Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
512 conjugacy classes of subgroups; only the 162 normal subgroups are shown.
This group has 512 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 | C22×D4×C59 | C2×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 |
|---|---|---|
| 3. C4×#101×C59 | C2 | semidirect |
| 4. C59×#1394 | C2 | semidirect |
| 16. C59×#355 | C4 | semidirect |
| 38. #101×C59 | C2×C4 | semidirect |
| 112. #12632 | C59 | direct (N × H) |
| 134. C4×#101 | C2×C59 | semidirect |
| 135. #1394 | C2×C59 | semidirect |
| 153. #355 | C4×C59 | semidirect |
| 155. C59 | #12632 | direct (N × H) |
| 176. #101 | C2×C4×C59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C59×#2326 | 2 |
| C2×C59×#355 | 2 |
| C4×#101×C59 | 2 |
| C59×#1394 | 2 |
| #12632 | 59 |