Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
500 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 102 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×#2631 | C2 |
| LCS | G ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C59 ◁ C22×C4×C59 ◁ C2×C4×D4×C59 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C4×#99×C59 | C2 | semidirect |
| 3. C59×#1459 | C2 | semidirect |
| 4. C59×#1351 | C2 | semidirect |
| 5. C59×#1343 | C2 | semidirect |
| 6. C2×#124×C59 | C4 | semidirect |
| 11. C59×#393 | C4 | semidirect |
| 14. C59×#392 | C4 | semidirect |
| 18. C59×#383 | C4 | semidirect |
| 157. #11730 | C59 | direct (N × H) |
| 191. C4×#99 | C2×C59 | semidirect |
| 192. #1459 | C2×C59 | semidirect |
| 193. #1351 | C2×C59 | semidirect |
| 194. #1343 | C2×C59 | semidirect |
| 203. C2×#124 | C4×C59 | semidirect |
| 208. #393 | C4×C59 | semidirect |
| 211. #392 | C4×C59 | semidirect |
| 215. #383 | C4×C59 | semidirect |
| 220. C59 | #11730 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C59×#2631 | 2 |
| C4×#99×C59 | 2 |
| C59×#1459 | 2 |
| C59×#1351 | 2 |
| C59×#1343 | 2 |
| #11730 | 59 |