Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
1112 conjugacy classes of subgroups; only the 218 normal subgroups are shown.
This group has 1112 conjugacy classes of subgroups — too many to draw. Only its 218 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4×C59 | B(4,𝔽2) |
| commutator, Frattini, cosocle | C2×Q8 | C24×C59 |
| socle | C2×C59 | C2×B(4,𝔽2) |
| LCS | G ▷ C2×Q8 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×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×#3529 | C2 | semidirect |
| 2. C59×#3018 | C2 | semidirect |
| 3. C59×#2203 | C2 | semidirect |
| 4. C59×#2202 | C2 | semidirect |
| 5. C59×#2132 | C2 | semidirect |
| 6. C59×#585 | C22 | semidirect |
| 8. C59×#563 | C22 | semidirect |
| 10. C59×H(3,𝔽4) | C22 | semidirect |
| 15. C59×#456 | C22 | semidirect |
| 20. C59×#413 | C22 | semidirect |
| 21. C59×#356 | C22 | semidirect |
| 22. C59×#355 | C22 | semidirect |
| 148. #33564 | C59 | direct (N × H) |
| 164. #3529 | C2×C59 | semidirect |
| 165. #3018 | C2×C59 | semidirect |
| 166. #2203 | C2×C59 | semidirect |
| 167. #2202 | C2×C59 | semidirect |
| 168. #2132 | C2×C59 | semidirect |
| 174. #585 | C22×C59 | semidirect |
| 176. #563 | C22×C59 | semidirect |
| 178. H(3,𝔽4) | C22×C59 | semidirect |
| 183. #456 | C22×C59 | semidirect |
| 188. #413 | C22×C59 | semidirect |
| 189. #356 | C22×C59 | semidirect |
| 190. #355 | C22×C59 | semidirect |
| 191. C59 | #33564 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C59×#3529 | 2 |
| C59×#3018 | 2 |
| C59×#2203 | 2 |
| C59×#2202 | 2 |
| C59×#2132 | 2 |
| #33564 | 59 |