Finite Group Databasebeta

← C5×#11925894⋊C2 #27130886

Subgroups — C5×#11925894⋊C2 #27130886

Order 12100.

164 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#11925898C211yesmaximal, characteristic, complemented
2C5×#11925897C211yesmaximal, characteristic, complemented
3C5×#11925894C211yesmaximal, characteristic, complemented
4C5×#10597244C2211yescharacteristic, complemented, Hall
5C5×D112C511yesmaximal, characteristic, complemented
6#11925894⋊C2C515yesmaximal, direct product factor
7C5×C11⋊D11C2×C511yescharacteristic, complemented
8C5×C11×D11C2×C511yescharacteristic, complemented
9C5×C11×D11C2×C511yescharacteristic, complemented
10#11925898C2×C515yescomplemented
11#11925897C2×C515yescomplemented
12#11925894C2×C515yescomplemented
13C2×C5×AGL(1,𝔽11)—111nomaximal
14C2×C5×AGL(1,𝔽11)—111nomaximal
15C5×C112C22×C511yescharacteristic, complemented
16#10597244C22×C515yescomplemented
17C2×C5×C11⋊C5—111no—
18C2×C5×C11⋊C5—111no—
19C5×AGL(1,𝔽11)—111no—
20C5×AGL(1,𝔽11)—111no—
21C5×AGL(1,𝔽11)—111no—
22C5×AGL(1,𝔽11)—111no—
23D112C5211yescharacteristic, complemented, Hall
24C5×C11⋊C5—111no—
25C5×C11⋊C5—111no—
26C11⋊D11C2×C5211yescharacteristic, complemented
27C11×D11C2×C5211yescharacteristic, complemented
28C11×D11C2×C5211yescharacteristic, complemented
29C2×C5×D11—111no—
30C2×C5×D11—111no—
31C2×AGL(1,𝔽11)—115no—
32C2×AGL(1,𝔽11)—115no—
33C112C22×C5211yescharacteristic, complemented, Sylow
34C2×C5×C11—111no—
35C2×C5×C11—111no—
36C5×D11—111no—
37C5×D11—111no—
38C5×D11—1101no—
39C5×D11AGL(1,𝔽11)11yescharacteristic, complemented
40C5×D11AGL(1,𝔽11)11yescharacteristic, complemented
41C2×C11⋊C5—115no—
42C2×C11⋊C5—115no—
43AGL(1,𝔽11)—115no—
44AGL(1,𝔽11)—115no—
45AGL(1,𝔽11)—115no—
46AGL(1,𝔽11)—115no—
47C22×C52—1211noHall
48C5×C11—101no—
49C5×C11C2×AGL(1,𝔽11)11yescharacteristic, complemented
50C5×C11C2×AGL(1,𝔽11)11yescharacteristic, complemented
51C11⋊C5—115no—
52C11⋊C5—115no—
53C2×C52—1211no—
54C2×C52—1211no—
55C2×C52—1211no—
56C2×D11—111no—
57C2×D11—111no—
58C52—1211noSylow
59C2×C11—111no—
60C2×C11—111no—
61D11—111no—
62D11—111no—
63D11—1101no—
64D11C5×AGL(1,𝔽11)11yescharacteristic, complemented
65D11C5×AGL(1,𝔽11)11yescharacteristic, complemented
66C22×C5—1211no—
67C22×C5—1215no—
68C11—101no—
69C11C2×C5×AGL(1,𝔽11)11yescharacteristic, complemented
70C11C2×C5×AGL(1,𝔽11)11yescharacteristic, complemented
71C2×C5—111no—
72C2×C5—111no—
73C2×C5—1215no—
74C2×C5—1215no—
75C2×C5—1215no—
76C2×C5—1211no—
77C5—1215no—
78C5#11925894⋊C211yescharacteristic, direct product factor
79C22—1211noSylow
80C2—111no—
81C2—111no—
82C2—1211no—
subgroupG/H
center, hypercenterC5#11925894⋊C2
commutator, cosocle, hypocenterC112C22×C52
FrattiniC1G
Fitting, socleC5×C112C22×C5
LCSG ▷ C112
UCSC1 ◁ C5

Complements

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

NH ≅ G/Ntype
1. C5×#11925898C2semidirect
2. C5×#11925897C2semidirect
3. C5×#11925894C2semidirect
4. C5×#10597244C22semidirect
5. C5×D112C5semidirect
6. #11925894⋊C2C5direct (N × H)
7. C5×C11⋊D11C2×C5semidirect
8. C5×C11×D11C2×C5semidirect
9. C5×C11×D11C2×C5semidirect
10. #11925898C2×C5semidirect
11. #11925897C2×C5semidirect
12. #11925894C2×C5semidirect
15. C5×C112C22×C5semidirect
16. #10597244C22×C5semidirect
23. D112C52semidirect
26. C11⋊D11C2×C52semidirect
27. C11×D11C2×C52semidirect
28. C11×D11C2×C52semidirect
33. C112C22×C52semidirect
39. C5×D11AGL(1,𝔽11)semidirect
40. C5×D11AGL(1,𝔽11)semidirect
49. C5×C11C2×AGL(1,𝔽11)semidirect
50. C5×C11C2×AGL(1,𝔽11)semidirect
64. D11C5×AGL(1,𝔽11)semidirect
65. D11C5×AGL(1,𝔽11)semidirect
69. C11C2×C5×AGL(1,𝔽11)semidirect
70. C11C2×C5×AGL(1,𝔽11)semidirect
78. C5#11925894⋊C2direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#119258982
C5×#119258972
C5×#119258942
C5×D1125
#11925894⋊C25
C2×C5×AGL(1,𝔽11)11