Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
268 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 82 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 | #459 |
| commutator, Frattini, cosocle | C4×C8 | C23×C59 |
| prime radical | C59×#1712 | C2 |
| LCS | G ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C59 ◁ C42×C59 ◁ C82×C59 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C59×#2207 | C2 | semidirect |
| 3. C59×#1591 | C2 | semidirect |
| 4. C59×#1367 | C2 | semidirect |
| 5. C59×#1361 | C2 | semidirect |
| 74. C8×C59 | SD32 | semidirect |
| 76. #12492 | C59 | direct (N × H) |
| 88. #2207 | C2×C59 | semidirect |
| 90. #1591 | C2×C59 | semidirect |
| 91. #1367 | C2×C59 | semidirect |
| 92. #1361 | C2×C59 | semidirect |
| 108. C59 | #12492 | direct (N × H) |
| 166. C8 | SD32×C59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C59×#2207 | 2 |
| C59×#1712 | 2 |
| C59×#1591 | 2 |
| C59×#1367 | 2 |
| C59×#1361 | 2 |
| #12492 | 59 |