Finite Group Databasebeta

← D5×C3⋊((C11⋊C5)⋊D11) #49137491

Subgroups — D5×C3⋊((C11⋊C5)⋊D11) #49137491

Order 36300.

232 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 232 conjugacy classes of subgroups — too many to draw. Only its 44 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
1C3⋊(C5⋊((C11⋊C5)⋊D11))C211yesmaximal, characteristic, complemented
2C5×C3⋊((C11⋊C5)⋊D11)C211yesmaximal, characteristic, complemented
3C3×D5×C11×C11⋊C5C211yesmaximal, characteristic, complemented
4D5×(C11⋊C5)⋊D11—31nomaximal, Hall
5C3×C5×C11×C11⋊C5C2211yescharacteristic, complemented, Hall
6D5×C3⋊(C11⋊D11)C511yesmaximal, characteristic, complemented
7C2×C3⋊((C11⋊C5)⋊D11)—51nomaximal
8C5⋊((C11⋊C5)⋊D11)—31no—
9D5×C11×C11⋊C5D311yescharacteristic, complemented
10C5×(C11⋊C5)⋊D11—31no—
11C3⋊(C5⋊(C11⋊D11))C2×C511yescharacteristic, complemented
12C5×C3⋊(C11⋊D11)C2×C511yescharacteristic, complemented
13C3×D5×C112C2×C511yescharacteristic, complemented
14C2×C3×C11×C11⋊C5—51no—
15C3⋊((C11⋊C5)⋊D11)—22no—
16C3⋊((C11⋊C5)⋊D11)—51no—
17C3⋊((C11⋊C5)⋊D11)D511yescharacteristic, direct product factor
18C5×D5×D33—111nomaximal
19D5×C3⋊AGL(1,𝔽11)—111nomaximal
20C5×C11×C11⋊C5C2×D311yescharacteristic, complemented, Hall
21D5×C11⋊D11—31no—
22C2×(C11⋊C5)⋊D11—151no—
23C3×C5×C112C22×C511yescharacteristic, complemented
24C3×C11×C11⋊C5—22no—
25C3×C11×C11⋊C5C2×D511yescharacteristic, complemented
26C5×D165—111no—
27C52×D33—111no—
28C3×C5×D5×C11—221no—
29C3⋊(C5⋊AGL(1,𝔽11))—111no—
30C5×C3⋊AGL(1,𝔽11)—111no—
31C3×D5×C11⋊C5D1111yescharacteristic, complemented
32C2×C3⋊(C11⋊D11)—51noHall
33C5⋊(C11⋊D11)—31no—
34D5×C112C5×D311yescharacteristic, complemented
35C5×C11⋊D11—31no—
36C2×C11×C11⋊C5—51no—
37(C11⋊C5)⋊D11—31no—
38(C11⋊C5)⋊D11—62no—
39(C11⋊C5)⋊D11—151no—
40C5×D5×D11—331no—
41D5×AGL(1,𝔽11)—331no—
42C3×C52×C11—221no—
43C3×C5×C11⋊C5C2×D1111yescharacteristic, complemented
44C2×C3×C112—51no—
45C3⋊(C11⋊D11)—51no—
46C3⋊(C11⋊D11)C5×D511yescharacteristic, complemented
47C2×C5×D33—551no—
48D5×D33—111no—
49D5×D33—111no—
50D5×D33—552no—
51C2×C3⋊AGL(1,𝔽11)—551no—
52C5×C112C2×C5×D311yescharacteristic, complemented
53C11×C11⋊C5—22no—
54C11×C11⋊C5D3×D511yescharacteristic, complemented
55C5×D55—331no—
56C5×D5×C11—221no—
57C52×D11—331no—
58C5⋊AGL(1,𝔽11)—331no—
59D5×C11⋊C5D3311yescharacteristic, complemented
60C5×AGL(1,𝔽11)—331no—
61C2×C11⋊D11—151noHall
62C3×C112C2×C5×D511yescharacteristic, complemented, Hall
63C2×C3×C5×C11—1101no—
64D165—111no—
65D165—111no—
66D165—552no—
67C5×D33—111no—
68C5×D33—111no—
69C5×D33—111no—
70C5×D33—222no—
71C5×D33—551no—
72C5×D33—552no—
73C3×D5×C11—52no—
74C3×D5×C11AGL(1,𝔽11)11yescharacteristic, complemented
75C3×D5×C11C5×D1111yescharacteristic, complemented
76C2×C3×C11⋊C5—51no—
77C3⋊AGL(1,𝔽11)—111no—
78C3⋊AGL(1,𝔽11)—222no—
79C3⋊AGL(1,𝔽11)—551no—
80C5×D3×D5—1211noHall
81C52×C11—221no—
82C5×C11⋊C5C2×D3311yescharacteristic, complemented
83C2×C112—51no—
84C11⋊D11—31no—
85C11⋊D11—151no—
86C2×C5×D11—1651no—
87D5×D11—331no—
88D5×D11—331no—
89D5×D11—1652no—
90C2×AGL(1,𝔽11)—1651no—
91C3×C5×C11—52no—
92C3×C5×C11—221no—
93C3×C5×C11—442no—
94C3×C5×C11C2×AGL(1,𝔽11)11yescharacteristic, complemented
95C3×C5×C11C2×C5×D1111yescharacteristic, complemented
96C3×C11⋊C5—22no—
97C3×C11⋊C5D5×D1111yescharacteristic, complemented
98C5×D15—1211no—
99C52×D3—1211no—
100C3×C5×D5—221no—
101C2×D33—2752no—
102C2×D33—551no—
103C2×D33—551no—
104C112C5×D3×D511yescharacteristic, complemented, Sylow
105C2×C5×C11—1101no—
106D55—331no—
107D55—331no—
108D55—1652no—
109C5×D11—331no—
110C5×D11—331no—
111C5×D11—331no—
112C5×D11—662no—
113C5×D11—1651no—
114C5×D11—1652no—
115D5×C11—52no—
116D5×C11C3⋊AGL(1,𝔽11)11yescharacteristic, complemented
117D5×C11C5×D3311yescharacteristic, complemented
118C2×C11⋊C5—51no—
119AGL(1,𝔽11)—331no—
120AGL(1,𝔽11)—662no—
121AGL(1,𝔽11)—1651no—
122C2×C5×D5—3631noHall
123C3×C52—221noHall
124C2×C3×C11—51no—
125C2×C3×C11—51no—
126C2×C3×C11—252no—
127D33—111no—
128D33—111no—
129D33—2752no—
130D33—551no—
131D33—551no—
132D33—552no—
133C2×C5×D3—6051no—
134D3×D5—1211no—
135C5×C11—52no—
136C5×C11—221no—
137C5×C11—442no—
138C5×C11C2×C3⋊AGL(1,𝔽11)11yescharacteristic, complemented
139C5×C11C2×C5×D3311yescharacteristic, complemented
140C11⋊C5—22no—
141C11⋊C5D5×D3311yescharacteristic, complemented
142C2×C52—3631no—
143C5×D5—221no—
144C5×D5—3631no—
145C2×D11—8252no—
146C2×D11—1651no—
147C2×D11—1651no—
148C3×C11—52no—
149C3×C11D5×AGL(1,𝔽11)11yescharacteristic, complemented
150C3×C11C5×D5×D1111yescharacteristic, complemented
151C2×C3×C5—1101no—
152D15—1211no—
153C3×D5(C11⋊C5)⋊D1111yescharacteristic, complemented
154C5×D3—6051no—
155C5×D3—1211no—
156C5×D3—1211no—
157C5×D3—2422no—
158C52—221noSylow
159C2×C11—51no—
160C2×C11—51no—
161C2×C11—252no—
162D11—331no—
163D11—331no—
164D11—8252no—
165D11—1651no—
166D11—1651no—
167D11—1652no—
168C22×C5—18151no—
169C2×D5—3631no—
170C3×C5—221no—
171C3×C5—442no—
172C3×C5C2×(C11⋊C5)⋊D1111yescharacteristic, complemented
173C2×D3—6051noHall
174C11—52no—
175C11D5×C3⋊AGL(1,𝔽11)11yescharacteristic, complemented
176C11C5×D5×D3311yescharacteristic, complemented
177C2×C5—18151no—
178C2×C5—3631no—
179C2×C5—3631no—
180C2×C5—1101no—
181C2×C5—7262no—
182D5—3631no—
183D5C3⋊((C11⋊C5)⋊D11)11yescharacteristic, direct product factor
184C2×C3—51no—
185D3—6051no—
186D3—1211no—
187C5—221no—
188C5—442no—
189C5C2×C3⋊((C11⋊C5)⋊D11)11yescharacteristic, complemented
190C22—18151noSylow
191C3D5×(C11⋊C5)⋊D1111yescharacteristic, complemented, Sylow
192C2—51no—
193C2—18151no—
194C2—3631no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C5×C112C22×C5
LCSG ▷ C3×C5×C112
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3⋊(C5⋊((C11⋊C5)⋊D11))C2semidirect
2. C5×C3⋊((C11⋊C5)⋊D11)C2semidirect
3. C3×D5×C11×C11⋊C5C2semidirect
5. C3×C5×C11×C11⋊C5C22semidirect
6. D5×C3⋊(C11⋊D11)C5semidirect
9. D5×C11×C11⋊C5D3semidirect
11. C3⋊(C5⋊(C11⋊D11))C2×C5semidirect
12. C5×C3⋊(C11⋊D11)C2×C5semidirect
13. C3×D5×C112C2×C5semidirect
17. C3⋊((C11⋊C5)⋊D11)D5direct (N × H)
20. C5×C11×C11⋊C5C2×D3semidirect
23. C3×C5×C112C22×C5semidirect
25. C3×C11×C11⋊C5C2×D5semidirect
31. C3×D5×C11⋊C5D11semidirect
34. D5×C112C5×D3semidirect
43. C3×C5×C11⋊C5C2×D11semidirect
46. C3⋊(C11⋊D11)C5×D5semidirect
52. C5×C112C2×C5×D3semidirect
54. C11×C11⋊C5D3×D5semidirect
59. D5×C11⋊C5D33semidirect
62. C3×C112C2×C5×D5semidirect
74. C3×D5×C11AGL(1,𝔽11)semidirect
75. C3×D5×C11C5×D11semidirect
82. C5×C11⋊C5C2×D33semidirect
94. C3×C5×C11C2×AGL(1,𝔽11)semidirect
95. C3×C5×C11C2×C5×D11semidirect
97. C3×C11⋊C5D5×D11semidirect
104. C112C5×D3×D5semidirect
116. D5×C11C3⋊AGL(1,𝔽11)semidirect
117. D5×C11C5×D33semidirect
138. C5×C11C2×C3⋊AGL(1,𝔽11)semidirect
139. C5×C11C2×C5×D33semidirect
141. C11⋊C5D5×D33semidirect
149. C3×C11D5×AGL(1,𝔽11)semidirect
150. C3×C11C5×D5×D11semidirect
153. C3×D5(C11⋊C5)⋊D11semidirect
172. C3×C5C2×(C11⋊C5)⋊D11semidirect
175. C11D5×C3⋊AGL(1,𝔽11)semidirect
176. C11C5×D5×D33semidirect
183. D5C3⋊((C11⋊C5)⋊D11)direct (N × H)
189. C5C2×C3⋊((C11⋊C5)⋊D11)semidirect
191. C3D5×(C11⋊C5)⋊D11semidirect

Maximal subgroups

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

subgroupindex
C3⋊(C5⋊((C11⋊C5)⋊D11))2
C5×C3⋊((C11⋊C5)⋊D11)2
C3×D5×C11×C11⋊C52
D5×(C11⋊C5)⋊D113
D5×C3⋊(C11⋊D11)5
C2×C3⋊((C11⋊C5)⋊D11)5
C5×D5×D3311
D5×C3⋊AGL(1,𝔽11)11