Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
686 conjugacy classes of subgroups; only the 142 normal subgroups are shown.
This group has 686 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, socle | C22×C59 | C2×#99 |
| commutator | C23 | C22×C8×C59 |
| Frattini, cosocle | C2×C22⋊C4 | C23×C59 |
| prime radical | C23×D4×C59 | C4 |
| LCS | G ▷ C23 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C59 ◁ C22×C4×C59 ◁ C2×#117×C59 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C59×#1458 | C2 | semidirect |
| 3. C59×#1316 | C2 | semidirect |
| 20. C22×D4×C59 | C8 | semidirect |
| 105. #11427 | C59 | direct (N × H) |
| 129. #1458 | C2×C59 | semidirect |
| 130. #1316 | C2×C59 | semidirect |
| 148. C59 | #11427 | direct (N × H) |
| 155. C22×D4 | C8×C59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C59×#2309 | 2 |
| C59×#1458 | 2 |
| C59×#1316 | 2 |
| #11427 | 59 |