Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
456 conjugacy classes of subgroups; only the 162 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 162 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C59 | C2×C22⋊C4 |
| commutator | C22×C4 | C22×C4×C59 |
| Frattini, cosocle | C2×C42 | C23×C59 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C59 ◁ C43×C59 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 83. #8580 | C59 | direct (N × H) |
| 97. C4×C59 | #330 | semidirect |
| 118. C59 | #8580 | direct (N × H) |
| 199. C4 | C59×#330 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#125×C59 | 2 |
| C59×#1767 | 2 |
| C2×C59×#330 | 2 |
| C59×#1295 | 2 |
| #8580 | 59 |