Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
482 conjugacy classes of subgroups; only the 270 normal subgroups are shown.
This group has 482 conjugacy classes of subgroups — too many to draw. Only its 270 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 | C2×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C59 |
| socle | C22×C59 | C22×D8 |
| prime radical | C23×C59 | C2×D8 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C59 ◁ C2×C42×C59 ◁ C2×C4×C8×C59 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C59×#2255 | C2 | semidirect |
| 25. C2×C16×C59 | Q8 | semidirect |
| 61. #33728 | C59 | direct (N × H) |
| 71. #2255 | C2×C59 | semidirect |
| 89. C59 | #33728 | direct (N × H) |
| 98. C2×C16 | Q8×C59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C59×#3160 | 2 |
| C59×#2255 | 2 |
| C59×#2158 | 2 |
| C2×C59×#346 | 2 |
| #33728 | 59 |