Finite Group Databasebeta

← C3×D5×#11925894 #49137403

Subgroups — C3×D5×#11925894 #49137403

Order 36300.

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

normal subgroups only

This group has 232 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×D5×#10597244C211yesmaximal, characteristic, complemented
2C3×C5⋊#11925894C211yesmaximal, characteristic, complemented
3C3×C5×#11925894C211yesmaximal, characteristic, complemented
4D5×#11925894C311yesmaximal, characteristic, direct product factor, Hall
5C3×C5×#10597244C2211yescharacteristic, complemented, Hall
6C3×D5×C11⋊D11C511yesmaximal, characteristic, complemented
7C2×C3×#11925894—51nomaximal
8D5×#10597244C2×C311yescharacteristic, complemented
9C5⋊#11925894C2×C311yescharacteristic, complemented
10C5×#11925894C2×C311yescharacteristic, complemented
11C3×C5⋊(C11⋊D11)C2×C511yescharacteristic, complemented
12C3×D5×C112C2×C511yescharacteristic, complemented
13C3×C5×C11⋊D11C2×C511yescharacteristic, complemented
14C2×C3×#10597244—51no—
15C3×#11925894—21no—
16C3×#11925894—21no—
17C3×#11925894—51no—
18C3×#11925894D511yescharacteristic, direct product factor
19C3×D5×AGL(1,𝔽11)—111nomaximal
20C3×D5×AGL(1,𝔽11)—111nomaximal
21C5×#10597244C22×C311yescharacteristic, complemented, Hall
22D5×C11⋊D11C3×C511yescharacteristic, complemented
23C2×#11925894—51no—
24C3×C5×C112C22×C511yescharacteristic, complemented
25C3×#10597244—21no—
26C3×#10597244—21no—
27C3×#10597244C2×D511yescharacteristic, complemented
28C3×C5⋊AGL(1,𝔽11)—111no—
29C3×C5⋊AGL(1,𝔽11)—111no—
30C3×D5×C11⋊C5—221no—
31C3×D5×C11⋊C5—221no—
32C3×C5×AGL(1,𝔽11)—111no—
33C3×C5×AGL(1,𝔽11)—111no—
34C2×C3×C11⋊D11—51noHall
35C5⋊(C11⋊D11)C2×C3×C511yescharacteristic, complemented
36D5×C112C2×C3×C511yescharacteristic, complemented
37C5×C11⋊D11C2×C3×C511yescharacteristic, complemented
38C2×#10597244—51no—
39#11925894—21no—
40#11925894—21no—
41#11925894—51no—
42#11925894C3×D511yescharacteristic, direct product factor
43D5×AGL(1,𝔽11)—111no—
44D5×AGL(1,𝔽11)—111no—
45C3×C5×C11⋊C5—221no—
46C3×C5×C11⋊C5—221no—
47C2×C3×C112—51no—
48C3×C11⋊D11—51no—
49C3×C11⋊D11C5×D511yescharacteristic, complemented
50C3×D5×D11—111no—
51C3×D5×D11—111no—
52C3×D5×D11—552no—
53C2×C3×AGL(1,𝔽11)—551no—
54C2×C3×AGL(1,𝔽11)—551no—
55C5×C112C22×C3×C511yescharacteristic, complemented
56#10597244—21no—
57#10597244—21no—
58#10597244C2×C3×D511yescharacteristic, complemented
59C5⋊AGL(1,𝔽11)—111no—
60C5⋊AGL(1,𝔽11)—111no—
61D5×C11⋊C5—221no—
62D5×C11⋊C5—221no—
63C5×AGL(1,𝔽11)—111no—
64C5×AGL(1,𝔽11)—111no—
65C2×C11⋊D11—51noHall
66C3×C112C2×C5×D511yescharacteristic, complemented, Hall
67C3×D55—111no—
68C3×D55—111no—
69C3×D55—552no—
70C3×D5×C11—52no—
71C3×D5×C11AGL(1,𝔽11)11yescharacteristic, complemented
72C3×D5×C11AGL(1,𝔽11)11yescharacteristic, complemented
73C3×C5×D11—111no—
74C3×C5×D11—111no—
75C3×C5×D11—552no—
76C2×C3×C11⋊C5—1101no—
77C2×C3×C11⋊C5—1101no—
78C3×AGL(1,𝔽11)—111no—
79C3×AGL(1,𝔽11)—111no—
80C3×AGL(1,𝔽11)—221no—
81C3×AGL(1,𝔽11)—221no—
82C3×AGL(1,𝔽11)—221no—
83C3×AGL(1,𝔽11)—221no—
84C3×AGL(1,𝔽11)—551no—
85C3×AGL(1,𝔽11)—551no—
86C2×C3×C5×D5—1211noHall
87C5×C11⋊C5—221no—
88C5×C11⋊C5—221no—
89C2×C112—51no—
90C11⋊D11—51no—
91C11⋊D11C3×C5×D511yescharacteristic, complemented
92D5×D11—111no—
93D5×D11—111no—
94D5×D11—552no—
95C2×AGL(1,𝔽11)—551no—
96C2×AGL(1,𝔽11)—551no—
97C3×C5×C11—52no—
98C3×C5×C11C2×AGL(1,𝔽11)11yescharacteristic, complemented
99C3×C5×C11C2×AGL(1,𝔽11)11yescharacteristic, complemented
100C3×C11⋊C5—221no—
101C3×C11⋊C5—221no—
102C3×C11⋊C5—221no—
103C3×C11⋊C5—221no—
104C3×C11⋊C5—441no—
105C3×C11⋊C5—441no—
106C2×C3×C52—1211no—
107C3×C5×D5—1211no—
108C3×C5×D5—2421no—
109C2×C3×D11—2752no—
110C2×C3×D11—551no—
111C2×C3×D11—551no—
112C112C2×C3×C5×D511yescharacteristic, complemented, Sylow
113D55—111no—
114D55—111no—
115D55—552no—
116C5×D11—111no—
117C5×D11—111no—
118C5×D11—552no—
119D5×C11—52no—
120D5×C11C3×AGL(1,𝔽11)11yescharacteristic, complemented
121D5×C11C3×AGL(1,𝔽11)11yescharacteristic, complemented
122C2×C11⋊C5—1101no—
123C2×C11⋊C5—1101no—
124AGL(1,𝔽11)—111no—
125AGL(1,𝔽11)—111no—
126AGL(1,𝔽11)—221no—
127AGL(1,𝔽11)—221no—
128AGL(1,𝔽11)—221no—
129AGL(1,𝔽11)—221no—
130AGL(1,𝔽11)—551no—
131AGL(1,𝔽11)—551no—
132C2×C5×D5—1211noHall
133C3×C52—2421noHall
134C2×C3×C11—51no—
135C2×C3×C11—51no—
136C2×C3×C11—252no—
137C3×D11—111no—
138C3×D11—111no—
139C3×D11—2752no—
140C3×D11—551no—
141C3×D11—551no—
142C3×D11—552no—
143C22×C3×C5—6051no—
144C2×C3×D5—1211no—
145C5×C11—52no—
146C5×C11C2×C3×AGL(1,𝔽11)11yescharacteristic, complemented
147C5×C11C2×C3×AGL(1,𝔽11)11yescharacteristic, complemented
148C11⋊C5—221no—
149C11⋊C5—221no—
150C11⋊C5—221no—
151C11⋊C5—441no—
152C11⋊C5—441no—
153C11⋊C5—441no—
154C2×C52—1211no—
155C5×D5—1211no—
156C5×D5—2421no—
157C2×D11—2752no—
158C2×D11—551no—
159C2×D11—551no—
160C3×C11—52no—
161C3×C11D5×AGL(1,𝔽11)11yescharacteristic, complemented
162C3×C11D5×AGL(1,𝔽11)11yescharacteristic, complemented
163C2×C3×C5—6051no—
164C2×C3×C5—1211no—
165C2×C3×C5—1211no—
166C2×C3×C5—12101no—
167C2×C3×C5—2421no—
168C2×C3×C5—2421no—
169C3×D5—1211no—
170C3×D5#1192589411yescharacteristic, direct product factor
171C52—2421noSylow
172C2×C11—51no—
173C2×C11—51no—
174C2×C11—252no—
175D11—111no—
176D11—111no—
177D11—2752no—
178D11—551no—
179D11—551no—
180D11—552no—
181C22×C5—6051no—
182C2×D5—1211no—
183C3×C5—4841no—
184C3×C5—4841no—
185C3×C5—2421no—
186C3×C5C2×#1192589411yescharacteristic, complemented
187C22×C3—6051noHall
188C11—52no—
189C11C3×D5×AGL(1,𝔽11)11yescharacteristic, complemented
190C11C3×D5×AGL(1,𝔽11)11yescharacteristic, complemented
191C2×C5—6051no—
192C2×C5—1211no—
193C2×C5—1211no—
194C2×C5—12101no—
195C2×C5—2421no—
196C2×C5—2421no—
197D5—1211no—
198D5C3×#1192589411yescharacteristic, direct product factor
199C2×C3—51no—
200C2×C3—6051no—
201C2×C3—1211no—
202C5—4841no—
203C5—4841no—
204C5—2421no—
205C5C2×C3×#1192589411yescharacteristic, complemented
206C22—6051noSylow
207C3D5×#1192589411yescharacteristic, direct product factor, Sylow
208C2—51no—
209C2—6051no—
210C2—1211no—
subgroupG/H
center, hypercenterC3D5×#11925894
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⋊#11925894C2semidirect
3. C3×C5×#11925894C2semidirect
4. D5×#11925894C3direct (N × H)
5. C3×C5×#10597244C22semidirect
6. C3×D5×C11⋊D11C5semidirect
8. D5×#10597244C2×C3semidirect
9. C5⋊#11925894C2×C3semidirect
10. C5×#11925894C2×C3semidirect
11. C3×C5⋊(C11⋊D11)C2×C5semidirect
12. C3×D5×C112C2×C5semidirect
13. C3×C5×C11⋊D11C2×C5semidirect
18. C3×#11925894D5direct (N × H)
21. C5×#10597244C22×C3semidirect
22. D5×C11⋊D11C3×C5semidirect
24. C3×C5×C112C22×C5semidirect
27. C3×#10597244C2×D5semidirect
35. C5⋊(C11⋊D11)C2×C3×C5semidirect
36. D5×C112C2×C3×C5semidirect
37. C5×C11⋊D11C2×C3×C5semidirect
42. #11925894C3×D5direct (N × H)
49. C3×C11⋊D11C5×D5semidirect
55. C5×C112C22×C3×C5semidirect
58. #10597244C2×C3×D5semidirect
66. C3×C112C2×C5×D5semidirect
71. C3×D5×C11AGL(1,𝔽11)semidirect
72. C3×D5×C11AGL(1,𝔽11)semidirect
91. C11⋊D11C3×C5×D5semidirect
98. C3×C5×C11C2×AGL(1,𝔽11)semidirect
99. C3×C5×C11C2×AGL(1,𝔽11)semidirect
112. C112C2×C3×C5×D5semidirect
120. D5×C11C3×AGL(1,𝔽11)semidirect
121. D5×C11C3×AGL(1,𝔽11)semidirect
146. C5×C11C2×C3×AGL(1,𝔽11)semidirect
147. C5×C11C2×C3×AGL(1,𝔽11)semidirect
161. C3×C11D5×AGL(1,𝔽11)semidirect
162. C3×C11D5×AGL(1,𝔽11)semidirect
170. C3×D5#11925894direct (N × H)
186. C3×C5C2×#11925894semidirect
189. C11C3×D5×AGL(1,𝔽11)semidirect
190. C11C3×D5×AGL(1,𝔽11)semidirect
198. D5C3×#11925894direct (N × H)
205. C5C2×C3×#11925894semidirect
207. C3D5×#11925894direct (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⋊#119258942
C3×C5×#119258942
D5×#119258943
C3×D5×C11⋊D115
C2×C3×#119258945
C3×D5×AGL(1,𝔽11)11