Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
410 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 138 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C8×C59 | #127 |
| commutator | C22×C4 | C22×C4×C59 |
| Frattini, cosocle | C22×C8 | C23×C59 |
| socle | C2×C59 | #1955 |
| prime radical | C59×#575 | C4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C8×C59 ◁ C22×C8×C59 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C59×#2151 | C2 | semidirect |
| 3. C59×#2117 | C2 | semidirect |
| 4. C59×#2113 | C2 | semidirect |
| 5. C59×#2110 | C2 | semidirect |
| 97. #13198 | C59 | direct (N × H) |
| 109. #2151 | C2×C59 | semidirect |
| 110. #2117 | C2×C59 | semidirect |
| 111. #2113 | C2×C59 | semidirect |
| 112. #2110 | C2×C59 | semidirect |
| 131. C59 | #13198 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C59×#2955 | 2 |
| C59×#2151 | 2 |
| C59×#2117 | 2 |
| C59×#2113 | 2 |
| C59×#2110 | 2 |
| #13198 | 59 |