Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
624 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 624 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 | C4×C59 | B(4,𝔽2) |
| commutator | C2×D4 | C22×C4×C59 |
| Frattini, cosocle | C2×#41 | C23×C59 |
| socle | C2×C59 | #1889 |
| prime radical | C59×#3018 | C2 |
| LCS | G ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C59 ◁ C2×C4×C59 ◁ C2×#41×C59 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C59×#2980 | C2 | semidirect |
| 3. C59×#2132 | C2 | semidirect |
| 4. C59×#1791 | C2 | semidirect |
| 5. C59×#1392 | C2 | semidirect |
| 169. #13052 | C59 | direct (N × H) |
| 189. #2980 | C2×C59 | semidirect |
| 190. #2132 | C2×C59 | semidirect |
| 191. #1791 | C2×C59 | semidirect |
| 192. #1392 | C2×C59 | semidirect |
| 218. C59 | #13052 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C59×#3018 | 2 |
| C59×#2980 | 2 |
| C59×#2132 | 2 |
| C59×#1791 | 2 |
| C59×#1392 | 2 |
| #13052 | 59 |