Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
362 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 122 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C59 | C2×D8 |
| commutator, Frattini, cosocle | C22×C8 | C23×C59 |
| prime radical | C22×D8×C59 | C22 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C59 ◁ C2×C42×C59 ◁ C2×C4×C8×C59 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C59×#1846 | C2 | semidirect |
| 4. C59×#1380 | C2 | semidirect |
| 5. C59×#1374 | C2 | semidirect |
| 92. #13482 | C59 | direct (N × H) |
| 112. #1846 | C2×C59 | semidirect |
| 113. #1380 | C2×C59 | semidirect |
| 114. #1374 | C2×C59 | semidirect |
| 131. C59 | #13482 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C59×#357 | 2 |
| C59×#1970 | 2 |
| C59×#1846 | 2 |
| C59×#1380 | 2 |
| C59×#1374 | 2 |
| #13482 | 59 |