Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
322 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 78 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 | #342 |
| commutator | C22×C4 | C42×C59 |
| Frattini, cosocle | C2×C4×D4 | C22×C59 |
| prime radical | C22×D4×C59 | Q8 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C59 ◁ C22×C4×C59 ◁ C2×C4×D4×C59 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 106. #7247 | C59 | direct (N × H) |
| 150. C59 | #7247 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C59×#1869 | 2 |
| C59×#1466 | 2 |
| C59×#1465 | 2 |
| #7247 | 59 |