Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
600 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 600 conjugacy classes of subgroups — too many to draw. Only its 114 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C59 | #120 |
| commutator, Frattini, cosocle | C2×C42 | C23×C59 |
| prime radical | C59×#2819 | C2 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C59 ◁ C2×C42×C59 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C59×#489 | C2 | semidirect |
| 3. C59×#1960 | C2 | semidirect |
| 4. C2×C59×#329 | C2 | semidirect |
| 5. C59×#1295 | C2 | semidirect |
| 28. C4⋊Q8×C59 | D4 | semidirect |
| 44. #97×C59 | D4 | semidirect |
| 110. #10085 | C59 | direct (N × H) |
| 127. C2×#489 | C2×C59 | semidirect |
| 129. #1960 | C2×C59 | semidirect |
| 130. C2×#329 | C2×C59 | semidirect |
| 131. #1295 | C2×C59 | semidirect |
| 151. C59 | #10085 | direct (N × H) |
| 160. C4⋊Q8 | D4×C59 | semidirect |
| 176. #97 | D4×C59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C59×#489 | 2 |
| C59×#2819 | 2 |
| C59×#1960 | 2 |
| C2×C59×#329 | 2 |
| C59×#1295 | 2 |
| #10085 | 59 |