Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
2818 conjugacy classes of subgroups; only the 350 normal subgroups are shown.
This group has 2818 conjugacy classes of subgroups — too many to draw. Only its 350 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C59 | #120 |
| commutator, Frattini, cosocle | C24 | C24×C59 |
| prime radical | C26×C59 | C22 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C59 ◁ C25×C59 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C59×#543 | C2 | semidirect |
| 3. C59×#2029 | C2 | direct (N × H) |
| 4. C2×C59×#342 | C2 | semidirect |
| 7. C59×#543 | C22 | semidirect |
| 14. C59×#342 | C22 | semidirect |
| 19. C25×C59 | Q8 | semidirect |
| 55. C24×C59 | C2×Q8 | semidirect |
| 111. C2×#2029 | C59 | direct (N × H) |
| 135. C2×#543 | C2×C59 | semidirect |
| 137. #2029 | C2×C59 | direct (N × H) |
| 138. C2×#342 | C2×C59 | semidirect |
| 143. C2×C59 | #2029 | direct (N × H) |
| 148. #543 | C22×C59 | semidirect |
| 155. #342 | C22×C59 | semidirect |
| 156. C59 | C2×#2029 | direct (N × H) |
| 161. C25 | Q8×C59 | semidirect |
| 197. C24 | C2×Q8×C59 | semidirect |
| 280. C2 | C59×#2029 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C59×#543 | 2 |
| C2×C59×#379 | 2 |
| C59×#2029 | 2 |
| C2×C59×#342 | 2 |
| C2×#2029 | 59 |