Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
440 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 86 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 | #2044 |
| commutator, Frattini, cosocle | C2×#41 | C23×C59 |
| prime radical | C59×#3199 | C2 |
| 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 |
|---|---|---|
| 2. C59×#2128 | C2 | semidirect |
| 3. C59×#2122 | C2 | semidirect |
| 4. C59×#1914 | C2 | semidirect |
| 5. C59×#1910 | C2 | semidirect |
| 6. C59×#1868 | C2 | semidirect |
| 7. C59×#1395 | C2 | semidirect |
| 170. #13432 | C59 | direct (N × H) |
| 196. #2128 | C2×C59 | semidirect |
| 197. #2122 | C2×C59 | semidirect |
| 198. #1914 | C2×C59 | semidirect |
| 199. #1910 | C2×C59 | semidirect |
| 200. #1868 | C2×C59 | semidirect |
| 201. #1395 | C2×C59 | semidirect |
| 230. C59 | #13432 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C59×#3199 | 2 |
| C59×#2128 | 2 |
| C59×#2122 | 2 |
| C59×#1914 | 2 |
| C59×#1910 | 2 |
| C59×#1868 | 2 |
| C59×#1395 | 2 |
| #13432 | 59 |