Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
238 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 42 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C59 | #1343 |
| commutator | C22×C8 | C2×C4×C59 |
| Frattini, cosocle | #408 | C22×C59 |
| prime radical | C2×#41×C59 | D4 |
| LCS | G ▷ C22×C8 ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C59 ◁ C2×C4×C59 ◁ C22×C4×C59 ◁ C59×#408 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 5. C22×Q16×C59 | C4 | semidirect |
| 10. C59×#341 | C4 | semidirect |
| 80. #7399 | C59 | direct (N × H) |
| 100. C22×Q16 | C4×C59 | semidirect |
| 105. #341 | C4×C59 | semidirect |
| 106. C59 | #7399 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C59×#2020 | 2 |
| C59×#1391 | 2 |
| C59×#1321 | 2 |
| #7399 | 59 |