Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
6578 conjugacy classes of subgroups; only the 6270 normal subgroups are shown.
This group has 6578 conjugacy classes of subgroups — too many to draw. Only its 6270 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 | C26 |
| commutator, Frattini, cosocle | C22 | C26×C59 |
| prime radical | C24×C59 | C24 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C59 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C59×#3502 | C2 | semidirect |
| 5. Q82×C59 | C22 | semidirect |
| 6. C59×#557 | C22 | semidirect |
| 13. C22×Q8×C59 | Q8 | semidirect |
| 45. #62849 | C59 | direct (N × H) |
| 52. #3502 | C2×C59 | semidirect |
| 59. Q82 | C22×C59 | semidirect |
| 60. #557 | C22×C59 | semidirect |
| 67. C59 | #62849 | direct (N × H) |
| 68. C22×Q8 | Q8×C59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C59×#3502 | 2 |
| C59×#3458 | 2 |
| C2×C59×#519 | 2 |
| #62849 | 59 |