Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
738 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 738 conjugacy classes of subgroups — too many to draw. Only its 94 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 | #2021 |
| commutator, Frattini, cosocle | C2×#41 | C23×C59 |
| LCS | G ▷ C2×#41 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C59 ◁ C2×C4×C59 ◁ C2×#41×C59 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C59×#3199 | C2 | semidirect |
| 2. C59×#3027 | C2 | semidirect |
| 3. C59×#2128 | C2 | semidirect |
| 4. C59×#1794 | C2 | semidirect |
| 5. C59×#1391 | C2 | semidirect |
| 31. C22×D4×C59 | D4 | semidirect |
| 34. C2×M16×C59 | D4 | semidirect |
| 35. C22×C8×C59 | D4 | semidirect |
| 48. #117×C59 | D4 | semidirect |
| 59. #99×C59 | D4 | semidirect |
| 157. #13350 | C59 | direct (N × H) |
| 178. #3199 | C2×C59 | semidirect |
| 179. #3027 | C2×C59 | semidirect |
| 180. #2128 | C2×C59 | semidirect |
| 181. #1794 | C2×C59 | semidirect |
| 182. #1391 | C2×C59 | semidirect |
| 205. C59 | #13350 | direct (N × H) |
| 215. C22×D4 | D4×C59 | semidirect |
| 218. C2×M16 | D4×C59 | semidirect |
| 219. C22×C8 | D4×C59 | semidirect |
| 232. #117 | D4×C59 | semidirect |
| 243. #99 | D4×C59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C59×#3199 | 2 |
| C59×#3027 | 2 |
| C59×#2128 | 2 |
| C59×#1794 | 2 |
| C59×#1391 | 2 |
| #13350 | 59 |