Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
322 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 110 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C59 | #99 |
| commutator | C2×C4 | C4×C8×C59 |
| Frattini, cosocle | C2×#117 | C22×C59 |
| socle | C22×C59 | #342 |
| prime radical | C24×C59 | C4⋊C4 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C59 ◁ C22×C4×C59 ◁ C2×#117×C59 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 14. C2×M16×C59 | C8 | semidirect |
| 20. C22×C8×C59 | C8 | semidirect |
| 90. #7190 | C59 | direct (N × H) |
| 124. C59 | #7190 | direct (N × H) |
| 129. C2×M16 | C8×C59 | semidirect |
| 135. C22×C8 | C8×C59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C59×#1729 | 2 |
| C59×#1458 | 2 |
| #7190 | 59 |