Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
970 conjugacy classes of subgroups; only the 243 normal subgroups are shown.
This group has 970 conjugacy classes of subgroups — too many to draw. Only its 243 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, prime radical, cosocle | C24×C59 | C24 |
| Fitting | C59×#1444 | C2 |
| hypercenter | #1444 | D59 |
| hypocenter | C59 | #17302 |
| LCS | G ▷ C24×C59 ▷ C59 | |
| UCS | C1 ◁ C24 ◁ #1444 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 178. C59 | #17302 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21422359 | 2 |
| #21422358 | 2 |
| #21422357 | 2 |
| #21422355 | 2 |
| #21422347 | 2 |
| C59×#1444 | 2 |
| #17302 | 59 |