | C59 | direct (N × H) |
| 99. #1837 | C2×C59 | semidirect |
| 100. #1493 | C2×C59 | semidirect |
| 102. C2×C82 | C2×C59 | semidirect |
| 120. C59 | #9857 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C59×#3131 | 2 |
| C59×#1837 | 2 |
| C59×#1493 | 2 |
| C59×#1492 | 2 |
| C2×C82×C59 | 2 |
| #9857 | 59 |