Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
434 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 434 conjugacy classes of subgroups — too many to draw. Only its 106 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C59 | #99 |
| commutator | C22×C4 | C22×C4×C59 |
| Frattini, cosocle | C2×C4⋊C4 | C23×C59 |
| socle | C22×C59 | C2×#99 |
| prime radical | C22×D4×C59 | C2×C4 |
| LCS | G ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C59 ◁ C22×C4×C59 ◁ C2×C4×Q8×C59 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C4×#101×C59 | C2 | semidirect |
| 3. C59×#1461 | C2 | semidirect |
| 4. C59×#1353 | C2 | semidirect |
| 139. #11734 | C59 | direct (N × H) |
| 164. C4×#101 | C2×C59 | semidirect |
| 165. #1461 | C2×C59 | semidirect |
| 166. #1353 | C2×C59 | semidirect |
| 191. C59 | #11734 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C59×#2398 | 2 |
| C4×#101×C59 | 2 |
| C59×#1461 | 2 |
| C59×#1353 | 2 |
| C59×#1345 | 2 |
| #11734 | 59 |