Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
380 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 102 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 | C23 | C4×C8×C59 |
| Frattini, cosocle | C2×C4×D4 | C22×C59 |
| socle | C22×C59 | #342 |
| prime radical | C22×D4×C59 | C2×C4 |
| LCS | G ▷ C23 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C59 ◁ C22×C4×C59 ◁ C2×C4×D4×C59 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. C23×C8×C59 | C4 | semidirect |
| 9. C2×C22⋊C8×C59 | C4 | semidirect |
| 14. C59×#323 | C4 | semidirect |
| 32. #99×C59 | C8 | semidirect |
| 115. #7204 | C59 | direct (N × H) |
| 152. C23×C8 | C4×C59 | semidirect |
| 157. C2×C22⋊C8 | C4×C59 | semidirect |
| 162. #323 | C4×C59 | semidirect |
| 163. C59 | #7204 | direct (N × H) |
| 181. #99 | C8×C59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C59×#1869 | 2 |
| C4×#99×C59 | 2 |
| C59×#1460 | 2 |
| #7204 | 59 |