Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
888 conjugacy classes of subgroups; only the 150 normal subgroups are shown.
This group has 888 conjugacy classes of subgroups — too many to draw. Only its 150 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 | #379 |
| commutator | C42 | C22×C4×C59 |
| Frattini, cosocle | C2×C42 | C23×C59 |
| prime radical | C59×#3549 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C59 ◁ C2×C42×C59 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C59×#1962 | C2 | semidirect |
| 3. C59×#1560 | C2 | semidirect |
| 4. C59×H(3,𝔽4) | C4 | semidirect |
| 9. C59×#423 | C22 | semidirect |
| 11. C43×C59 | C22 | semidirect |
| 73. #8530 | C59 | direct (N × H) |
| 85. #1962 | C2×C59 | semidirect |
| 86. #1560 | C2×C59 | semidirect |
| 90. H(3,𝔽4) | C4×C59 | semidirect |
| 95. #423 | C22×C59 | semidirect |
| 97. C43 | C22×C59 | semidirect |
| 100. C59 | #8530 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C59×#3549 | 2 |
| C59×#1962 | 2 |
| C59×#1560 | 2 |
| #8530 | 59 |