Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
278 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 278 conjugacy classes of subgroups — too many to draw. Only its 94 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4×C59 | #482 |
| commutator, Frattini, cosocle | C22×C8 | C23×C59 |
| socle | C2×C59 | #2073 |
| prime radical | C2×#135×C59 | C22 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C59 ◁ C22×C4×C59 ◁ C59×#405 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. C59×#1833 | C2 | semidirect |
| 5. C59×#1384 | C2 | semidirect |
| 6. C59×#1382 | C2 | semidirect |
| 7. C59×#1379 | C2 | semidirect |
| 117. #13489 | C59 | direct (N × H) |
| 135. #1833 | C2×C59 | semidirect |
| 136. #1384 | C2×C59 | semidirect |
| 137. #1382 | C2×C59 | semidirect |
| 138. #1379 | C2×C59 | semidirect |
| 159. C59 | #13489 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C59×#2148 | 2 |
| C59×#2138 | 2 |
| C59×#1976 | 2 |
| C59×#1833 | 2 |
| C59×#1384 | 2 |
| C59×#1382 | 2 |
| C59×#1379 | 2 |
| #13489 | 59 |