Finite Group Databasebeta

← D11×C22⋊AGL(1,𝔽5) #13183320

Subgroups — D11×C22⋊AGL(1,𝔽5) #13183320

Order 1760.

264 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 60 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D5×D11C211yesmaximal, characteristic
2C2×AGL(1,𝔽5)×D11C212yesmaximal, complemented
3C22⋊(C11⋊AGL(1,𝔽5))C211yesmaximal, characteristic, complemented
4C11×C22⋊AGL(1,𝔽5)C211yesmaximal, characteristic, complemented
5(C2×AGL(1,𝔽5))⋊D11C212yesmaximal, complemented
6C22×D55C411yescharacteristic, complemented
7C22×D5×C11C2211yescharacteristic
8C22×C5×D11C411yescharacteristic, complemented
9C2×D5×D11—24no—
10C2×D5×D11C411yescharacteristic, complemented
11C2×D5×D11C411yescharacteristic, complemented
12C2×D5×D11C2211yescharacteristic
13C2×D5×D11C2211yescharacteristic
14C2×C11⋊AGL(1,𝔽5)C2212yescomplemented
15C2×C11×AGL(1,𝔽5)C2212yescomplemented
16AGL(1,𝔽5)×D11—24no—
17C22⋊C4×D11—51nomaximal, Hall
18C22×C5×C11C2×C411yescharacteristic, complemented
19C2×D55—22no—
20C2×D55C2×C411yescharacteristic
21C2×D55C2×C411yescharacteristic, complemented
22C2×D5×C11—22no—
23C2×D5×C11C2×C411yescharacteristic, complemented
24C2×D5×C11C2311yescharacteristic
25C2×C5×D11—22no—
26C2×C5×D11C2×C411yescharacteristic
27C2×C5×D11C2×C411yescharacteristic, complemented
28D5×D11—22no—
29D5×D11—22no—
30D5×D11—22no—
31D5×D11D414yes—
32C11⋊AGL(1,𝔽5)—22no—
33C11×AGL(1,𝔽5)—22no—
34C23×D11—51no—
35C2×C4×D11—52no—
36C11×C22⋊C4—51no—
37C22⋊Dic11—51no—
38(C2×D11)⋊C4—52no—
39C2×C22⋊AGL(1,𝔽5)—111nomaximal, Hall
40C2×C5×C11—21no—
41C2×C5×C11C22×C411yescharacteristic
42D55—21no—
43D55C22⋊C412yescomplemented
44C5×D11—21no—
45C5×D11C22⋊C412yescomplemented
46D5×C11—21no—
47D5×C11C2×D412yes—
48C23×C11—51no—
49C22×D11—51no—
50C22×D11—51no—
51C22×D11—51no—
52C22×D11—51no—
53C22×D11—51no—
54C22×D11—104no—
55C22×D11AGL(1,𝔽5)11yescharacteristic, complemented
56C2×C4×C11—52no—
57C2×Dic11—52no—
58C4×D11—104no—
59C23×D5—111no—
60C22×AGL(1,𝔽5)—112no—
61C22⋊AGL(1,𝔽5)—111no—
62C22⋊AGL(1,𝔽5)—112no—
63C22⋊AGL(1,𝔽5)D1111yescharacteristic, direct product factor
64C5×C11C2×C22⋊C411yescharacteristic, complemented, Hall
65C22×C11—51no—
66C22×C11—51no—
67C22×C11—102no—
68C22×C11C2×AGL(1,𝔽5)11yescharacteristic, complemented
69C2×D11—22no—
70C2×D11—51no—
71C2×D11—54no—
72C2×D11—51no—
73C2×D11—102no—
74C2×D11—102no—
75C2×D11—102no—
76C2×D11—102no—
77C2×D11C2×AGL(1,𝔽5)11yescharacteristic
78C2×D11C2×AGL(1,𝔽5)11yescharacteristic, complemented
79C4×C11—102no—
80Dic11—102no—
81C23×C5—111no—
82C22×D5—111no—
83C22×D5—111no—
84C22×D5—111no—
85C22×D5—111no—
86C22×D5—111no—
87C22×D5—224no—
88C22×D5C2×D1111yescharacteristic
89C2×AGL(1,𝔽5)—112no—
90C2×AGL(1,𝔽5)—224no—
91C2×AGL(1,𝔽5)C2×D1112yescomplemented
92C2×C22⋊C4—551noSylow
93C2×C11—21no—
94C2×C11—52no—
95C2×C11—101no—
96C2×C11C22×AGL(1,𝔽5)11yescharacteristic
97D11—21no—
98D11—52no—
99D11—101no—
100D11C22⋊AGL(1,𝔽5)12yesdirect product factor
101C22×C5—111no—
102C22×C5—111no—
103C22×C5—222no—
104C22×C5C4×D1111yescharacteristic, complemented
105C2×D5—22no—
106C2×D5—111no—
107C2×D5—114no—
108C2×D5—111no—
109C2×D5—222no—
110C2×D5—222no—
111C2×D5—222no—
112C2×D5—222no—
113C2×D5C4×D1111yescharacteristic, complemented
114C2×D5C22×D1111yescharacteristic
115AGL(1,𝔽5)—22no—
116AGL(1,𝔽5)—222no—
117C24—551no—
118C22×C4—552no—
119C22⋊C4—51no—
120C22⋊C4—552no—
121C22⋊C4—551no—
122C11C2×C22⋊AGL(1,𝔽5)11yescharacteristic, complemented, Sylow
123C2×C5—21no—
124C2×C5—112no—
125C2×C5—221no—
126C2×C5C2×C4×D1111yescharacteristic
127D5—21no—
128D5—112no—
129D5—221no—
130D5D4×D1112yes—
131C23—51no—
132C23—111no—
133C23—551no—
134C23—551no—
135C23—551no—
136C23—551no—
137C23—551no—
138C23—1104no—
139C2×C4—52no—
140C2×C4—552no—
141C2×C4—1104no—
142C5C22⋊C4×D1111yescharacteristic, complemented, Sylow
143C22—51no—
144C22—51no—
145C22—102no—
146C22—111no—
147C22—111no—
148C22—222no—
149C22—554no—
150C22—551no—
151C22—551no—
152C22—1102no—
153C22—1102no—
154C22—1102no—
155C22—1102no—
156C22AGL(1,𝔽5)×D1111yescharacteristic, complemented
157C4—102no—
158C4—1102no—
159C2—21no—
160C2—52no—
161C2—101no—
162C2—112no—
163C2—221no—
164C2—552no—
165C2—1101no—
166C2C2×AGL(1,𝔽5)×D1111yescharacteristic
subgroupG/H
center, FrattiniC2C2×AGL(1,𝔽5)×D11
commutator, socleC2×C5×C11C22×C4
FittingC22×C5×C11C2×C4
prime radicalC22×D5×D11C2
cosocleC2×D5×C11C23
hypercenterC22AGL(1,𝔽5)×D11
hypocenterC5×C11C2×C22⋊C4
LCSG ▷ C2×C5×C11 ▷ C5×C11
UCSC1 ◁ C2 ◁ C22

Complements

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

NH ≅ G/Ntype
2. C2×AGL(1,𝔽5)×D11C2semidirect
3. C22⋊(C11⋊AGL(1,𝔽5))C2semidirect
4. C11×C22⋊AGL(1,𝔽5)C2semidirect
5. (C2×AGL(1,𝔽5))⋊D11C2semidirect
6. C22×D55C4semidirect
8. C22×C5×D11C4semidirect
10. C2×D5×D11C4semidirect
11. C2×D5×D11C4semidirect
14. C2×C11⋊AGL(1,𝔽5)C22semidirect
15. C2×C11×AGL(1,𝔽5)C22semidirect
18. C22×C5×C11C2×C4semidirect
21. C2×D55C2×C4semidirect
23. C2×D5×C11C2×C4semidirect
27. C2×C5×D11C2×C4semidirect
43. D55C22⋊C4semidirect
45. C5×D11C22⋊C4semidirect
55. C22×D11AGL(1,𝔽5)semidirect
63. C22⋊AGL(1,𝔽5)D11direct (N × H)
64. C5×C11C2×C22⋊C4semidirect
68. C22×C11C2×AGL(1,𝔽5)semidirect
78. C2×D11C2×AGL(1,𝔽5)semidirect
91. C2×AGL(1,𝔽5)C2×D11semidirect
100. D11C22⋊AGL(1,𝔽5)direct (N × H)
104. C22×C5C4×D11semidirect
113. C2×D5C4×D11semidirect
122. C11C2×C22⋊AGL(1,𝔽5)semidirect
142. C5C22⋊C4×D11semidirect
156. C22AGL(1,𝔽5)×D11semidirect

Maximal subgroups

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

subgroupindex
C22×D5×D112
C2×AGL(1,𝔽5)×D112
C22⋊(C11⋊AGL(1,𝔽5))2
C11×C22⋊AGL(1,𝔽5)2
(C2×AGL(1,𝔽5))⋊D112
C22⋊C4×D115
C2×C22⋊AGL(1,𝔽5)11