Finite Group Databasebeta

← C2×Dic3×#713 #14478940

Subgroups — C2×Dic3×#713 #14478940

Order 1920.

3456 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#713C211yesmaximal, characteristic
2C2×Q8×Dic15C211yesmaximal, characteristic, complemented
3C2×C5×Q8×Dic3C211yesmaximal, characteristic, complemented
4Dic3×#713C2116yesmaximal, direct product factor
5C2×#91434C213yesmaximal, complemented
6C2×Dic3×D20C213yesmaximal, complemented
7C2×C4×D5×Dic3C213yesmaximal, complemented
8C2×#91358C213yesmaximal, complemented
9C2×C4×#713—31nomaximal, Hall
10C22×C3×C5×Q8C2211yescharacteristic
11C2×C3×#713C4116yescomplemented
12C2×C3×#713C2218yes—
13C22×C3×D20C2213yes—
14C22×C3×C4×D5C2213yes—
15C22×D5×Dic3C2213yes—
16C22×D5×Dic3C2213yes—
17Q8×Dic15C2218yescomplemented
18C2×C4⋊Dic15C2213yes—
19C2×C4×Dic15C2213yes—
20C5×Q8×Dic3C2218yescomplemented
21C2×C5×C4⋊Dic3C2213yes—
22C2×C4×C5×Dic3C2213yes—
23C2×#6665C2216yes—
24C2×Dic3×Dic5C2211yescharacteristic
25C2×Dic3×Dic5C2213yes—
26#91434C22124yescomplemented
27Dic3×D20C22124yescomplemented
28C4×D5×Dic3C22124yescomplemented
29#91358C22124yescomplemented
30C2×Dic3×#41—51nomaximal, Hall
31C22×#713D311yescharacteristic
32C2×C4×C5×Q8—31no—
33C2×Q8×Dic5—31no—
34C4×#713—316no—
35C2×#4039—33no—
36C2×#4038—33no—
37C2×C4×D20—33no—
38C2×C42×D5—33no—
39C23×C3×D5C2313yes—
40C2×C3×C5×Q8C2×C418yescomplemented
41C2×C3×C5×Q8C2314yes—
42C22×C3×C4×C5C2313yes—
43C22×Dic15C2313yes—
44C22×Dic15C2311yescharacteristic
45C22×C5×Dic3C2313yes—
46C22×C5×Dic3C2311yescharacteristic
47C22×C3×Dic5C2311yescharacteristic
48C3×#713C2×C4164yescomplemented
49C2×C3×D20C2×C4124yescomplemented
50C2×C3×D20C23112yes—
51C2×C3×C4×D5C2×C4124yescomplemented
52C2×C3×C4×D5C23112yes—
53C2×D5×Dic3—212no—
54C2×D5×Dic3—212no—
55C2×D5×Dic3C23112yes—
56C2×D5×Dic3C23112yes—
57C4⋊Dic15C23112yes—
58C4×Dic15C23112yes—
59C5×C4⋊Dic3C23112yes—
60C4×C5×Dic3C23112yes—
61#6665C23124yes—
62Dic3×Dic5C23112yes—
63Dic3×Dic5C2314yes—
64C22×C3×#41—51no—
65Dic3×#41—516no—
66C2×Q8×Dic3—51no—
67C2×Q8×Dic3D511yescharacteristic, complemented
68C2×D4×Dic3—53no—
69C2×D4×Dic3—53no—
70C2×#926—53no—
71C22×C4×Dic3—53no—
72C22×C5×Q8C2×D311yescharacteristic
73C2×#713Dic3116yesdirect product factor
74C2×#713C2×D318yes—
75C22×D20C2×D313yes—
76C22×C4×D5—33no—
77C22×C4×D5—33no—
78C22×C4×D5C2×D313yes—
79C4×C5×Q8—38no—
80C2×C5×C4⋊C4—33no—
81C2×C42×C5—33no—
82Q8×Dic5—38no—
83C2×#685—36no—
84C2×C4⋊Dic5—33no—
85C2×C4×Dic5—33no—
86C2×C4×Dic5—31no—
87C2×C4×Dic5—33no—
88#4039—324no—
89#4038—324no—
90C4×D20—324no—
91C42×D5—324no—
92C2×C4×#41—151noSylow
93C23×C3×C5C2411yescharacteristic
94C22×C3×D5—26no—
95C22×C3×D5—26no—
96C22×C3×D5C22×C4112yes—
97C22×C3×D5C2416yes—
98C3×C5×Q8C22×C4116yescomplemented
99C2×C3×C4×C5C22×C4112yes—
100C2×C3×C4×C5C2416yes—
101C2×Dic15—26no—
102C2×Dic15#4114yescomplemented
103C2×Dic15C2416yes—
104C2×Dic15C2412yes—
105C2×C5×Dic3—26no—
106C2×C5×Dic3#4114yescomplemented
107C2×C5×Dic3C2416yes—
108C2×C5×Dic3C2412yes—
109C2×C3×Dic5C22×C414yes—
110C2×C3×Dic5C2412yes—
111C3×D20C22×C4148yescomplemented
112C3×C4×D5C22×C4148yescomplemented
113D5×Dic3—224no—
114D5×Dic3—224no—
115C2×C3×#41—516no—
116C2×C3×#41—58no—
117C22×C3×Q8C2×D511yescharacteristic
118C22×C3×D4—53no—
119C23×C3×C4—53no—
120C23×Dic3—53no—
121C23×Dic3—53no—
122C2×#217—56no—
123Q8×Dic3—58no—
124Q8×Dic3C2×D518yescomplemented
125D4×Dic3—524no—
126D4×Dic3—524no—
127#926—524no—
128C2×C4⋊Dic3—53no—
129C2×C4⋊Dic3C2×D513yes—
130C2×C4×Dic3—53no—
131C2×C4×Dic3—51no—
132C2×C4×Dic3—53no—
133C2×C4×Dic3—524no—
134C2×C4×Dic3C2×D513yes—
135C23×D5C22×D313yes—
136C2×C5×Q8C2×Dic318yescomplemented
137C2×C5×Q8C22×D314yes—
138C22×C4×C5—31no—
139C22×C4×C5—33no—
140C22×C4×C5C22×D313yes—
141C22×Dic5—31no—
142C22×Dic5—33no—
143C22×Dic5C22×D311yescharacteristic
144#713C2×Dic3164yesdirect product factor
145C2×D20C2×Dic3124yescomplemented
146C2×D20C22×D3112yes—
147C2×C4×D5—312no—
148C2×C4×D5—312no—
149C2×C4×D5—612no—
150C2×C4×D5—612no—
151C2×C4×D5C2×Dic3124yescomplemented
152C2×C4×D5C22×D3112yes—
153C5×C4⋊C4—312no—
154C42×C5—312no—
155#685—324no—
156C4⋊Dic5—312no—
157C4×Dic5—312no—
158C4×Dic5—34no—
159C4×Dic5—312no—
160C22×#41—51no—
161C4×#41—1516no—
162C2×C4×Q8—31no—
163C2×C4×Q8—151no—
164C2×C4×D4—153no—
165C2×C4×D4—153no—
166C2×#117—153no—
167C22×C42—153no—
168C22×C3×C5C23×C412yes—
169C22×C3×C5C2×#4112yes—
170C22×C3×C5C2×#4112yes—
171C22×C3×C5C2511yescharacteristic
172C2×C3×D5—224no—
173C2×C3×D5—26no—
174C2×C3×D5—26no—
175C2×C3×D5C23×C4112yes—
176C3×C4×C5C23×C4112yes—
177Dic15—26no—
178Dic15C2×#4114yescomplemented
179C3×Dic5C23×C414yes—
180C5×Dic3—26no—
181C5×Dic3C2×#4114yescomplemented
182C24×C3—53no—
183C3×#41—564no—
184C2×C3×Q8C4×D518yescomplemented
185C2×C3×Q8C22×D514yes—
186C2×C3×D4—524no—
187C2×C3×D4—512no—
188C22×C3×C4—51no—
189C22×C3×C4—524no—
190C22×C3×C4—512no—
191C22×C3×C4C22×D513yes—
192C22×Dic3—51no—
193C22×Dic3—53no—
194C22×Dic3—512no—
195C22×Dic3—512no—
196C22×Dic3—1012no—
197C22×Dic3—1012no—
198C22×Dic3C22×D513yes—
199C22×Dic3C22×D511yescharacteristic
200#217—524no—
201C4⋊Dic3—512no—
202C4⋊Dic3C22×D5112yes—
203C4×Dic3—512no—
204C4×Dic3—54no—
205C4×Dic3—512no—
206C4×Dic3C22×D5112yes—
207C23×C5C23×D311yescharacteristic
208C22×D5—26no—
209C22×D5—26no—
210C22×D5C22×Dic3112yes—
211C22×D5C23×D316yes—
212C5×Q8C22×Dic3116yescomplemented
213C2×C4×C5—34no—
214C2×C4×C5—32no—
215C2×C4×C5—36no—
216C2×C4×C5—66no—
217C2×C4×C5C22×Dic3112yes—
218C2×C4×C5C23×D316yes—
219C2×Dic5—34no—
220C2×Dic5—32no—
221C2×Dic5—36no—
222C2×Dic5—66no—
223C2×Dic5C22×Dic314yes—
224C2×Dic5C23×D312yes—
225D20C22×Dic3148yescomplemented
226C4×D5—624no—
227C4×D5—624no—
228C4×D5C22×Dic3148yescomplemented
229C2×#41—516no—
230C2×#41—58no—
231C22×Q8D3×D511yescharacteristic
232C22×D4—53no—
233C23×C4—53no—
234C23×C4—153no—
235C23×C4—153no—
236C4×Q8—38no—
237C4×Q8—158no—
238C4×D4—1524no—
239C4×D4—1524no—
240#117—1524no—
241C2×C4⋊C4—33no—
242C2×C4⋊C4—153no—
243C2×C22⋊C4—156no—
244C2×C42—33no—
245C2×C42—1524no—
246C2×C42—153no—
247C2×C42—151no—
248C2×C42—153no—
249C2×C3×C5C4×#4114yescomplemented
250C2×C3×C5C24×C411yescharacteristic
251C2×C3×C5C22×#4111yescharacteristic
252C2×C3×C5C22×#4111yescharacteristic
253C3×D5—212no—
254C23×C3—512no—
255C23×C3—56no—
256C23×C3—106no—
257C23×C3—106no—
258C23×C3C23×D511yescharacteristic
259C3×Q8C2×C4×D5116yescomplemented
260C3×D4—548no—
261C2×C3×C4—54no—
262C2×C3×C4—52no—
263C2×C3×C4—548no—
264C2×C3×C4C2×C4×D5112yes—
265C2×C3×C4C23×D516yes—
266C2×Dic3—26no—
267C2×Dic3—54no—
268C2×Dic3—52no—
269C2×Dic3—56no—
270C2×Dic3—1024no—
271C2×Dic3—106no—
272C2×Dic3—1024no—
273C2×Dic3#71314yesdirect product factor
274C2×Dic3C23×D516yes—
275C2×Dic3C23×D512yes—
276C22×C5D3×#4112yes—
277C22×C5D3×#4112yes—
278C22×C5C23×Dic312yes—
279C22×C5C24×D311yescharacteristic
280C2×D5—26no—
281C2×D5—26no—
282C2×D5—224no—
283C2×D5C23×Dic3112yes—
284C4×C5—34no—
285C4×C5—66no—
286C4×C5C23×Dic3112yes—
287Dic5—34no—
288Dic5—66no—
289Dic5C23×Dic314yes—
290C24—53no—
291#41—564no—
292C2×Q8D5×Dic318yescomplemented
293C2×Q8C2×D3×D514yes—
294C2×D4—524no—
295C2×D4—512no—
296C22×C4—31no—
297C22×C4—33no—
298C22×C4—51no—
299C22×C4—524no—
300C22×C4—512no—
301C22×C4—1512no—
302C22×C4—1512no—
303C22×C4—151no—
304C22×C4—153no—
305C22×C4—3012no—
306C22×C4—3012no—
307C22×C4C2×D3×D513yes—
308C4⋊C4—312no—
309C4⋊C4—1512no—
310C22⋊C4—1524no—
311C42—312no—
312C42—154no—
313C42—1512no—
314C42—1512no—
315C3×C5C2×C4×#4111yescharacteristic, complemented, Hall
316C22×C3—512no—
317C22×C3—1024no—
318C22×C3—106no—
319C22×C3—106no—
320C22×C3C22×C4×D512yes—
321C22×C3C2×#71312yes—
322C22×C3D5×#4112yes—
323C22×C3C24×D511yescharacteristic
324C3×C4—54no—
325C3×C4C22×C4×D5112yes—
326Dic3—26no—
327Dic3—54no—
328Dic3—106no—
329Dic3C2×#71314yesdirect product factor
330C2×C5Dic3×#4114yescomplemented
331C2×C5C2×D3×#4111yescharacteristic
332C2×C5C2×D3×#4111yescharacteristic
333C2×C5C24×Dic311yescharacteristic
334D5—212no—
335C23—512no—
336C23—56no—
337C23—106no—
338C23—106no—
339C23C22×D3×D511yescharacteristic
340Q8C2×D5×Dic3116yescomplemented
341D4—548no—
342C2×C4—34no—
343C2×C4—32no—
344C2×C4—36no—
345C2×C4—54no—
346C2×C4—52no—
347C2×C4—548no—
348C2×C4—66no—
349C2×C4—154no—
350C2×C4—152no—
351C2×C4—156no—
352C2×C4—3024no—
353C2×C4—3024no—
354C2×C4—306no—
355C2×C4C2×D5×Dic3112yes—
356C2×C4C22×D3×D516yes—
357C2×C3—1012no—
358C2×C3C4×#71314yescomplemented
359C2×C3C23×C4×D511yescharacteristic
360C2×C3C22×#71311yescharacteristic
361C2×C3C2×D5×#4111yescharacteristic
362C5C2×Dic3×#4111yescharacteristic, complemented, Sylow
363C22—512no—
364C22—1024no—
365C22—106no—
366C22—106no—
367C22D3×#71312yes—
368C22#9203412yes—
369C22C22×D5×Dic312yes—
370C22C23×D3×D511yescharacteristic
371C4—34no—
372C4—54no—
373C4—66no—
374C4—154no—
375C4—306no—
376C4C22×D5×Dic3112yes—
377C3C2×C4×#71311yescharacteristic, complemented, Sylow
378C2—1012no—
379C2Dic3×#71314yesdirect product factor
380C2C2×D3×#71311yescharacteristic
381C2C2×#9203411yescharacteristic
382C2C23×D5×Dic311yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutatorC2×C3×C5C24×C4
FrattiniC22C23×D3×D5
FittingC22×C3×C5×Q8C22
socleC23×C3×C5C24
prime radicalC22×C3×#713C2
cosocleC22×C3×C5C25
hypercenterC22×Q8D3×D5
hypocenterC3×C5C2×C4×#41
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
2. C2×Q8×Dic15C2semidirect
3. C2×C5×Q8×Dic3C2semidirect
4. Dic3×#713C2direct (N × H)
5. C2×#91434C2semidirect
6. C2×Dic3×D20C2semidirect
7. C2×C4×D5×Dic3C2semidirect
8. C2×#91358C2semidirect
11. C2×C3×#713C4semidirect
17. Q8×Dic15C22semidirect
20. C5×Q8×Dic3C22semidirect
26. #91434C22semidirect
27. Dic3×D20C22semidirect
28. C4×D5×Dic3C22semidirect
29. #91358C22semidirect
40. C2×C3×C5×Q8C2×C4semidirect
48. C3×#713C2×C4semidirect
49. C2×C3×D20C2×C4semidirect
51. C2×C3×C4×D5C2×C4semidirect
67. C2×Q8×Dic3D5semidirect
73. C2×#713Dic3direct (N × H)
98. C3×C5×Q8C22×C4semidirect
102. C2×Dic15#41semidirect
106. C2×C5×Dic3#41semidirect
111. C3×D20C22×C4semidirect
112. C3×C4×D5C22×C4semidirect
124. Q8×Dic3C2×D5semidirect
136. C2×C5×Q8C2×Dic3semidirect
144. #713C2×Dic3direct (N × H)
145. C2×D20C2×Dic3semidirect
151. C2×C4×D5C2×Dic3semidirect
178. Dic15C2×#41semidirect
181. C5×Dic3C2×#41semidirect
184. C2×C3×Q8C4×D5semidirect
212. C5×Q8C22×Dic3semidirect
225. D20C22×Dic3semidirect
228. C4×D5C22×Dic3semidirect
249. C2×C3×C5C4×#41semidirect
259. C3×Q8C2×C4×D5semidirect
273. C2×Dic3#713direct (N × H)
292. C2×Q8D5×Dic3semidirect
315. C3×C5C2×C4×#41semidirect
329. Dic3C2×#713direct (N × H)
330. C2×C5Dic3×#41semidirect
340. Q8C2×D5×Dic3semidirect
358. C2×C3C4×#713semidirect
362. C5C2×Dic3×#41semidirect
377. C3C2×C4×#713semidirect
379. C2Dic3×#713direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#7132
C2×Q8×Dic152
C2×C5×Q8×Dic32
Dic3×#7132
C2×#914342
C2×Dic3×D202
C2×C4×D5×Dic32
C2×#913582
C2×C4×#7133
C2×Dic3×#415