Finite Group Databasebeta

← D5×(C11⋊C5)⋊D11 #27130926

Subgroups — D5×(C11⋊C5)⋊D11 #27130926

Order 12100.

116 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5⋊((C11⋊C5)⋊D11)C211yesmaximal, characteristic, complemented
2D5×C11×C11⋊C5C211yesmaximal, characteristic, complemented
3C5×(C11⋊C5)⋊D11C211yesmaximal, characteristic, complemented
4C5×C11×C11⋊C5C2211yescharacteristic, complemented, Hall
5D5×C11⋊D11C511yesmaximal, characteristic, complemented
6C2×(C11⋊C5)⋊D11—51nomaximal
7C5⋊(C11⋊D11)C2×C511yescharacteristic, complemented
8D5×C112C2×C511yescharacteristic, complemented
9C5×C11⋊D11C2×C511yescharacteristic, complemented
10C2×C11×C11⋊C5—51no—
11(C11⋊C5)⋊D11—22no—
12(C11⋊C5)⋊D11—51no—
13(C11⋊C5)⋊D11D511yescharacteristic, direct product factor
14C5×D5×D11—111nomaximal
15D5×AGL(1,𝔽11)—111nomaximal
16C5×C112C22×C511yescharacteristic, complemented
17C11×C11⋊C5—22no—
18C11×C11⋊C5C2×D511yescharacteristic, complemented
19C5×D55—111no—
20C5×D5×C11—111no—
21C52×D11—111no—
22C5⋊AGL(1,𝔽11)—111no—
23D5×C11⋊C5D1111yescharacteristic, complemented
24C5×AGL(1,𝔽11)—111no—
25C2×C11⋊D11—51noHall
26C52×C11—111no—
27C5×C11⋊C5C2×D1111yescharacteristic, complemented
28C2×C112—51no—
29C11⋊D11—51no—
30C11⋊D11C5×D511yescharacteristic, complemented
31C2×C5×D11—551no—
32D5×D11—111no—
33D5×D11—111no—
34D5×D11—552no—
35C2×AGL(1,𝔽11)—551no—
36C112C2×C5×D511yescharacteristic, complemented, Sylow
37C2×C5×C11—551no—
38D55—111no—
39D55—111no—
40D55—552no—
41C5×D11—111no—
42C5×D11—111no—
43C5×D11—111no—
44C5×D11—222no—
45C5×D11—551no—
46C5×D11—552no—
47D5×C11—52no—
48D5×C11AGL(1,𝔽11)11yescharacteristic, complemented
49D5×C11C5×D1111yescharacteristic, complemented
50C2×C11⋊C5—51no—
51AGL(1,𝔽11)—111no—
52AGL(1,𝔽11)—222no—
53AGL(1,𝔽11)—551no—
54C2×C5×D5—1211noHall
55C5×C11—52no—
56C5×C11—111no—
57C5×C11—222no—
58C5×C11C2×AGL(1,𝔽11)11yescharacteristic, complemented
59C5×C11C2×C5×D1111yescharacteristic, complemented
60C11⋊C5—22no—
61C11⋊C5D5×D1111yescharacteristic, complemented
62C2×C52—1211no—
63C5×D5—111no—
64C5×D5—1211no—
65C2×D11—2752no—
66C2×D11—551no—
67C2×D11—551no—
68C52—111noSylow
69C2×C11—51no—
70C2×C11—51no—
71C2×C11—252no—
72D11—111no—
73D11—111no—
74D11—2752no—
75D11—551no—
76D11—551no—
77D11—552no—
78C22×C5—6051no—
79C2×D5—1211no—
80C11—52no—
81C11D5×AGL(1,𝔽11)11yescharacteristic, complemented
82C11C5×D5×D1111yescharacteristic, complemented
83C2×C5—551no—
84C2×C5—6051no—
85C2×C5—1211no—
86C2×C5—1211no—
87C2×C5—2422no—
88D5—1211no—
89D5(C11⋊C5)⋊D1111yescharacteristic, direct product factor
90C5—111no—
91C5—222no—
92C5C2×(C11⋊C5)⋊D1111yescharacteristic, complemented
93C22—6051noSylow
94C2—51no—
95C2—6051no—
96C2—1211no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC5×C112C22×C5
LCSG ▷ C5×C112
UCSC1

Complements

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

NH ≅ G/Ntype
1. C5⋊((C11⋊C5)⋊D11)C2semidirect
2. D5×C11×C11⋊C5C2semidirect
3. C5×(C11⋊C5)⋊D11C2semidirect
4. C5×C11×C11⋊C5C22semidirect
5. D5×C11⋊D11C5semidirect
7. C5⋊(C11⋊D11)C2×C5semidirect
8. D5×C112C2×C5semidirect
9. C5×C11⋊D11C2×C5semidirect
13. (C11⋊C5)⋊D11D5direct (N × H)
16. C5×C112C22×C5semidirect
18. C11×C11⋊C5C2×D5semidirect
23. D5×C11⋊C5D11semidirect
27. C5×C11⋊C5C2×D11semidirect
30. C11⋊D11C5×D5semidirect
36. C112C2×C5×D5semidirect
48. D5×C11AGL(1,𝔽11)semidirect
49. D5×C11C5×D11semidirect
58. C5×C11C2×AGL(1,𝔽11)semidirect
59. C5×C11C2×C5×D11semidirect
61. C11⋊C5D5×D11semidirect
81. C11D5×AGL(1,𝔽11)semidirect
82. C11C5×D5×D11semidirect
89. D5(C11⋊C5)⋊D11direct (N × H)
92. C5C2×(C11⋊C5)⋊D11semidirect

Maximal subgroups

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

subgroupindex
C5⋊((C11⋊C5)⋊D11)2
D5×C11×C11⋊C52
C5×(C11⋊C5)⋊D112
D5×C11⋊D115
C2×(C11⋊C5)⋊D115
C5×D5×D1111
D5×AGL(1,𝔽11)11