Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
452 conjugacy classes of subgroups; only the 202 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 202 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 | C22×D16 |
| commutator, Frattini, cosocle | C16 | C24×C59 |
| LCS | G ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C59 ◁ #41×C59 ◁ #131×C59 ◁ C59×#504 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C59×#3417 | C2 | semidirect |
| 2. C59×#2264 | C2 | semidirect |
| 3. C59×#2262 | C2 | semidirect |
| 4. C2×C59×Q64 | C2 | semidirect |
| 5. C59×#2258 | C2 | semidirect |
| 54. #33984 | C59 | direct (N × H) |
| 60. #3417 | C2×C59 | semidirect |
| 61. #2264 | C2×C59 | semidirect |
| 62. #2262 | C2×C59 | semidirect |
| 63. C2×Q64 | C2×C59 | semidirect |
| 64. #2258 | C2×C59 | semidirect |
| 79. C59 | #33984 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C59×#3417 | 2 |
| C59×#2264 | 2 |
| C59×#2262 | 2 |
| C2×C59×Q64 | 2 |
| C59×#2258 | 2 |
| #33984 | 59 |