Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
412 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 126 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 | #120 |
| commutator | C42 | C22×C4×C59 |
| Frattini, cosocle | C2×C42 | C23×C59 |
| socle | C22×C59 | #385 |
| 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 |
|---|---|---|
| 3. C59×#1574 | C2 | semidirect |
| 5. C59×#1276 | C2 | semidirect |
| 17. C59×#333 | C4 | semidirect |
| 18. C59×#333 | C4 | semidirect |
| 19. C59×#331 | C4 | semidirect |
| 95. #8935 | C59 | direct (N × H) |
| 111. #1574 | C2×C59 | semidirect |
| 113. #1276 | C2×C59 | semidirect |
| 129. #333 | C4×C59 | semidirect |
| 130. #333 | C4×C59 | semidirect |
| 131. #331 | C4×C59 | semidirect |
| 132. C59 | #8935 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C59×#2979 | 2 |
| C59×#1962 | 2 |
| C59×#1574 | 2 |
| C59×#1543 | 2 |
| C59×#1276 | 2 |
| #8935 | 59 |