Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
1278 conjugacy classes of subgroups; only the 290 normal subgroups are shown.
This group has 1278 conjugacy classes of subgroups — too many to draw. Only its 290 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C59 | #2847 |
| commutator, Frattini, cosocle | C22×C4 | C24×C59 |
| prime radical | C59×#585 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C59 ◁ C22×C4×C59 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C59×#3059 | C2 | semidirect |
| 4. C59×#1909 | C2 | semidirect |
| 5. C59×#1812 | C2 | semidirect |
| 7. C22×Q16×C59 | C22 | semidirect |
| 16. C59×#427 | C22 | semidirect |
| 17. C59×#419 | C22 | semidirect |
| 19. C59×H(3,ℤ/4) | C22 | semidirect |
| 103. #32949 | C59 | direct (N × H) |
| 115. #3059 | C2×C59 | semidirect |
| 117. #1909 | C2×C59 | semidirect |
| 118. #1812 | C2×C59 | semidirect |
| 123. C22×Q16 | C22×C59 | semidirect |
| 132. #427 | C22×C59 | semidirect |
| 133. #419 | C22×C59 | semidirect |
| 135. H(3,ℤ/4) | C22×C59 | semidirect |
| 136. C59 | #32949 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C59×#3573 | 2 |
| C59×#3059 | 2 |
| C59×#3028 | 2 |
| C59×#1909 | 2 |
| C59×#1812 | 2 |
| #32949 | 59 |