Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
200 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 102 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C59 | #95 |
| commutator | C23 | C4×C8×C59 |
| Frattini, cosocle | C2×C4×C8 | C22×C59 |
| socle | C22×C59 | #336 |
| prime radical | C23×C59 | C4×C8 |
| LCS | G ▷ C23 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C59 ◁ C2×C4×C8×C59 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 68. #7211 | C59 | direct (N × H) |
| 98. C59 | #7211 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C59×#2163 | 2 |
| C59×#2150 | 2 |
| C59×#1451 | 2 |
| #7211 | 59 |