Finite Group Databasebeta

← C2×(C11⋊C5)⋊D109 #37561845

Subgroups — C2×(C11⋊C5)⋊D109 #37561845

Order 23980.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1(C11⋊C5)⋊D109C211yesmaximal, characteristic, direct product factor
2(C11⋊C5)⋊D109C211yesmaximal, characteristic, direct product factor
3C2×C11⋊C5×C109C211yesmaximal, characteristic, complemented
4C11⋊C5×C109C2211yescharacteristic, complemented, Hall
5C2×D1199C511yesmaximal, characteristic, complemented, Hall
6C2×C11×C109C2×C511yescharacteristic, complemented
7D1199C2×C511yescharacteristic, complemented
8D1199C2×C511yescharacteristic, complemented
9C2×C5×D109—111nomaximal, Hall
10C11×C109C22×C511yescharacteristic, complemented, Hall
11C2×C5×C109—111no—
12C5×D109—111no—
13C5×D109—111no—
14C5×C109—111noHall
15C2×D109—551noHall
16C2×AGL(1,𝔽11)—1091nomaximal, Hall
17C2×C109AGL(1,𝔽11)11yescharacteristic, complemented
18D109—551no—
19D109—551no—
20C2×C11⋊C5D10911yescharacteristic, complemented
21AGL(1,𝔽11)—1091no—
22AGL(1,𝔽11)—1091no—
23C109C2×AGL(1,𝔽11)11yescharacteristic, complemented, Sylow
24C11⋊C5C2×D10911yescharacteristic, complemented, Hall
25C2×D11—1091noHall
26C2×C11C5×D10911yescharacteristic, complemented
27D11—1091no—
28D11—1091no—
29C22×C5—11991noHall
30C11C2×C5×D10911yescharacteristic, complemented, Sylow
31C2×C5—111no—
32C2×C5—11991no—
33C2×C5—11991no—
34C5—111noSylow
35C22—59951noSylow
36C2—59951no—
37C2—11991no—
38C2(C11⋊C5)⋊D10911yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2(C11⋊C5)⋊D109
commutator, cosocle, hypocenterC11×C109C22×C5
FrattiniC1G
Fitting, socleC2×C11×C109C2×C5
LCSG ▷ C11×C109
UCSC1 ◁ C2

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. (C11⋊C5)⋊D109C2direct (N × H)
2. (C11⋊C5)⋊D109C2direct (N × H)
3. C2×C11⋊C5×C109C2semidirect
4. C11⋊C5×C109C22semidirect
5. C2×D1199C5semidirect
6. C2×C11×C109C2×C5semidirect
7. D1199C2×C5semidirect
8. D1199C2×C5semidirect
10. C11×C109C22×C5semidirect
17. C2×C109AGL(1,𝔽11)semidirect
20. C2×C11⋊C5D109semidirect
23. C109C2×AGL(1,𝔽11)semidirect
24. C11⋊C5C2×D109semidirect
26. C2×C11C5×D109semidirect
30. C11C2×C5×D109semidirect
38. C2(C11⋊C5)⋊D109direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
(C11⋊C5)⋊D1092
C2×C11⋊C5×C1092
C2×D11995
C2×C5×D10911
C2×AGL(1,𝔽11)109