Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
712 conjugacy classes of subgroups; only the 518 normal subgroups are shown.
This group has 712 conjugacy classes of subgroups — too many to draw. Only its 518 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C42×C59 | C24 |
| commutator | C22 | C22×C42×C59 |
| Frattini, cosocle | C42 | C24×C59 |
| socle | C22×C59 | C22×C42 |
| prime radical | C24×C59 | C42 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C42×C59 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C59×#1453 | C2 | semidirect |
| 9. C59×#322 | C22 | semidirect |
| 10. C82×C59 | C22 | semidirect |
| 44. #17338 | C59 | direct (N × H) |
| 53. #1453 | C2×C59 | semidirect |
| 62. #322 | C22×C59 | semidirect |
| 63. C82 | C22×C59 | semidirect |
| 64. C59 | #17338 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C59×#2920 | 2 |
| C59×#1453 | 2 |
| #17338 | 59 |