Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
1630 conjugacy classes of subgroups; only the 366 normal subgroups are shown.
This group has 1630 conjugacy classes of subgroups — too many to draw. Only its 366 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 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C59 |
| prime radical | C25×C59 | D4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C59 ◁ C24×C4×C59 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C59×#467 | C2 | semidirect |
| 4. C59×#1892 | C2 | semidirect |
| 5. C59×#1808 | C2 | semidirect |
| 7. C22×Q16×C59 | C22 | semidirect |
| 13. C2×#107×C59 | C22 | semidirect |
| 14. C2×#103×C59 | C22 | semidirect |
| 18. C59×#340 | C22 | semidirect |
| 44. C24×C59 | Q16 | semidirect |
| 95. #32931 | C59 | direct (N × H) |
| 101. C22×C59 | #467 | semidirect |
| 111. C2×#467 | C2×C59 | semidirect |
| 113. #1892 | C2×C59 | semidirect |
| 114. #1808 | C2×C59 | semidirect |
| 120. C22×Q16 | C22×C59 | semidirect |
| 126. C2×#107 | C22×C59 | semidirect |
| 127. C2×#103 | C22×C59 | semidirect |
| 131. #340 | C22×C59 | semidirect |
| 132. C59 | #32931 | direct (N × H) |
| 158. C24 | Q16×C59 | semidirect |
| 214. C22 | C59×#467 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×C8×C59 | 2 |
| C2×C59×#467 | 2 |
| C59×#2848 | 2 |
| C59×#1892 | 2 |
| C59×#1808 | 2 |
| #32931 | 59 |