Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
464 conjugacy classes of subgroups; only the 162 normal subgroups are shown.
This group has 464 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 | C22×C59 | C2×#99 |
| commutator | C2×C4 | C2×C42×C59 |
| Frattini, cosocle | C22×Q8 | C23×C59 |
| prime radical | C23×C59 | C2×C22⋊C4 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C59 ◁ C22×C4×C59 ◁ C2×C4×Q8×C59 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 16. C59×#356 | C4 | semidirect |
| 106. #12631 | C59 | direct (N × H) |
| 142. #356 | C4×C59 | semidirect |
| 144. C59 | #12631 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C59×#2327 | 2 |
| C2×C59×#356 | 2 |
| C4×#101×C59 | 2 |
| C59×#1394 | 2 |
| #12631 | 59 |