Finite Group Databasebeta

← #49137518

Subgroups — #49137518

Order 36300.

352 conjugacy classes of subgroups; only the 35 normal subgroups are shown.

normal subgroups only

This group has 352 conjugacy classes of subgroups — too many to draw. Only its 35 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⋊#11925895)C211yesmaximal, characteristic, complemented
2C5×C3⋊#11925892C211yesmaximal, characteristic, complemented
3C3×C5⋊#11925895C211yesmaximal, characteristic, complemented
4#27130913—31nomaximal, Hall
5C3×C5×#10597243C2211yescharacteristic, complemented, Hall
6D55⋊D33C511yesmaximal, characteristic, complemented
7#11925895⋊D3—51nomaximal
8C5⋊#11925895—31no—
9C5⋊#11925895D311yescharacteristic, complemented
10C5×#11925892—31no—
11C11×D165C2×C511yescharacteristic, complemented
12C5×C3⋊(C11⋊D11)C2×C511yescharacteristic, complemented
13C3×C11×D55C2×C511yescharacteristic, complemented
14C3⋊#11925895—51no—
15C3⋊#11925892—21no—
16C3⋊#11925892—21no—
17C3⋊#11925892D511yescharacteristic, complemented
18C3×#11925895—51no—
19D15⋊AGL(1,𝔽11)—111nomaximal
20D5×C3⋊AGL(1,𝔽11)—111nomaximal
21C5×#10597243C2×D311yescharacteristic, complemented, Hall
22D55⋊D11—31no—
23#11925892⋊C2—151no—
24C3×C5×C112C22×C511yescharacteristic, complemented
25C3×#10597243—21no—
26C3×#10597243—21no—
27C3×#10597243C2×D511yescharacteristic, complemented
28C3⋊(C5⋊AGL(1,𝔽11))—221no—
29D15×C11⋊C5—111no—
30C5×C3⋊AGL(1,𝔽11)—111no—
31C5×C3⋊AGL(1,𝔽11)—111no—
32C5×C3⋊AGL(1,𝔽11)—221no—
33C5×C3⋊AGL(1,𝔽11)—222no—
34C5×C3⋊AGL(1,𝔽11)—221no—
35C5×C3⋊AGL(1,𝔽11)—221no—
36C3×C5⋊AGL(1,𝔽11)—221no—
37C3×D5×C11⋊C5—111no—
38D11×D33—51noHall
39C11×D55—31no—
40C11×D55C5×D311yescharacteristic, complemented
41C5×C11⋊D11—31no—
42#11925895—51no—
43#11925895—151no—
44#11925892—31no—
45#11925892—61no—
46#11925892—61no—
47D5×AGL(1,𝔽11)—331no—
48D5×AGL(1,𝔽11)—331no—
49C3×C5×C11⋊C5—221no—
50C3×C5×C11⋊C5—221no—
51C3×C5×C11⋊C5—221no—
52C3×C5×C11⋊C5—442no—
53C3×C5×C11⋊C5—441no—
54C3×C5×C11⋊C5—441no—
55C3⋊(C11⋊D11)C5×D511yescharacteristic, complemented
56C11×D33—51no—
57C3×C11×D11—51no—
58D15⋊D11—111no—
59D5×D33—111no—
60C2×C3⋊AGL(1,𝔽11)—551no—
61D3×AGL(1,𝔽11)—551no—
62C5×C112C2×C5×D311yescharacteristic, complemented
63#10597243—21no—
64#10597243—21no—
65#10597243D3×D511yescharacteristic, complemented
66C5⋊AGL(1,𝔽11)—221no—
67C5⋊AGL(1,𝔽11)—661no—
68D5×C11⋊C5—111no—
69D5×C11⋊C5—331no—
70C5×AGL(1,𝔽11)—331no—
71C5×AGL(1,𝔽11)—331no—
72C5×AGL(1,𝔽11)—661no—
73C5×AGL(1,𝔽11)—661no—
74C5×AGL(1,𝔽11)—661no—
75C5×AGL(1,𝔽11)—662no—
76D112—151noHall
77C3×C112C2×C5×D511yescharacteristic, complemented, Hall
78D165AGL(1,𝔽11)11yescharacteristic, complemented
79C11×D15—111no—
80C5×D33—111no—
81C5×D33—111no—
82C5×D33—221no—
83C5×D33—222no—
84C5×D33—221no—
85C5×D33—221no—
86C3×D55AGL(1,𝔽11)11yescharacteristic, complemented
87C3×D5×C11—111no—
88C2×C3×C11⋊C5—551no—
89C3⋊AGL(1,𝔽11)—111no—
90C3⋊AGL(1,𝔽11)—111no—
91C3⋊AGL(1,𝔽11)—221no—
92C3⋊AGL(1,𝔽11)—221no—
93C3⋊AGL(1,𝔽11)—221no—
94C3⋊AGL(1,𝔽11)—221no—
95C3⋊AGL(1,𝔽11)—221no—
96C3⋊AGL(1,𝔽11)—222no—
97C3⋊AGL(1,𝔽11)—221no—
98C3⋊AGL(1,𝔽11)—221no—
99C3⋊AGL(1,𝔽11)—222no—
100C3⋊AGL(1,𝔽11)—221no—
101C3⋊AGL(1,𝔽11)—221no—
102C3⋊AGL(1,𝔽11)—222no—
103C3⋊AGL(1,𝔽11)—222no—
104C3⋊AGL(1,𝔽11)—222no—
105C3⋊AGL(1,𝔽11)—224no—
106C3⋊AGL(1,𝔽11)—221no—
107C3⋊AGL(1,𝔽11)—222no—
108C3⋊AGL(1,𝔽11)—222no—
109C3⋊AGL(1,𝔽11)—221no—
110C3⋊AGL(1,𝔽11)—1101no—
111D3×C11⋊C5—551no—
112C3×AGL(1,𝔽11)—1101no—
113C5×D3×D5—1211noHall
114C5×C11⋊C5—221no—
115C5×C11⋊C5—221no—
116C5×C11⋊C5—441no—
117C5×C11⋊C5—441no—
118C5×C11⋊C5—441no—
119C5×C11⋊C5—442no—
120C11⋊D11—31no—
121C11×D11—51no—
122C11×D11—151no—
123D5×D11—331no—
124D5×D11—331no—
125C2×AGL(1,𝔽11)—1651no—
126C2×AGL(1,𝔽11)—1651no—
127C3×C5×C11—21no—
128C3×C5×C11—22no—
129C3×C5×C11—21no—
130C3×C5×C11—21no—
131C3×C5×C11C2×AGL(1,𝔽11)11yescharacteristic, complemented
132C3×C5×C11C2×AGL(1,𝔽11)11yescharacteristic, complemented
133C3×C11⋊C5—221no—
134C3×C11⋊C5—221no—
135C3×C11⋊C5—222no—
136C3×C11⋊C5—441no—
137C3×C11⋊C5—441no—
138C3×C11⋊C5—441no—
139C3×C11⋊C5—441no—
140C3×C11⋊C5—442no—
141C3×C11⋊C5—441no—
142C3×C11⋊C5—441no—
143C3×C11⋊C5—442no—
144C3×C11⋊C5—442no—
145C3×C11⋊C5—442no—
146C3×C11⋊C5—441no—
147C3×C11⋊C5—442no—
148C3×C11⋊C5—444no—
149C3×C11⋊C5—442no—
150C3×C11⋊C5—441no—
151C3×C11⋊C5—441no—
152C3×C11⋊C5—441no—
153C3×C11⋊C5—441no—
154C5×D15—2421no—
155C52×D3—1211no—
156C3×C5×D5—2421no—
157C2×D33—551no—
158D3×D11—551no—
159C112C5×D3×D511yescharacteristic, complemented, Sylow
160D55—31no—
161D55C3⋊AGL(1,𝔽11)11yescharacteristic, complemented
162C5×D11—331no—
163C5×D11—331no—
164C5×D11—661no—
165C5×D11—661no—
166C5×D11—661no—
167C5×D11—662no—
168D5×C11—111no—
169D5×C11—331no—
170C2×C11⋊C5—551no—
171C2×C11⋊C5—1651no—
172AGL(1,𝔽11)—331no—
173AGL(1,𝔽11)—331no—
174AGL(1,𝔽11)—661no—
175AGL(1,𝔽11)—661no—
176AGL(1,𝔽11)—661no—
177AGL(1,𝔽11)—662no—
178AGL(1,𝔽11)—661no—
179AGL(1,𝔽11)—661no—
180AGL(1,𝔽11)—661no—
181AGL(1,𝔽11)—661no—
182AGL(1,𝔽11)—661no—
183AGL(1,𝔽11)—661no—
184AGL(1,𝔽11)—662no—
185AGL(1,𝔽11)—661no—
186AGL(1,𝔽11)—662no—
187AGL(1,𝔽11)—662no—
188AGL(1,𝔽11)—662no—
189AGL(1,𝔽11)—662no—
190AGL(1,𝔽11)—661no—
191AGL(1,𝔽11)—662no—
192AGL(1,𝔽11)—664no—
193AGL(1,𝔽11)—1101no—
194AGL(1,𝔽11)—1651no—
195C2×C5×D5—3631noHall
196C3×C52—2421noHall
197C2×C3×C11—551no—
198D33—51no—
199D33—111no—
200D33—111no—
201D33—222no—
202D33—221no—
203D33—221no—
204D33—221no—
205C3×D11—51no—
206D3×C11—551no—
207C2×C5×D3—6051no—
208D3×D5—1211no—
209C5×C11—21no—
210C5×C11—21no—
211C5×C11—21no—
212C5×C11—22no—
213C5×C11D3×AGL(1,𝔽11)11yescharacteristic, complemented
214C5×C11C2×C3⋊AGL(1,𝔽11)11yescharacteristic, complemented
215C11⋊C5—111no—
216C11⋊C5—221no—
217C11⋊C5—221no—
218C11⋊C5—221no—
219C11⋊C5—221no—
220C11⋊C5—442no—
221C11⋊C5—441no—
222C11⋊C5—442no—
223C11⋊C5—442no—
224C11⋊C5—442no—
225C11⋊C5—442no—
226C11⋊C5—441no—
227C11⋊C5—442no—
228C11⋊C5—444no—
229C11⋊C5—441no—
230C11⋊C5—441no—
231C11⋊C5—441no—
232C11⋊C5—442no—
233C11⋊C5—441no—
234C11⋊C5—441no—
235C11⋊C5—441no—
236C2×C52—3631no—
237C5×D5—7261no—
238C5×D5—2421no—
239C2×D11—1651no—
240C2×D11—1651no—
241C3×C11—22no—
242C3×C11—21no—
243C3×C11—21no—
244C3×C11—21no—
245C3×C11D5×AGL(1,𝔽11)11yescharacteristic, complemented
246C3×C11D5×AGL(1,𝔽11)11yescharacteristic, complemented
247C2×C3×C5—6051no—
248D15—111no—
249C3×D5—111no—
250C5×D3—6051no—
251C5×D3—1211no—
252C5×D3—1211no—
253C5×D3—2421no—
254C5×D3—2421no—
255C52—4841noSylow
256C2×C11—551no—
257C2×C11—1651no—
258D11—51no—
259D11—151no—
260D11—331no—
261D11—331no—
262D11—661no—
263D11—661no—
264D11—662no—
265D11—661no—
266C22×C5—18151no—
267C2×D5—3631no—
268C3×C5—1211no—
269C3×C5—4841no—
270C3×C5—4841no—
271C3×C5#11925892⋊C211yescharacteristic, complemented
272C2×D3—6051noHall
273C11—21no—
274C11—21no—
275C11—22no—
276C11—21no—
277C11D5×C3⋊AGL(1,𝔽11)11yescharacteristic, complemented
278C11D15⋊AGL(1,𝔽11)11yescharacteristic, complemented
279C2×C5—36301no—
280C2×C5—3631no—
281C2×C5—3631no—
282C2×C5—12101no—
283C2×C5—7261no—
284C2×C5—7261no—
285D5—111no—
286D5—331no—
287C2×C3—551no—
288D3—551no—
289D3—1211no—
290C5—4841no—
291C5—4841no—
292C5—4841no—
293C5#11925895⋊D311yescharacteristic, complemented
294C22—18151noSylow
295C3#2713091311yescharacteristic, complemented, Sylow
296C2—551no—
297C2—3631no—
298C2—1651no—
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⋊#11925895)C2semidirect
2. C5×C3⋊#11925892C2semidirect
3. C3×C5⋊#11925895C2semidirect
5. C3×C5×#10597243C22semidirect
6. D55⋊D33C5semidirect
9. C5⋊#11925895D3semidirect
11. C11×D165C2×C5semidirect
12. C5×C3⋊(C11⋊D11)C2×C5semidirect
13. C3×C11×D55C2×C5semidirect
17. C3⋊#11925892D5semidirect
21. C5×#10597243C2×D3semidirect
24. C3×C5×C112C22×C5semidirect
27. C3×#10597243C2×D5semidirect
40. C11×D55C5×D3semidirect
55. C3⋊(C11⋊D11)C5×D5semidirect
62. C5×C112C2×C5×D3semidirect
65. #10597243D3×D5semidirect
77. C3×C112C2×C5×D5semidirect
78. D165AGL(1,𝔽11)semidirect
86. C3×D55AGL(1,𝔽11)semidirect
131. C3×C5×C11C2×AGL(1,𝔽11)semidirect
132. C3×C5×C11C2×AGL(1,𝔽11)semidirect
159. C112C5×D3×D5semidirect
161. D55C3⋊AGL(1,𝔽11)semidirect
213. C5×C11D3×AGL(1,𝔽11)semidirect
214. C5×C11C2×C3⋊AGL(1,𝔽11)semidirect
245. C3×C11D5×AGL(1,𝔽11)semidirect
246. C3×C11D5×AGL(1,𝔽11)semidirect
271. C3×C5#11925892⋊C2semidirect
277. C11D5×C3⋊AGL(1,𝔽11)semidirect
278. C11D15⋊AGL(1,𝔽11)semidirect
293. C5#11925895⋊D3semidirect
295. C3#27130913semidirect

Maximal subgroups

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

subgroupindex
C3⋊(C5⋊#11925895)2
C5×C3⋊#119258922
C3×C5⋊#119258952
#271309133
D55⋊D335
#11925895⋊D35
D15⋊AGL(1,𝔽11)11
D5×C3⋊AGL(1,𝔽11)11