Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
618 conjugacy classes of subgroups; only the 158 normal subgroups are shown.
This group has 618 conjugacy classes of subgroups — too many to draw. Only its 158 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 | #99 |
| commutator | C2×C4 | C22×C8×C59 |
| Frattini, cosocle | C2×C4⋊C4 | C23×C59 |
| prime radical | C24×C59 | C22⋊C4 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C59 ◁ C24×C59 ◁ C22×C4⋊C4×C59 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C59×#1319 | C2 | direct (N × H) |
| 19. C22×Q8×C59 | C8 | semidirect |
| 49. C2×Q8×C59 | C2×C8 | semidirect |
| 115. C2×#1319 | C59 | direct (N × H) |
| 138. #1319 | C2×C59 | direct (N × H) |
| 142. C2×C59 | #1319 | direct (N × H) |
| 156. C59 | C2×#1319 | direct (N × H) |
| 162. C22×Q8 | C8×C59 | semidirect |
| 192. C2×Q8 | C2×C8×C59 | semidirect |
| 281. C2 | C59×#1319 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C59×#391 | 2 |
| C2×C59×#324 | 2 |
| C59×#1319 | 2 |
| C2×#1319 | 59 |