Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
452 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 452 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, socle | C22×C59 | C2×#99 |
| commutator | C22×C4 | C22×C4×C59 |
| Frattini, cosocle | C2×C4⋊C4 | C23×C59 |
| prime radical | C24×C59 | C22⋊C4 |
| LCS | G ▷ C22×C4 ▷ C23 ▷ 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 |
|---|---|---|
| 4. C59×#1346 | C2 | semidirect |
| 125. #11700 | C59 | direct (N × H) |
| 149. #1346 | C2×C59 | semidirect |
| 171. C59 | #11700 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C59×#2621 | 2 |
| C59×#1742 | 2 |
| C59×#1458 | 2 |
| C59×#1346 | 2 |
| #11700 | 59 |