Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
808 conjugacy classes of subgroups; only the 230 normal subgroups are shown.
This group has 808 conjugacy classes of subgroups — too many to draw. Only its 230 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×#120 |
| commutator, Frattini, cosocle | C42 | C24×C59 |
| prime radical | C23×C59 | #120 |
| 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 |
|---|---|---|
| 4. C59×#1636 | C2 | semidirect |
| 119. #18732 | C59 | direct (N × H) |
| 134. #1636 | C2×C59 | semidirect |
| 160. C59 | #18732 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C59×#3556 | 2 |
| C59×#3230 | 2 |
| C59×#3139 | 2 |
| C59×#1636 | 2 |
| C59×#1544 | 2 |
| C59×#1485 | 2 |
| #18732 | 59 |