Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
396 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 396 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 | C23×C59 | #120 |
| commutator, Frattini, cosocle | C2×C42 | C23×C59 |
| prime radical | C22×D4×C59 | D4 |
| LCS | G ▷ C2×C42 ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C59 ◁ C2×C42×C59 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C59×#2084 | C2 | semidirect |
| 4. C59×#2072 | C2 | semidirect |
| 5. C59×#1272 | C2 | semidirect |
| 6. C59×#1271 | C2 | semidirect |
| 153. #7820 | C59 | direct (N × H) |
| 182. #2084 | C2×C59 | semidirect |
| 183. #2072 | C2×C59 | semidirect |
| 184. #1272 | C2×C59 | semidirect |
| 185. #1271 | C2×C59 | semidirect |
| 214. C59 | #7820 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C59×#2808 | 2 |
| C59×#2093 | 2 |
| C59×#2084 | 2 |
| C59×#2072 | 2 |
| C59×#1272 | 2 |
| C59×#1271 | 2 |
| C59×#1270 | 2 |
| #7820 | 59 |