Finite Group Databasebeta

← C3×D5×#11925898 #49137402

Subgroups — C3×D5×#11925898 #49137402

Order 36300.

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

normal subgroups only

This group has 200 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
1C3×D5×#10597244C211yesmaximal, characteristic, complemented
2C3×C5⋊#11925898C211yesmaximal, characteristic, complemented
3C3×C5×#11925898C211yesmaximal, characteristic, complemented
4D5×#11925898C311yesmaximal, characteristic, direct product factor, Hall
5C3×C5×#10597244C2211yescharacteristic, complemented, Hall
6C3×D5×C11×D11C511yesmaximal, characteristic, complemented
7C2×C3×#11925898—51nomaximal
8D5×#10597244C2×C311yescharacteristic, complemented
9C5⋊#11925898C2×C311yescharacteristic, complemented
10C5×#11925898C2×C311yescharacteristic, complemented
11C3×C11×D55C2×C511yescharacteristic, complemented
12C3×D5×C112C2×C511yescharacteristic, complemented
13C3×C5×C11×D11C2×C511yescharacteristic, complemented
14C2×C3×#10597244—51no—
15C3×#11925898—21no—
16C3×#11925898—21no—
17C3×#11925898—51no—
18C3×#11925898D511yescharacteristic, direct product factor
19C2×C3×D5×C11⋊C5—111nomaximal
20C3×D5×AGL(1,𝔽11)—111nomaximal
21C5×#10597244C22×C311yescharacteristic, complemented, Hall
22D5×C11×D11C3×C511yescharacteristic, complemented
23C2×#11925898—51no—
24C3×C5×C112C22×C511yescharacteristic, complemented
25C3×#10597244—21no—
26C3×#10597244—21no—
27C3×#10597244C2×D511yescharacteristic, complemented
28C2×C3×C5×C11⋊C5—111no—
29C3×C5⋊AGL(1,𝔽11)—111no—
30C3×D5×C11⋊C5—111no—
31C3×D5×C11⋊C5—111no—
32C3×D5×C11⋊C5—221no—
33C3×C5×AGL(1,𝔽11)—111no—
34C2×C3×C11×D11—51noHall
35C11×D55C2×C3×C511yescharacteristic, complemented
36D5×C112C2×C3×C511yescharacteristic, complemented
37C5×C11×D11C2×C3×C511yescharacteristic, complemented
38C2×#10597244—51no—
39#11925898—21no—
40#11925898—21no—
41#11925898—51no—
42#11925898C3×D511yescharacteristic, direct product factor
43C2×D5×C11⋊C5—111no—
44D5×AGL(1,𝔽11)—111no—
45C3×C5×C11⋊C5—111no—
46C3×C5×C11⋊C5—221no—
47C2×C3×C112—51no—
48C3×C11×D11—51no—
49C3×C11×D11C5×D511yescharacteristic, complemented
50C2×C3×D5×C11—111no—
51C3×D5×D11C11⋊C511yescharacteristic, complemented
52C22×C3×C11⋊C5—551no—
53C2×C3×AGL(1,𝔽11)—551no—
54C5×C112C22×C3×C511yescharacteristic, complemented
55#10597244—21no—
56#10597244—21no—
57#10597244C2×C3×D511yescharacteristic, complemented
58C2×C5×C11⋊C5—111no—
59C5⋊AGL(1,𝔽11)—111no—
60D5×C11⋊C5—111no—
61D5×C11⋊C5—111no—
62D5×C11⋊C5—221no—
63C5×AGL(1,𝔽11)—111no—
64C2×C11×D11—51noHall
65C3×C112C2×C5×D511yescharacteristic, complemented, Hall
66C2×C3×C5×C11—111no—
67C3×D55C2×C11⋊C511yescharacteristic, complemented
68C3×D5×C11—101no—
69C3×D5×C11—111no—
70C3×D5×C11AGL(1,𝔽11)11yescharacteristic, complemented
71C3×D5×C11C2×C11⋊C511yescharacteristic, complemented
72C3×C5×D11C2×C11⋊C511yescharacteristic, complemented
73C2×C3×C11⋊C5—111no—
74C2×C3×C11⋊C5—221no—
75C2×C3×C11⋊C5—221no—
76C2×C3×C11⋊C5—551no—
77C2×C3×C11⋊C5—551no—
78C2×C3×C11⋊C5—1101no—
79C3×AGL(1,𝔽11)—111no—
80C3×AGL(1,𝔽11)—221no—
81C3×AGL(1,𝔽11)—221no—
82C3×AGL(1,𝔽11)—551no—
83C2×C3×C5×D5—1211noHall
84C5×C11⋊C5—111no—
85C5×C11⋊C5—221no—
86C2×C112—51no—
87C11×D11—51no—
88C11×D11C3×C5×D511yescharacteristic, complemented
89C2×D5×C11—111no—
90D5×D11C3×C11⋊C511yescharacteristic, complemented
91C22×C11⋊C5—551no—
92C2×AGL(1,𝔽11)—551no—
93C3×C5×C11—101no—
94C3×C5×C11C2×AGL(1,𝔽11)11yescharacteristic, complemented
95C3×C5×C11C22×C11⋊C511yescharacteristic, complemented
96C3×C11⋊C5—111no—
97C3×C11⋊C5—221no—
98C3×C11⋊C5—221no—
99C3×C11⋊C5—221no—
100C3×C11⋊C5—221no—
101C3×C11⋊C5—441no—
102C2×C3×C52—1211no—
103C3×C5×D5—1211no—
104C3×C5×D5—2421no—
105C22×C3×C11—551no—
106C2×C3×D11—51no—
107C112C2×C3×C5×D511yescharacteristic, complemented, Sylow
108C2×C5×C11—111no—
109D55C2×C3×C11⋊C511yescharacteristic, complemented
110C5×D11C2×C3×C11⋊C511yescharacteristic, complemented
111D5×C11—101no—
112D5×C11—111no—
113D5×C11C3×AGL(1,𝔽11)11yescharacteristic, complemented
114D5×C11C2×C3×C11⋊C511yescharacteristic, complemented
115C2×C11⋊C5—111no—
116C2×C11⋊C5—221no—
117C2×C11⋊C5—221no—
118C2×C11⋊C5—551no—
119C2×C11⋊C5—551no—
120C2×C11⋊C5—1101no—
121AGL(1,𝔽11)—111no—
122AGL(1,𝔽11)—221no—
123AGL(1,𝔽11)—221no—
124AGL(1,𝔽11)—551no—
125C2×C5×D5—1211noHall
126C3×C52—2421noHall
127C2×C3×C11—51no—
128C2×C3×C11—51no—
129C2×C3×C11—111no—
130C2×C3×C11—501no—
131C2×C3×C11—551no—
132C3×D11—51no—
133C3×D11D5×C11⋊C511yescharacteristic, complemented
134C22×C3×C5—6051no—
135C2×C3×D5—111no—
136C5×C11—101no—
137C5×C11C2×C3×AGL(1,𝔽11)11yescharacteristic, complemented
138C5×C11C22×C3×C11⋊C511yescharacteristic, complemented
139C11⋊C5—111no—
140C11⋊C5—221no—
141C11⋊C5—221no—
142C11⋊C5—221no—
143C11⋊C5—441no—
144C11⋊C5—441no—
145C2×C52—1211no—
146C5×D5—1211no—
147C5×D5—2421no—
148C22×C11—551no—
149C2×D11—51no—
150C3×C11—101no—
151C3×C11D5×AGL(1,𝔽11)11yescharacteristic, complemented
152C3×C11C2×D5×C11⋊C511yescharacteristic, complemented
153C2×C3×C5—111no—
154C2×C3×C5—6051no—
155C2×C3×C5—1211no—
156C2×C3×C5—12101no—
157C2×C3×C5—2421no—
158C2×C3×C5—2421no—
159C3×D5—111no—
160C3×D5#1192589811yescharacteristic, direct product factor
161C52—2421noSylow
162C2×C11—51no—
163C2×C11—51no—
164C2×C11—111no—
165C2×C11—501no—
166C2×C11—551no—
167D11—51no—
168D11C3×D5×C11⋊C511yescharacteristic, complemented
169C22×C5—6051no—
170C2×D5—111no—
171C3×C5—4841no—
172C3×C5—4841no—
173C3×C5—2421no—
174C3×C5C2×#1192589811yescharacteristic, complemented
175C22×C3—551noHall
176C11—101no—
177C11C3×D5×AGL(1,𝔽11)11yescharacteristic, complemented
178C11C2×C3×D5×C11⋊C511yescharacteristic, complemented
179C2×C5—111no—
180C2×C5—6051no—
181C2×C5—1211no—
182C2×C5—12101no—
183C2×C5—2421no—
184C2×C5—2421no—
185D5—111no—
186D5C3×#1192589811yescharacteristic, direct product factor
187C2×C3—51no—
188C2×C3—111no—
189C2×C3—551no—
190C5—4841no—
191C5—4841no—
192C5—2421no—
193C5C2×C3×#1192589811yescharacteristic, complemented
194C22—551noSylow
195C3D5×#1192589811yescharacteristic, direct product factor, Sylow
196C2—51no—
197C2—111no—
198C2—551no—
subgroupG/H
center, hypercenterC3D5×#11925898
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×D5×#10597244C2semidirect
2. C3×C5⋊#11925898C2semidirect
3. C3×C5×#11925898C2semidirect
4. D5×#11925898C3direct (N × H)
5. C3×C5×#10597244C22semidirect
6. C3×D5×C11×D11C5semidirect
8. D5×#10597244C2×C3semidirect
9. C5⋊#11925898C2×C3semidirect
10. C5×#11925898C2×C3semidirect
11. C3×C11×D55C2×C5semidirect
12. C3×D5×C112C2×C5semidirect
13. C3×C5×C11×D11C2×C5semidirect
18. C3×#11925898D5direct (N × H)
21. C5×#10597244C22×C3semidirect
22. D5×C11×D11C3×C5semidirect
24. C3×C5×C112C22×C5semidirect
27. C3×#10597244C2×D5semidirect
35. C11×D55C2×C3×C5semidirect
36. D5×C112C2×C3×C5semidirect
37. C5×C11×D11C2×C3×C5semidirect
42. #11925898C3×D5direct (N × H)
49. C3×C11×D11C5×D5semidirect
51. C3×D5×D11C11⋊C5semidirect
54. C5×C112C22×C3×C5semidirect
57. #10597244C2×C3×D5semidirect
65. C3×C112C2×C5×D5semidirect
67. C3×D55C2×C11⋊C5semidirect
70. C3×D5×C11AGL(1,𝔽11)semidirect
71. C3×D5×C11C2×C11⋊C5semidirect
72. C3×C5×D11C2×C11⋊C5semidirect
88. C11×D11C3×C5×D5semidirect
90. D5×D11C3×C11⋊C5semidirect
94. C3×C5×C11C2×AGL(1,𝔽11)semidirect
95. C3×C5×C11C22×C11⋊C5semidirect
107. C112C2×C3×C5×D5semidirect
109. D55C2×C3×C11⋊C5semidirect
110. C5×D11C2×C3×C11⋊C5semidirect
113. D5×C11C3×AGL(1,𝔽11)semidirect
114. D5×C11C2×C3×C11⋊C5semidirect
133. C3×D11D5×C11⋊C5semidirect
137. C5×C11C2×C3×AGL(1,𝔽11)semidirect
138. C5×C11C22×C3×C11⋊C5semidirect
151. C3×C11D5×AGL(1,𝔽11)semidirect
152. C3×C11C2×D5×C11⋊C5semidirect
160. C3×D5#11925898direct (N × H)
168. D11C3×D5×C11⋊C5semidirect
174. C3×C5C2×#11925898semidirect
177. C11C3×D5×AGL(1,𝔽11)semidirect
178. C11C2×C3×D5×C11⋊C5semidirect
186. D5C3×#11925898direct (N × H)
193. C5C2×C3×#11925898semidirect
195. C3D5×#11925898direct (N × H)

Maximal subgroups

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

subgroupindex
C3×D5×#105972442
C3×C5⋊#119258982
C3×C5×#119258982
D5×#119258983
C3×D5×C11×D115
C2×C3×#119258985
C2×C3×D5×C11⋊C511
C3×D5×AGL(1,𝔽11)11