Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
574 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 574 conjugacy classes of subgroups — too many to draw. Only its 98 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C59 | C2×#99 |
| commutator | C22×C4 | C22×C4×C59 |
| Frattini, cosocle | C2×C22⋊C4 | C23×C59 |
| prime radical | C59×#2617 | C2 |
| LCS | G ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C59 ◁ C24×C59 ◁ C22×C22⋊C4×C59 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C59×#1819 | C2 | semidirect |
| 3. C59×#1462 | C2 | semidirect |
| 4. C59×#1344 | C2 | semidirect |
| 5. C59×#1343 | C2 | semidirect |
| 6. C2×#121×C59 | C4 | semidirect |
| 10. C59×#397 | C4 | semidirect |
| 14. C59×#392 | C4 | semidirect |
| 17. C59×#380 | C4 | semidirect |
| 173. #11799 | C59 | direct (N × H) |
| 215. #1819 | C2×C59 | semidirect |
| 216. #1462 | C2×C59 | semidirect |
| 217. #1344 | C2×C59 | semidirect |
| 218. #1343 | C2×C59 | semidirect |
| 229. C2×#121 | C4×C59 | semidirect |
| 233. #397 | C4×C59 | semidirect |
| 237. #392 | C4×C59 | semidirect |
| 240. #380 | C4×C59 | semidirect |
| 246. C59 | #11799 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C59×#2617 | 2 |
| C59×#1819 | 2 |
| C59×#1462 | 2 |
| C59×#1344 | 2 |
| C59×#1343 | 2 |
| #11799 | 59 |