Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
2158 conjugacy classes of subgroups; only the 499 normal subgroups are shown.
This group has 2158 conjugacy classes of subgroups — too many to draw. Only its 499 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C24 | C23×D59 |
| commutator, socle, cosocle | C24×C59 | C24 |
| Fitting | C4×#95×C59 | C2 |
| prime radical | C23×D236 | C22 |
| hypercenter | C4×#95 | D59 |
| hypocenter | C59 | #15155 |
| LCS | G ▷ C24×C59 ▷ C59 | |
| UCS | C1 ◁ C24 ◁ C4×#95 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#16837339 | C2 | semidirect |
| 3. C2×#16837272 | C2 | semidirect |
| 4. C4×#95×C59 | C2 | semidirect |
| 29. #95×C59 | D4 | semidirect |
| 90. C4×C59 | #399 | semidirect |
| 95. C4×#95 | D59 | semidirect |
| 111. C59 | #15155 | semidirect |
| 127. #95 | D236 | semidirect |
| 188. C4 | #16837339 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837339 | 2 |
| C2×#16837304 | 2 |
| C2×#16837272 | 2 |
| C4×#95×C59 | 2 |
| #15155 | 59 |