Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
234 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 98 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 | #102 |
| commutator | C2×C8 | C42×C59 |
| Frattini, cosocle | C2×C4×C8 | C22×C59 |
| socle | C22×C59 | #340 |
| prime radical | C23×C59 | #102 |
| LCS | G ▷ C2×C8 ▷ C2×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 |
|---|---|---|
| 8. C59×C4⋊C16 | C4 | semidirect |
| 12. C59×#335 | C4 | semidirect |
| 67. #7299 | C59 | direct (N × H) |
| 91. C4⋊C16 | C4×C59 | semidirect |
| 95. #335 | C4×C59 | semidirect |
| 97. C59 | #7299 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C59×#2162 | 2 |
| C4×#106×C59 | 2 |
| C59×#1568 | 2 |
| #7299 | 59 |