Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
120 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 58 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C16×C59 | D8 |
| commutator | C8 | C2×C16×C59 |
| Frattini, cosocle | C4×C16 | C22×C59 |
| socle | C2×C59 | D4⋊C16 |
| prime radical | #135×C59 | C8 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C16×C59 ◁ C2×C16×C59 ◁ C4×C16×C59 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C59×#1422 | C2 | semidirect |
| 3. C4×C32×C59 | C2 | semidirect |
| 48. #7381 | C59 | direct (N × H) |
| 56. #1422 | C2×C59 | semidirect |
| 57. C4×C32 | C2×C59 | semidirect |
| 68. C59 | #7381 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C59×#2170 | 2 |
| C59×#1422 | 2 |
| C4×C32×C59 | 2 |
| #7381 | 59 |