Finite Group Databasebeta

← D3×C5⋊#11925892 #49137505

Subgroups — D3×C5⋊#11925892 #49137505

Order 36300.

672 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 672 conjugacy classes of subgroups — too many to draw. Only its 98 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⋊#11925892)C211yesmaximal, characteristic, complemented
2C5×D3×#10597243C211yesmaximal, characteristic, complemented
3C3×C5⋊#11925892C211yesmaximal, characteristic, complemented
4C2×C5⋊#11925892—31nomaximal, Hall
5C3×C5×#10597243C2211yescharacteristic, complemented, Hall
6D3×C5⋊(C11⋊D11)C511yesmaximal, characteristic, complemented
7D3×#11925892—51nomaximal
8C2×C5×#10597243—31no—
9C5⋊#11925892—31no—
10C5⋊#11925892D311yescharacteristic, direct product factor
11C3⋊(C5⋊(C11⋊D11))C2×C511yescharacteristic, complemented
12C5×D3×C112C2×C511yescharacteristic, complemented
13C3×C5⋊(C11⋊D11)C2×C511yescharacteristic, complemented
14D3×#10597243—22no—
15D3×#10597243D511yescharacteristic, complemented
16C3⋊#11925892—51no—
17C3×#11925892—51no—
18D3×C5⋊AGL(1,𝔽11)—111nomaximal
19D3×C5⋊AGL(1,𝔽11)—111nomaximal
20D3×C5⋊AGL(1,𝔽11)—111nomaximal
21D3×C5⋊AGL(1,𝔽11)—111nomaximal
22D3×C5⋊AGL(1,𝔽11)—111nomaximal
23D3×C5⋊AGL(1,𝔽11)—117nomaximal
24C5×#10597243C2×D311yescharacteristic, complemented, Hall
25C2×C5⋊(C11⋊D11)—31no—
26C2×#11925892—151no—
27C3×C5×C112C22×C511yescharacteristic, complemented
28C3×#10597243—22no—
29C3×#10597243C2×D511yescharacteristic, complemented
30C3⋊(C5⋊AGL(1,𝔽11))—111no—
31C3⋊(C5⋊AGL(1,𝔽11))—111no—
32C3⋊(C5⋊AGL(1,𝔽11))—111no—
33C3⋊(C5⋊AGL(1,𝔽11))—111no—
34C3⋊(C5⋊AGL(1,𝔽11))—111no—
35C3⋊(C5⋊AGL(1,𝔽11))—117no—
36C5×D3×C11⋊C5—111no—
37C5×D3×C11⋊C5—221no—
38C5×D3×C11⋊C5—221no—
39C5×D3×C11⋊C5—221no—
40C5×D3×C11⋊C5—221no—
41C5×D3×C11⋊C5—227no—
42C3×C5⋊AGL(1,𝔽11)—111no—
43C3×C5⋊AGL(1,𝔽11)—111no—
44C3×C5⋊AGL(1,𝔽11)—111no—
45C3×C5⋊AGL(1,𝔽11)—111no—
46C3×C5⋊AGL(1,𝔽11)—111no—
47C3×C5⋊AGL(1,𝔽11)—117no—
48D3×C11⋊D11—51noHall
49C2×C5×C112—31no—
50C5⋊(C11⋊D11)—31no—
51C5⋊(C11⋊D11)C5×D311yescharacteristic, complemented
52C2×#10597243—31no—
53C2×#10597243—62no—
54#11925892—51no—
55#11925892—151no—
56C2×C5⋊AGL(1,𝔽11)—331no—
57C2×C5⋊AGL(1,𝔽11)—331no—
58C2×C5⋊AGL(1,𝔽11)—331no—
59C2×C5⋊AGL(1,𝔽11)—331no—
60C2×C5⋊AGL(1,𝔽11)—331no—
61C2×C5⋊AGL(1,𝔽11)—337no—
62C3×C5×C11⋊C5—111no—
63C3×C5×C11⋊C5—221no—
64C3×C5×C11⋊C5—221no—
65C3×C5×C11⋊C5—221no—
66C3×C5×C11⋊C5—221no—
67C3×C5×C11⋊C5—227no—
68C3⋊(C11⋊D11)—51no—
69D3×C112C5×D511yescharacteristic, complemented
70C3×C11⋊D11—51no—
71D3×D55—111no—
72D3×D55—111no—
73D3×D55—111no—
74D3×D55—111no—
75D3×D55—111no—
76D3×D55—117no—
77D3×AGL(1,𝔽11)—551no—
78D3×AGL(1,𝔽11)—551no—
79D3×AGL(1,𝔽11)—551no—
80D3×AGL(1,𝔽11)—551no—
81D3×AGL(1,𝔽11)—551no—
82D3×AGL(1,𝔽11)—557no—
83C5×C112C2×C5×D311yescharacteristic, complemented
84#10597243—22no—
85#10597243D3×D511yescharacteristic, complemented
86C2×C5×C11⋊C5—331no—
87C2×C5×C11⋊C5—331no—
88C2×C5×C11⋊C5—661no—
89C2×C5×C11⋊C5—661no—
90C2×C5×C11⋊C5—661no—
91C2×C5×C11⋊C5—667no—
92C5⋊AGL(1,𝔽11)—111no—
93C5⋊AGL(1,𝔽11)—111no—
94C5⋊AGL(1,𝔽11)—111no—
95C5⋊AGL(1,𝔽11)—111no—
96C5⋊AGL(1,𝔽11)—111no—
97C5⋊AGL(1,𝔽11)—117no—
98C5⋊AGL(1,𝔽11)—331no—
99C5⋊AGL(1,𝔽11)—331no—
100C5⋊AGL(1,𝔽11)—331no—
101C5⋊AGL(1,𝔽11)—331no—
102C5⋊AGL(1,𝔽11)—331no—
103C5⋊AGL(1,𝔽11)—337no—
104C2×C11⋊D11—151noHall
105C3×C112C2×C5×D511yescharacteristic, complemented, Hall
106D165—111no—
107D165—111no—
108D165—111no—
109D165—111no—
110D165—111no—
111D165—117no—
112C5×D3×C11AGL(1,𝔽11)11yescharacteristic, complemented
113C5×D3×C11AGL(1,𝔽11)11yescharacteristic, complemented
114C5×D3×C11AGL(1,𝔽11)11yescharacteristic, complemented
115C5×D3×C11AGL(1,𝔽11)11yescharacteristic, complemented
116C5×D3×C11AGL(1,𝔽11)11yescharacteristic, complemented
117C5×D3×C11AGL(1,𝔽11)17yescomplemented
118C3×D55—111no—
119C3×D55—111no—
120C3×D55—111no—
121C3×D55—111no—
122C3×D55—111no—
123C3×D55—117no—
124C3⋊AGL(1,𝔽11)—551no—
125C3⋊AGL(1,𝔽11)—551no—
126C3⋊AGL(1,𝔽11)—551no—
127C3⋊AGL(1,𝔽11)—551no—
128C3⋊AGL(1,𝔽11)—551no—
129C3⋊AGL(1,𝔽11)—557no—
130D3×C11⋊C5—111no—
131D3×C11⋊C5—111no—
132D3×C11⋊C5—221no—
133D3×C11⋊C5—221no—
134D3×C11⋊C5—222no—
135D3×C11⋊C5—221no—
136D3×C11⋊C5—227no—
137D3×C11⋊C5—222no—
138D3×C11⋊C5—222no—
139D3×C11⋊C5—222no—
140D3×C11⋊C5—222no—
141D3×C11⋊C5—2214no—
142C3×AGL(1,𝔽11)—551no—
143C3×AGL(1,𝔽11)—551no—
144C3×AGL(1,𝔽11)—551no—
145C3×AGL(1,𝔽11)—551no—
146C3×AGL(1,𝔽11)—551no—
147C3×AGL(1,𝔽11)—557no—
148C5×D3×D5—1211noHall
149C5×C11⋊C5—111no—
150C5×C11⋊C5—111no—
151C5×C11⋊C5—221no—
152C5×C11⋊C5—221no—
153C5×C11⋊C5—221no—
154C5×C11⋊C5—227no—
155C2×C112—31no—
156C11⋊D11—51no—
157C11⋊D11—151no—
158C2×D55—331no—
159C2×D55—331no—
160C2×D55—331no—
161C2×D55—331no—
162C2×D55—331no—
163C2×D55—337no—
164C2×AGL(1,𝔽11)—1651no—
165C2×AGL(1,𝔽11)—1651no—
166C2×AGL(1,𝔽11)—1651no—
167C2×AGL(1,𝔽11)—1651no—
168C2×AGL(1,𝔽11)—1651no—
169C2×AGL(1,𝔽11)—1657no—
170C3×C5×C11C2×AGL(1,𝔽11)11yescharacteristic, complemented
171C3×C5×C11C2×AGL(1,𝔽11)11yescharacteristic, complemented
172C3×C5×C11C2×AGL(1,𝔽11)11yescharacteristic, complemented
173C3×C5×C11C2×AGL(1,𝔽11)11yescharacteristic, complemented
174C3×C5×C11C2×AGL(1,𝔽11)11yescharacteristic, complemented
175C3×C5×C11C2×AGL(1,𝔽11)17yescomplemented
176C3×C11⋊C5—111no—
177C3×C11⋊C5—111no—
178C3×C11⋊C5—221no—
179C3×C11⋊C5—222no—
180C3×C11⋊C5—222no—
181C3×C11⋊C5—222no—
182C3×C11⋊C5—222no—
183C3×C11⋊C5—222no—
184C3×C11⋊C5—2214no—
185C3×C11⋊C5—221no—
186C3×C11⋊C5—221no—
187C3×C11⋊C5—227no—
188C5×D15—1211no—
189C52×D3—2421no—
190C3×C5×D5—1211no—
191D3×D11—551no—
192D3×D11—551no—
193D3×D11—551no—
194D3×D11—551no—
195D3×D11—551no—
196D3×D11—557no—
197C112C5×D3×D511yescharacteristic, complemented, Sylow
198C2×C5×C11—31no—
199C2×C5×C11—31no—
200C2×C5×C11—31no—
201C2×C5×C11—31no—
202C2×C5×C11—31no—
203C2×C5×C11—37no—
204D55—111no—
205D55—111no—
206D55—111no—
207D55—111no—
208D55—111no—
209D55—117no—
210D55—331no—
211D55—331no—
212D55—331no—
213D55—331no—
214D55—331no—
215D55—337no—
216C2×C11⋊C5—331no—
217C2×C11⋊C5—661no—
218C2×C11⋊C5—661no—
219C2×C11⋊C5—662no—
220C2×C11⋊C5—662no—
221C2×C11⋊C5—661no—
222C2×C11⋊C5—661no—
223C2×C11⋊C5—667no—
224C2×C11⋊C5—662no—
225C2×C11⋊C5—662no—
226C2×C11⋊C5—662no—
227C2×C11⋊C5—6614no—
228AGL(1,𝔽11)—551no—
229AGL(1,𝔽11)—551no—
230AGL(1,𝔽11)—551no—
231AGL(1,𝔽11)—551no—
232AGL(1,𝔽11)—551no—
233AGL(1,𝔽11)—557no—
234AGL(1,𝔽11)—1651no—
235AGL(1,𝔽11)—1651no—
236AGL(1,𝔽11)—1651no—
237AGL(1,𝔽11)—1651no—
238AGL(1,𝔽11)—1651no—
239AGL(1,𝔽11)—1657no—
240C2×C5×D5—3631noHall
241C3×C52—2421noHall
242D33—551no—
243D33—551no—
244D33—551no—
245D33—551no—
246D33—551no—
247D33—557no—
248C3×D11—551no—
249C3×D11—551no—
250C3×D11—551no—
251C3×D11—551no—
252C3×D11—551no—
253C3×D11—557no—
254D3×C11C5⋊AGL(1,𝔽11)11yescharacteristic, complemented
255D3×C11C5⋊AGL(1,𝔽11)11yescharacteristic, complemented
256D3×C11C5⋊AGL(1,𝔽11)11yescharacteristic, complemented
257D3×C11C5⋊AGL(1,𝔽11)11yescharacteristic, complemented
258D3×C11C5⋊AGL(1,𝔽11)11yescharacteristic, complemented
259D3×C11C5⋊AGL(1,𝔽11)17yescomplemented
260C2×C5×D3—6051no—
261D3×D5—1211no—
262C5×C11D3×AGL(1,𝔽11)11yescharacteristic, complemented
263C5×C11D3×AGL(1,𝔽11)11yescharacteristic, complemented
264C5×C11D3×AGL(1,𝔽11)11yescharacteristic, complemented
265C5×C11D3×AGL(1,𝔽11)11yescharacteristic, complemented
266C5×C11D3×AGL(1,𝔽11)11yescharacteristic, complemented
267C5×C11D3×AGL(1,𝔽11)17yescomplemented
268C11⋊C5—111no—
269C11⋊C5—221no—
270C11⋊C5—221no—
271C11⋊C5—222no—
272C11⋊C5—222no—
273C11⋊C5—221no—
274C11⋊C5—221no—
275C11⋊C5—227no—
276C11⋊C5—222no—
277C11⋊C5—222no—
278C11⋊C5—222no—
279C11⋊C5—2214no—
280C2×C52—7261no—
281C5×D5—3631no—
282C5×D5—1211no—
283C2×D11—1651no—
284C2×D11—1651no—
285C2×D11—1651no—
286C2×D11—1651no—
287C2×D11—1651no—
288C2×D11—1657no—
289C3×C11C2×C5⋊AGL(1,𝔽11)11yescharacteristic, complemented
290C3×C11C2×C5⋊AGL(1,𝔽11)11yescharacteristic, complemented
291C3×C11C2×C5⋊AGL(1,𝔽11)11yescharacteristic, complemented
292C3×C11C2×C5⋊AGL(1,𝔽11)11yescharacteristic, complemented
293C3×C11C2×C5⋊AGL(1,𝔽11)11yescharacteristic, complemented
294C3×C11C2×C5⋊AGL(1,𝔽11)17yescomplemented
295C2×C3×C5—6051no—
296D15—1211no—
297C3×D5—1211no—
298C5×D3—6051no—
299C5×D3—2421no—
300C5×D3—2422no—
301C5×D3#1192589211yescharacteristic, complemented
302C52—2421noSylow
303C2×C11—31no—
304C2×C11—31no—
305C2×C11—31no—
306C2×C11—31no—
307C2×C11—31no—
308C2×C11—37no—
309D11—551no—
310D11—551no—
311D11—551no—
312D11—551no—
313D11—551no—
314D11—557no—
315D11—1651no—
316D11—1651no—
317D11—1651no—
318D11—1651no—
319D11—1651no—
320D11—1657no—
321C22×C5—18151no—
322C2×D5—3631no—
323C3×C5—2421no—
324C3×C5—2422no—
325C3×C5C2×#1192589211yescharacteristic, complemented
326C2×D3—6051noHall
327C11D3×C5⋊AGL(1,𝔽11)11yescharacteristic, complemented
328C11D3×C5⋊AGL(1,𝔽11)11yescharacteristic, complemented
329C11D3×C5⋊AGL(1,𝔽11)11yescharacteristic, complemented
330C11D3×C5⋊AGL(1,𝔽11)11yescharacteristic, complemented
331C11D3×C5⋊AGL(1,𝔽11)11yescharacteristic, complemented
332C11D3×C5⋊AGL(1,𝔽11)17yescomplemented
333C2×C5—31no—
334C2×C5—18151no—
335C2×C5—6051no—
336C2×C5—7261no—
337C2×C5—7262no—
338D5—3631no—
339D5—1211no—
340C2×C3—6051no—
341D3—6051no—
342D3C5⋊#1192589211yescharacteristic, direct product factor
343C5—2421no—
344C5—2422no—
345C5D3×#1192589211yescharacteristic, complemented
346C22—18151noSylow
347C3C2×C5⋊#1192589211yescharacteristic, complemented, Sylow
348C2—31no—
349C2—18151no—
350C2—6051no—
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⋊#11925892)C2semidirect
2. C5×D3×#10597243C2semidirect
3. C3×C5⋊#11925892C2semidirect
5. C3×C5×#10597243C22semidirect
6. D3×C5⋊(C11⋊D11)C5semidirect
10. C5⋊#11925892D3direct (N × H)
11. C3⋊(C5⋊(C11⋊D11))C2×C5semidirect
12. C5×D3×C112C2×C5semidirect
13. C3×C5⋊(C11⋊D11)C2×C5semidirect
15. D3×#10597243D5semidirect
24. C5×#10597243C2×D3semidirect
27. C3×C5×C112C22×C5semidirect
29. C3×#10597243C2×D5semidirect
51. C5⋊(C11⋊D11)C5×D3semidirect
69. D3×C112C5×D5semidirect
83. C5×C112C2×C5×D3semidirect
85. #10597243D3×D5semidirect
105. C3×C112C2×C5×D5semidirect
112. C5×D3×C11AGL(1,𝔽11)semidirect
113. C5×D3×C11AGL(1,𝔽11)semidirect
114. C5×D3×C11AGL(1,𝔽11)semidirect
115. C5×D3×C11AGL(1,𝔽11)semidirect
116. C5×D3×C11AGL(1,𝔽11)semidirect
117. C5×D3×C11AGL(1,𝔽11)semidirect
170. C3×C5×C11C2×AGL(1,𝔽11)semidirect
171. C3×C5×C11C2×AGL(1,𝔽11)semidirect
172. C3×C5×C11C2×AGL(1,𝔽11)semidirect
173. C3×C5×C11C2×AGL(1,𝔽11)semidirect
174. C3×C5×C11C2×AGL(1,𝔽11)semidirect
175. C3×C5×C11C2×AGL(1,𝔽11)semidirect
197. C112C5×D3×D5semidirect
254. D3×C11C5⋊AGL(1,𝔽11)semidirect
255. D3×C11C5⋊AGL(1,𝔽11)semidirect
256. D3×C11C5⋊AGL(1,𝔽11)semidirect
257. D3×C11C5⋊AGL(1,𝔽11)semidirect
258. D3×C11C5⋊AGL(1,𝔽11)semidirect
259. D3×C11C5⋊AGL(1,𝔽11)semidirect
262. C5×C11D3×AGL(1,𝔽11)semidirect
263. C5×C11D3×AGL(1,𝔽11)semidirect
264. C5×C11D3×AGL(1,𝔽11)semidirect
265. C5×C11D3×AGL(1,𝔽11)semidirect
266. C5×C11D3×AGL(1,𝔽11)semidirect
267. C5×C11D3×AGL(1,𝔽11)semidirect
289. C3×C11C2×C5⋊AGL(1,𝔽11)semidirect
290. C3×C11C2×C5⋊AGL(1,𝔽11)semidirect
291. C3×C11C2×C5⋊AGL(1,𝔽11)semidirect
292. C3×C11C2×C5⋊AGL(1,𝔽11)semidirect
293. C3×C11C2×C5⋊AGL(1,𝔽11)semidirect
294. C3×C11C2×C5⋊AGL(1,𝔽11)semidirect
301. C5×D3#11925892semidirect
325. C3×C5C2×#11925892semidirect
327. C11D3×C5⋊AGL(1,𝔽11)semidirect
328. C11D3×C5⋊AGL(1,𝔽11)semidirect
329. C11D3×C5⋊AGL(1,𝔽11)semidirect
330. C11D3×C5⋊AGL(1,𝔽11)semidirect
331. C11D3×C5⋊AGL(1,𝔽11)semidirect
332. C11D3×C5⋊AGL(1,𝔽11)semidirect
342. D3C5⋊#11925892direct (N × H)
345. C5D3×#11925892semidirect
347. C3C2×C5⋊#11925892semidirect

Maximal subgroups

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

subgroupindex
C3⋊(C5⋊#11925892)2
C5×D3×#105972432
C3×C5⋊#119258922
C2×C5⋊#119258923
D3×C5⋊(C11⋊D11)5
D3×#119258925
D3×C5⋊AGL(1,𝔽11)11