Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
404 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 126 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 | C2×#99 |
| commutator | C22×C4 | C22×C4×C59 |
| Frattini, cosocle | C22×Q8 | C23×C59 |
| prime radical | C23×C59 | C2×C22⋊C4 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C59 ◁ C22×C4×C59 ◁ C2×C4×Q8×C59 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 42. #101×C59 | Q8 | semidirect |
| 116. #13301 | C59 | direct (N × H) |
| 157. C59 | #13301 | direct (N × H) |
| 180. #101 | Q8×C59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C59×#2568 | 2 |
| C59×#1801 | 2 |
| C4×#101×C59 | 2 |
| C59×#1394 | 2 |
| #13301 | 59 |