Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
748 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 748 conjugacy classes of subgroups — too many to draw. Only its 106 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×#99 |
| commutator | C24 | C22×C4×C59 |
| Frattini, cosocle | C2×C22⋊C4 | C23×C59 |
| prime radical | C59×#2408 | C2 |
| LCS | G ▷ C24 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C59 ◁ C22×C4×C59 ◁ C2×C4×D4×C59 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C59×#1465 | C2 | semidirect |
| 3. C59×#1460 | C2 | semidirect |
| 4. C59×#1316 | C2 | semidirect |
| 148. #11561 | C59 | direct (N × H) |
| 181. #1465 | C2×C59 | semidirect |
| 182. #1460 | C2×C59 | semidirect |
| 183. #1316 | C2×C59 | semidirect |
| 207. C59 | #11561 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C59×#2408 | 2 |
| C59×#1465 | 2 |
| C59×#1460 | 2 |
| C59×#1316 | 2 |
| #11561 | 59 |