Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
356 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 356 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 | #127 |
| commutator, Frattini, cosocle | C2×C42 | C23×C59 |
| socle | C22×C59 | #399 |
| prime radical | C22×D4×C59 | Q8 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C59 ◁ C2×C42×C59 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C59×#1838 | C2 | semidirect |
| 3. C59×#1571 | C2 | semidirect |
| 4. C59×#1570 | C2 | semidirect |
| 7. C59×#1275 | C2 | semidirect |
| 111. #10659 | C59 | direct (N × H) |
| 130. #1838 | C2×C59 | semidirect |
| 131. #1571 | C2×C59 | semidirect |
| 132. #1570 | C2×C59 | semidirect |
| 135. #1275 | C2×C59 | semidirect |
| 154. C59 | #10659 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C59×#1955 | 2 |
| C59×#1838 | 2 |
| C59×#1571 | 2 |
| C59×#1570 | 2 |
| C59×#1486 | 2 |
| C59×#1275 | 2 |
| #10659 | 59 |