Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
316 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 78 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 | #447 |
| commutator, Frattini, cosocle | C22×C8 | C23×C59 |
| prime radical | C59×#466 | C22 |
| LCS | G ▷ C22×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C59 ◁ C22×C4×C59 ◁ C2×C4⋊C8×C59 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C59×#2236 | C2 | semidirect |
| 4. C59×#2087 | C2 | semidirect |
| 5. C59×#1348 | C2 | semidirect |
| 7. C59×#1322 | C2 | semidirect |
| 128. #12293 | C59 | direct (N × H) |
| 148. #2236 | C2×C59 | semidirect |
| 150. #2087 | C2×C59 | semidirect |
| 151. #1348 | C2×C59 | semidirect |
| 153. #1322 | C2×C59 | semidirect |
| 179. C59 | #12293 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C59×#3250 | 2 |
| C59×#2236 | 2 |
| C59×#2233 | 2 |
| C59×#2087 | 2 |
| C59×#1348 | 2 |
| C59×#1347 | 2 |
| C59×#1322 | 2 |
| #12293 | 59 |