Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
578 conjugacy classes of subgroups; only the 214 normal subgroups are shown.
This group has 578 conjugacy classes of subgroups — too many to draw. Only its 214 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 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C59 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C59 ◁ C2×C42×C59 ◁ C2×C4×C8×C59 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C59×#3169 | C2 | semidirect |
| 2. C59×#2224 | C2 | semidirect |
| 3. C59×#2215 | C2 | semidirect |
| 4. C59×#2206 | C2 | semidirect |
| 5. C2×C59×C4⋊C16 | C2 | semidirect |
| 81. C2×C4×C59 | D16 | semidirect |
| 90. #33811 | C59 | direct (N × H) |
| 104. #3169 | C2×C59 | semidirect |
| 105. #2224 | C2×C59 | semidirect |
| 106. #2215 | C2×C59 | semidirect |
| 107. #2206 | C2×C59 | semidirect |
| 108. C2×C4⋊C16 | C2×C59 | semidirect |
| 128. C59 | #33811 | direct (N × H) |
| 190. C2×C4 | D16×C59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C59×#3169 | 2 |
| C59×#2224 | 2 |
| C59×#2215 | 2 |
| C59×#2206 | 2 |
| C2×C59×C4⋊C16 | 2 |
| #33811 | 59 |