Finite Group Databasebeta

← C3×#11925897⋊D5 #49137409

Subgroups — C3×#11925897⋊D5 #49137409

Order 36300.

200 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 46 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⋊#11925898C211yesmaximal, characteristic, complemented
2C3×C5⋊#11925894C211yesmaximal, characteristic, complemented
3C3×C5×#11925897C211yesmaximal, characteristic, complemented
4#11925897⋊D5C311yesmaximal, characteristic, direct product factor, Hall
5C3×C5×#10597244C2211yescharacteristic, complemented, Hall
6C3×D11×D55C511yesmaximal, characteristic, complemented
7C3×#11925894⋊C2—51nomaximal
8C5⋊#11925898C2×C311yescharacteristic, complemented
9C5⋊#11925894C2×C311yescharacteristic, complemented
10C5×#11925897C2×C311yescharacteristic, complemented
11C3×C5⋊(C11⋊D11)C2×C511yescharacteristic, complemented
12C3×C11×D55C2×C511yescharacteristic, complemented
13C3×C5×C11×D11C2×C511yescharacteristic, complemented
14C3×#11925898—51no—
15C3×#11925897—22no—
16C3×#11925897D511yescharacteristic, complemented
17C3×#11925894—51no—
18C2×C3×C5⋊AGL(1,𝔽11)—111nomaximal
19C3×D5×AGL(1,𝔽11)—111nomaximal
20C5×#10597244C22×C311yescharacteristic, complemented, Hall
21D11×D55C3×C511yescharacteristic, complemented
22#11925894⋊C2—51no—
23C3×C5×C112C22×C511yescharacteristic, complemented
24C3×#10597244—22no—
25C3×#10597244C2×D511yescharacteristic, complemented
26C2×C3×C5×C11⋊C5—111no—
27C3×C5⋊AGL(1,𝔽11)—111no—
28C3×C5⋊AGL(1,𝔽11)—111no—
29C3×C5⋊AGL(1,𝔽11)—111no—
30C3×D5×C11⋊C5—111no—
31C3×C5×AGL(1,𝔽11)—221no—
32C3×D112—51noHall
33C5⋊(C11⋊D11)C2×C3×C511yescharacteristic, complemented
34C11×D55C2×C3×C511yescharacteristic, complemented
35C5×C11×D11C2×C3×C511yescharacteristic, complemented
36#11925898—51no—
37#11925897—22no—
38#11925897C3×D511yescharacteristic, complemented
39#11925894—51no—
40C2×C5⋊AGL(1,𝔽11)—111no—
41D5×AGL(1,𝔽11)—111no—
42C3×C5×C11⋊C5—111no—
43C3×C5×C11⋊C5—221no—
44C3×C11⋊D11—51no—
45C3×C11×D11—51no—
46C3×C11×D11C5×D511yescharacteristic, complemented
47C2×C3×D55—111no—
48C3×D5×D11—111no—
49C2×C3×AGL(1,𝔽11)—551no—
50C2×C3×AGL(1,𝔽11)—551no—
51C5×C112C22×C3×C511yescharacteristic, complemented
52#10597244—22no—
53#10597244C2×C3×D511yescharacteristic, complemented
54C2×C5×C11⋊C5—111no—
55C5⋊AGL(1,𝔽11)—111no—
56C5⋊AGL(1,𝔽11)—111no—
57C5⋊AGL(1,𝔽11)—221no—
58D5×C11⋊C5—111no—
59C5×AGL(1,𝔽11)—111no—
60D112—51noHall
61C3×C112C2×C5×D511yescharacteristic, complemented, Hall
62C2×C3×C5×C11—111no—
63C3×D55—111no—
64C3×D55—111no—
65C3×D55—1101no—
66C3×D55AGL(1,𝔽11)11yescharacteristic, complemented
67C3×D5×C11—111no—
68C3×C5×D11AGL(1,𝔽11)11yescharacteristic, complemented
69C2×C3×C11⋊C5—111no—
70C2×C3×C11⋊C5—222no—
71C2×C3×C11⋊C5—551no—
72C3×AGL(1,𝔽11)—221no—
73C3×AGL(1,𝔽11)—222no—
74C3×AGL(1,𝔽11)—551no—
75C3×AGL(1,𝔽11)—551no—
76C3×AGL(1,𝔽11)—1101no—
77C2×C3×C5×D5—1211noHall
78C5×C11⋊C5—111no—
79C5×C11⋊C5—221no—
80C11⋊D11—51no—
81C11×D11—51no—
82C11×D11C3×C5×D511yescharacteristic, complemented
83C2×D55—111no—
84D5×D11—111no—
85C2×AGL(1,𝔽11)—551no—
86C2×AGL(1,𝔽11)—551no—
87C3×C5×C11—101no—
88C3×C5×C11C2×AGL(1,𝔽11)11yescharacteristic, complemented
89C3×C5×C11C2×AGL(1,𝔽11)11yescharacteristic, complemented
90C3×C11⋊C5—221no—
91C3×C11⋊C5—221no—
92C3×C11⋊C5—222no—
93C3×C11⋊C5—442no—
94C2×C3×C52—2421no—
95C3×C5×D5—1211no—
96C3×C5×D5—2421no—
97C2×C3×D11—551no—
98C2×C3×D11—551no—
99C112C2×C3×C5×D511yescharacteristic, complemented, Sylow
100C2×C5×C11—111no—
101D55—111no—
102D55—111no—
103D55—1101no—
104D55C3×AGL(1,𝔽11)11yescharacteristic, complemented
105C5×D11C3×AGL(1,𝔽11)11yescharacteristic, complemented
106D5×C11—111no—
107C2×C11⋊C5—111no—
108C2×C11⋊C5—222no—
109C2×C11⋊C5—551no—
110AGL(1,𝔽11)—111no—
111AGL(1,𝔽11)—222no—
112AGL(1,𝔽11)—551no—
113AGL(1,𝔽11)—551no—
114AGL(1,𝔽11)—1101no—
115C2×C5×D5—1211noHall
116C3×C52—4841noHall
117C2×C3×C11—111no—
118C2×C3×C11—551no—
119C3×D11—51no—
120C3×D11—5501no—
121C3×D11—551no—
122C3×D11—551no—
123C3×D11C5⋊AGL(1,𝔽11)11yescharacteristic, complemented
124C22×C3×C5—6051no—
125C2×C3×D5—1211no—
126C5×C11—101no—
127C5×C11C2×C3×AGL(1,𝔽11)11yescharacteristic, complemented
128C5×C11C2×C3×AGL(1,𝔽11)11yescharacteristic, complemented
129C11⋊C5—111no—
130C11⋊C5—221no—
131C11⋊C5—222no—
132C11⋊C5—442no—
133C2×C52—2421no—
134C5×D5—1211no—
135C5×D5—2421no—
136C2×D11—551no—
137C2×D11—551no—
138C3×C11—101no—
139C3×C11D5×AGL(1,𝔽11)11yescharacteristic, complemented
140C3×C11C2×C5⋊AGL(1,𝔽11)11yescharacteristic, complemented
141C2×C3×C5—111no—
142C2×C3×C5—6051no—
143C2×C3×C5—12101no—
144C2×C3×C5—2421no—
145C2×C3×C5—2422no—
146C3×D5—111no—
147C3×D5—1211no—
148C52—4841noSylow
149C2×C11—111no—
150C2×C11—551no—
151D11—51no—
152D11—5501no—
153D11—551no—
154D11—551no—
155D11C3×C5⋊AGL(1,𝔽11)11yescharacteristic, complemented
156C22×C5—6051no—
157C2×D5—1211no—
158C3×C5—4841no—
159C3×C5—4842no—
160C3×C5#11925894⋊C211yescharacteristic, complemented
161C22×C3—6051noHall
162C11—101no—
163C11C3×D5×AGL(1,𝔽11)11yescharacteristic, complemented
164C11C2×C3×C5⋊AGL(1,𝔽11)11yescharacteristic, complemented
165C2×C5—111no—
166C2×C5—6051no—
167C2×C5—12101no—
168C2×C5—2421no—
169C2×C5—2422no—
170D5—111no—
171D5—1211no—
172C2×C3—111no—
173C2×C3—551no—
174C2×C3—6051no—
175C5—4841no—
176C5—4842no—
177C5C3×#11925894⋊C211yescharacteristic, complemented
178C22—6051noSylow
179C3#11925897⋊D511yescharacteristic, direct product factor, Sylow
180C2—111no—
181C2—551no—
182C2—6051no—
subgroupG/H
center, hypercenterC3#11925897⋊D5
commutator, cosocle, hypocenterC5×C112C22×C3×C5
FrattiniC1G
Fitting, socleC3×C5×C112C22×C5
LCSG ▷ C5×C112
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. C3×C5⋊#11925898C2semidirect
2. C3×C5⋊#11925894C2semidirect
3. C3×C5×#11925897C2semidirect
4. #11925897⋊D5C3direct (N × H)
5. C3×C5×#10597244C22semidirect
6. C3×D11×D55C5semidirect
8. C5⋊#11925898C2×C3semidirect
9. C5⋊#11925894C2×C3semidirect
10. C5×#11925897C2×C3semidirect
11. C3×C5⋊(C11⋊D11)C2×C5semidirect
12. C3×C11×D55C2×C5semidirect
13. C3×C5×C11×D11C2×C5semidirect
16. C3×#11925897D5semidirect
20. C5×#10597244C22×C3semidirect
21. D11×D55C3×C5semidirect
23. C3×C5×C112C22×C5semidirect
25. C3×#10597244C2×D5semidirect
33. C5⋊(C11⋊D11)C2×C3×C5semidirect
34. C11×D55C2×C3×C5semidirect
35. C5×C11×D11C2×C3×C5semidirect
38. #11925897C3×D5semidirect
46. C3×C11×D11C5×D5semidirect
51. C5×C112C22×C3×C5semidirect
53. #10597244C2×C3×D5semidirect
61. C3×C112C2×C5×D5semidirect
66. C3×D55AGL(1,𝔽11)semidirect
68. C3×C5×D11AGL(1,𝔽11)semidirect
82. C11×D11C3×C5×D5semidirect
88. C3×C5×C11C2×AGL(1,𝔽11)semidirect
89. C3×C5×C11C2×AGL(1,𝔽11)semidirect
99. C112C2×C3×C5×D5semidirect
104. D55C3×AGL(1,𝔽11)semidirect
105. C5×D11C3×AGL(1,𝔽11)semidirect
123. C3×D11C5⋊AGL(1,𝔽11)semidirect
127. C5×C11C2×C3×AGL(1,𝔽11)semidirect
128. C5×C11C2×C3×AGL(1,𝔽11)semidirect
139. C3×C11D5×AGL(1,𝔽11)semidirect
140. C3×C11C2×C5⋊AGL(1,𝔽11)semidirect
155. D11C3×C5⋊AGL(1,𝔽11)semidirect
160. C3×C5#11925894⋊C2semidirect
163. C11C3×D5×AGL(1,𝔽11)semidirect
164. C11C2×C3×C5⋊AGL(1,𝔽11)semidirect
177. C5C3×#11925894⋊C2semidirect
179. C3#11925897⋊D5direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5⋊#119258982
C3×C5⋊#119258942
C3×C5×#119258972
#11925897⋊D53
C3×D11×D555
C3×#11925894⋊C25
C2×C3×C5⋊AGL(1,𝔽11)11
C3×D5×AGL(1,𝔽11)11