Finite Group Databasebeta

← AGL(1,𝔽5)×C22⋊D11 #13183321

Subgroups — AGL(1,𝔽5)×C22⋊D11 #13183321

Order 1760.

188 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 188 conjugacy classes of subgroups — too many to draw. Only its 54 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×C11×AGL(1,𝔽5)C211yesmaximal, characteristic, complemented
2C2×AGL(1,𝔽5)×D11C211yesmaximal, characteristic, complemented
3D5×C22⋊D11C211yesmaximal, characteristic
4C22⋊(C11⋊AGL(1,𝔽5))C211yesmaximal, characteristic, complemented
5Dic11⋊AGL(1,𝔽5)C211yesmaximal, characteristic, complemented
6(C2×AGL(1,𝔽5))⋊D11C211yesmaximal, characteristic, complemented
7AGL(1,𝔽5)×Dic11C211yesmaximal, characteristic, complemented
8C22×D5×C11C2211yescharacteristic
9C2×D5×D11C2211yescharacteristic
10C2×C11⋊AGL(1,𝔽5)C2211yescharacteristic
11C2×C11⋊AGL(1,𝔽5)C2211yescharacteristic
12C2×C11×AGL(1,𝔽5)—22no—
13C2×C11×AGL(1,𝔽5)C2211yescharacteristic
14C2×C11×AGL(1,𝔽5)C2211yescharacteristic
15AGL(1,𝔽5)×D11—22no—
16C22⋊D55C411yescharacteristic, complemented
17C5×C22⋊D11C411yescharacteristic, complemented
18#89169C411yescharacteristic, complemented
19#89167C411yescharacteristic, complemented
20D5×Dic11C2211yescharacteristic
21C4×C22⋊D11—51nomaximal, Hall
22C22×C5×C11C2×C411yescharacteristic, complemented
23C2×D55C2×C411yescharacteristic, complemented
24C2×D5×C11—21no—
25C2×D5×C11—21no—
26C2×D5×C11C2×C411yescharacteristic, complemented
27C2×D5×C11C2311yescharacteristic
28C2×C5×D11C2×C411yescharacteristic, complemented
29D5×D11—21no—
30D5×D11—21no—
31C11⋊AGL(1,𝔽5)—21no—
32C11⋊AGL(1,𝔽5)—21no—
33C11×AGL(1,𝔽5)—21no—
34C11×AGL(1,𝔽5)D412yescomplemented
35Dic55C2×C411yescharacteristic, complemented
36C5×Dic11C2×C411yescharacteristic, complemented
37C22×C4×C11—51no—
38C2×C22⋊D11—51no—
39C2×C4×D11—51no—
40C22⋊Dic11—51no—
41(C2×D11)⋊C4—51no—
42Dic11⋊C4—51no—
43C4×Dic11—51no—
44D4×AGL(1,𝔽5)—111nomaximal, Hall
45C2×C5×C11—21no—
46C2×C5×C11C22×C411yescharacteristic
47D55—21no—
48C5×D11—21no—
49D5×C11—21no—
50D5×C11C2×D411yescharacteristic
51D5×C11#4111yescharacteristic
52C23×C11—51no—
53C22×D11—51no—
54C2×C4×C11—51no—
55C2×C4×C11—51no—
56C2×C4×C11—102no—
57C22⋊D11—51no—
58C22⋊D11—51no—
59C22⋊D11—51no—
60C22⋊D11AGL(1,𝔽5)11yescharacteristic, direct product factor
61C2×Dic11—51no—
62C2×Dic11—51no—
63C2×Dic11—51no—
64C4×D11—102no—
65C22×AGL(1,𝔽5)—111no—
66C22×AGL(1,𝔽5)D1111yescharacteristic, complemented
67D4×D5—111no—
68C22⋊AGL(1,𝔽5)—111no—
69C22⋊AGL(1,𝔽5)—111no—
70C4⋊AGL(1,𝔽5)—111no—
71C4×AGL(1,𝔽5)—111no—
72C5×C11C4×D411yescharacteristic, complemented, Hall
73C22×C11—51no—
74C22×C11—51no—
75C22×C11—101no—
76C22×C11—101no—
77C22×C11C2×AGL(1,𝔽5)11yescharacteristic, complemented
78C2×D11—51no—
79C2×D11—101no—
80C2×D11—101no—
81C2×D11C2×AGL(1,𝔽5)11yescharacteristic, complemented
82C4×C11—52no—
83C4×C11—101no—
84Dic11—51no—
85Dic11—101no—
86Dic11—101no—
87Dic11C2×AGL(1,𝔽5)11yescharacteristic, complemented
88C22×D5—111no—
89C22×D5C2×D1111yescharacteristic
90C2×AGL(1,𝔽5)—22no—
91C2×AGL(1,𝔽5)—111no—
92C2×AGL(1,𝔽5)—111no—
93C2×AGL(1,𝔽5)—222no—
94C2×AGL(1,𝔽5)C2×D1111yescharacteristic
95C2×AGL(1,𝔽5)C2×D1111yescharacteristic
96C5×D4—111no—
97C22⋊D5—111no—
98C22⋊D5—111no—
99D20—111no—
100C4×D5—111no—
101C4×D4—551noSylow
102C2×C11—21no—
103C2×C11—51no—
104C2×C11—51no—
105C2×C11—101no—
106C2×C11C22×AGL(1,𝔽5)11yescharacteristic
107D11—21no—
108D11—101no—
109C22×C5—111no—
110C22×C5C4×D1111yescharacteristic, complemented
111C2×D5—21no—
112C2×D5—21no—
113C2×D5—111no—
114C2×D5—221no—
115C2×D5—221no—
116C2×D5C4×D1111yescharacteristic, complemented
117C2×D5C22×D1111yescharacteristic
118AGL(1,𝔽5)—21no—
119AGL(1,𝔽5)—221no—
120AGL(1,𝔽5)—221no—
121AGL(1,𝔽5)C22⋊D1112yesdirect product factor
122C4×C5—111no—
123Dic5—111no—
124C2×D4—551no—
125C22×C4—51no—
126C22×C4—551no—
127C4⋊C4—551no—
128C22⋊C4—551no—
129C22⋊C4—551no—
130C42—551no—
131C11D4×AGL(1,𝔽5)11yescharacteristic, complemented, Sylow
132C2×C5—21no—
133C2×C5—221no—
134C2×C5C2×C4×D1111yescharacteristic
135D5—21no—
136D5—221no—
137D5#433911yescharacteristic
138D5C2×C22⋊D1111yescharacteristic
139C23—51no—
140C23—551no—
141D4—111no—
142D4—551no—
143D4—551no—
144D4—551no—
145C2×C4—51no—
146C2×C4—51no—
147C2×C4—102no—
148C2×C4—551no—
149C2×C4—551no—
150C2×C4—551no—
151C2×C4—1102no—
152C5C4×C22⋊D1111yescharacteristic, complemented, Sylow
153C22—51no—
154C22—51no—
155C22—101no—
156C22—101no—
157C22—111no—
158C22—551no—
159C22—1101no—
160C22—1101no—
161C22AGL(1,𝔽5)×D1111yescharacteristic, complemented
162C4—52no—
163C4—101no—
164C4—111no—
165C4—551no—
166C4—1101no—
167C4—1101no—
168C2—21no—
169C2—51no—
170C2—51no—
171C2—101no—
172C2—221no—
173C2—1101no—
174C2C2×AGL(1,𝔽5)×D1111yescharacteristic
subgroupG/H
center, FrattiniC2C2×AGL(1,𝔽5)×D11
commutator, socleC2×C5×C11C22×C4
FittingC22×C5×C11C2×C4
prime radicalD5×C22⋊D11C2
cosocleC2×D5×C11C23
hypercenterC22AGL(1,𝔽5)×D11
hypocenterC5×C11C4×D4
LCSG ▷ C2×C5×C11 ▷ C5×C11
UCSC1 ◁ C2 ◁ C22

Complements

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

NH ≅ G/Ntype
1. C22×C11×AGL(1,𝔽5)C2semidirect
2. C2×AGL(1,𝔽5)×D11C2semidirect
4. C22⋊(C11⋊AGL(1,𝔽5))C2semidirect
5. Dic11⋊AGL(1,𝔽5)C2semidirect
6. (C2×AGL(1,𝔽5))⋊D11C2semidirect
7. AGL(1,𝔽5)×Dic11C2semidirect
16. C22⋊D55C4semidirect
17. C5×C22⋊D11C4semidirect
18. #89169C4semidirect
19. #89167C4semidirect
22. C22×C5×C11C2×C4semidirect
23. C2×D55C2×C4semidirect
26. C2×D5×C11C2×C4semidirect
28. C2×C5×D11C2×C4semidirect
34. C11×AGL(1,𝔽5)D4semidirect
35. Dic55C2×C4semidirect
36. C5×Dic11C2×C4semidirect
60. C22⋊D11AGL(1,𝔽5)direct (N × H)
66. C22×AGL(1,𝔽5)D11semidirect
72. C5×C11C4×D4semidirect
77. C22×C11C2×AGL(1,𝔽5)semidirect
81. C2×D11C2×AGL(1,𝔽5)semidirect
87. Dic11C2×AGL(1,𝔽5)semidirect
110. C22×C5C4×D11semidirect
116. C2×D5C4×D11semidirect
121. AGL(1,𝔽5)C22⋊D11direct (N × H)
131. C11D4×AGL(1,𝔽5)semidirect
152. C5C4×C22⋊D11semidirect
161. 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×C11×AGL(1,𝔽5)2
C2×AGL(1,𝔽5)×D112
D5×C22⋊D112
C22⋊(C11⋊AGL(1,𝔽5))2
Dic11⋊AGL(1,𝔽5)2
(C2×AGL(1,𝔽5))⋊D112
AGL(1,𝔽5)×Dic112
C4×C22⋊D115
D4×AGL(1,𝔽5)11