Finite Group Databasebeta

← C2×Dic5×#239 #14478942

Subgroups — C2×Dic5×#239 #14478942

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×C5×#239C211yesmaximal, characteristic
2C2×Q8×Dic15C211yesmaximal, characteristic, complemented
3C2×C3×Q8×Dic5C211yesmaximal, characteristic, complemented
4Dic5×#239C2116yesmaximal, direct product factor
5C2×#91435C213yesmaximal, complemented
6C2×Dic5×D12C213yesmaximal, complemented
7C2×C4×D3×Dic5C213yesmaximal, complemented
8C2×#91338C213yesmaximal, complemented
9C2×#41×Dic5—31nomaximal, Hall
10C22×C3×C5×Q8C2211yescharacteristic
11C2×C5×#239C4116yescomplemented
12C2×C5×#239C2218yes—
13C22×C5×D12C2213yes—
14C22×C4×C5×D3C2213yes—
15C22×D3×Dic5C2213yes—
16C22×D3×Dic5C2213yes—
17Q8×Dic15C2218yescomplemented
18C2×C4⋊Dic15C2213yes—
19C2×C4×Dic15C2213yes—
20C3×Q8×Dic5C2218yescomplemented
21C2×C3×C4⋊Dic5C2213yes—
22C2×C3×C4×Dic5C2213yes—
23C2×(C2×D3)⋊Dic5C2216yes—
24C2×Dic3×Dic5C2211yescharacteristic
25C2×Dic3×Dic5C2213yes—
26#91435C22124yescomplemented
27Dic5×D12C22124yescomplemented
28C4×D3×Dic5C22124yescomplemented
29#91338C22124yescomplemented
30C2×C4×#239—51nomaximal, Hall
31C22×C5×#41—31no—
32#41×Dic5—316no—
33C2×Q8×Dic5—31no—
34C2×Q8×Dic5D311yescharacteristic, complemented
35C2×D4×Dic5—33no—
36C2×D4×Dic5—33no—
37C2×#4072—33no—
38C22×C4×Dic5—33no—
39C23×C5×D3C2313yes—
40C2×C3×C5×Q8C2×C418yescomplemented
41C2×C3×C5×Q8C2314yes—
42C22×C3×C4×C5C2313yes—
43C22×Dic15C2313yes—
44C22×Dic15C2311yescharacteristic
45C22×C5×Dic3C2311yescharacteristic
46C5×#239C2×C4164yescomplemented
47C2×C5×D12C2×C4124yescomplemented
48C2×C5×D12C23112yes—
49C2×C4×C5×D3C2×C4124yescomplemented
50C2×C4×C5×D3C23112yes—
51C22×C3×Dic5C2313yes—
52C22×C3×Dic5C2311yescharacteristic
53C2×D3×Dic5—212no—
54C2×D3×Dic5—212no—
55C2×D3×Dic5C23112yes—
56C2×D3×Dic5C23112yes—
57C4⋊Dic15C23112yes—
58C4×Dic15C23112yes—
59C3×C4⋊Dic5C23112yes—
60C3×C4×Dic5C23112yes—
61(C2×D3)⋊Dic5C23124yes—
62Dic3×Dic5C2314yes—
63Dic3×Dic5C23112yes—
64C22×#239D511yescharacteristic
65C2×C3×C4×Q8—51no—
66C2×Q8×Dic3—51no—
67C4×#239—516no—
68C2×#893—53no—
69C2×#892—53no—
70C2×C4×D12—53no—
71C2×C42×D3—53no—
72C2×C5×#41—316no—
73C2×C5×#41—38no—
74C22×C5×Q8C2×D311yescharacteristic
75C22×C5×D4—33no—
76C23×C4×C5—33no—
77C23×Dic5—33no—
78C23×Dic5—33no—
79C2×C22⋊Dic5—36no—
80Q8×Dic5—38no—
81Q8×Dic5C2×D318yescomplemented
82D4×Dic5—324no—
83D4×Dic5—324no—
84#4072—324no—
85C2×C4⋊Dic5—33no—
86C2×C4⋊Dic5C2×D313yes—
87C2×C4×Dic5—33no—
88C2×C4×Dic5—31no—
89C2×C4×Dic5—33no—
90C2×C4×Dic5—324no—
91C2×C4×Dic5C2×D313yes—
92C2×C4×#41—151noSylow
93C23×C3×C5C2411yescharacteristic
94C22×C5×D3—26no—
95C22×C5×D3—26no—
96C22×C5×D3C22×C4112yes—
97C22×C5×D3C2416yes—
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×Dic3C22×C414yes—
106C2×C5×Dic3C2412yes—
107C5×D12C22×C4148yescomplemented
108C4×C5×D3C22×C4148yescomplemented
109C2×C3×Dic5—26no—
110C2×C3×Dic5#4114yescomplemented
111C2×C3×Dic5C2416yes—
112C2×C3×Dic5C2412yes—
113D3×Dic5—224no—
114D3×Dic5—224no—
115C22×C3×Q8C2×D511yescharacteristic
116C2×#239Dic5116yesdirect product factor
117C2×#239C2×D518yes—
118C22×D12C2×D513yes—
119C22×C4×D3—53no—
120C22×C4×D3—53no—
121C22×C4×D3C2×D513yes—
122C3×C4×Q8—58no—
123C2×C3×C4⋊C4—53no—
124C2×C3×C42—53no—
125Q8×Dic3—58no—
126C2×(C2×D3)⋊C4—56no—
127C2×C4⋊Dic3—53no—
128C2×C4×Dic3—53no—
129C2×C4×Dic3—51no—
130C2×C4×Dic3—53no—
131#893—524no—
132#892—524no—
133C4×D12—524no—
134C42×D3—524no—
135C24×C5—33no—
136C5×#41—364no—
137C2×C5×Q8C4×D318yescomplemented
138C2×C5×Q8C22×D314yes—
139C2×C5×D4—324no—
140C2×C5×D4—312no—
141C22×C4×C5—31no—
142C22×C4×C5—324no—
143C22×C4×C5—312no—
144C22×C4×C5C22×D313yes—
145C22×Dic5—31no—
146C22×Dic5—33no—
147C22×Dic5—312no—
148C22×Dic5—312no—
149C22×Dic5—612no—
150C22×Dic5—612no—
151C22×Dic5C22×D313yes—
152C22×Dic5C22×D311yescharacteristic
153C22⋊Dic5—324no—
154C4⋊Dic5—312no—
155C4⋊Dic5C22×D3112yes—
156C4×Dic5—312no—
157C4×Dic5—34no—
158C4×Dic5—312no—
159C4×Dic5C22×D3112yes—
160C22×#41—31no—
161C4×#41—1516no—
162C2×C4×Q8—51no—
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×C5×D3—224no—
173C2×C5×D3—26no—
174C2×C5×D3—26no—
175C2×C5×D3C23×C4112yes—
176C3×C4×C5C23×C4112yes—
177Dic15—26no—
178Dic15C2×#4114yescomplemented
179C3×Dic5—26no—
180C3×Dic5C2×#4114yescomplemented
181C5×Dic3C23×C414yes—
182C23×D3C22×D513yes—
183C2×C3×Q8C2×Dic518yescomplemented
184C2×C3×Q8C22×D514yes—
185C22×C3×C4—51no—
186C22×C3×C4—53no—
187C22×C3×C4C22×D513yes—
188C22×Dic3—51no—
189C22×Dic3—53no—
190C22×Dic3C22×D511yescharacteristic
191#239C2×Dic5164yesdirect product factor
192C2×D12C2×Dic5124yescomplemented
193C2×D12C22×D5112yes—
194C2×C4×D3—512no—
195C2×C4×D3—512no—
196C2×C4×D3—1012no—
197C2×C4×D3—1012no—
198C2×C4×D3C2×Dic5124yescomplemented
199C2×C4×D3C22×D5112yes—
200C3×C4⋊C4—512no—
201C3×C42—512no—
202(C2×D3)⋊C4—524no—
203C4⋊Dic3—512no—
204C4×Dic3—512no—
205C4×Dic3—54no—
206C4×Dic3—512no—
207C23×C5—312no—
208C23×C5—36no—
209C23×C5—66no—
210C23×C5—66no—
211C23×C5C23×D311yescharacteristic
212C5×Q8C2×C4×D3116yescomplemented
213C5×D4—348no—
214C2×C4×C5—34no—
215C2×C4×C5—32no—
216C2×C4×C5—348no—
217C2×C4×C5C2×C4×D3112yes—
218C2×C4×C5C23×D316yes—
219C2×Dic5—26no—
220C2×Dic5—34no—
221C2×Dic5—32no—
222C2×Dic5—36no—
223C2×Dic5—624no—
224C2×Dic5—66no—
225C2×Dic5—624no—
226C2×Dic5#23914yesdirect product factor
227C2×Dic5C23×D316yes—
228C2×Dic5C23×D312yes—
229C2×#41—316no—
230C2×#41—38no—
231C22×Q8D3×D511yescharacteristic
232C22×D4—33no—
233C23×C4—33no—
234C23×C4—153no—
235C23×C4—153no—
236C4×Q8—58no—
237C4×Q8—158no—
238C4×D4—1524no—
239C4×D4—1524no—
240#117—1524no—
241C2×C4⋊C4—53no—
242C2×C4⋊C4—153no—
243C2×C22⋊C4—156no—
244C2×C42—53no—
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
253C5×D3—212no—
254C23×C3C23×D511yescharacteristic
255C22×D3—26no—
256C22×D3—26no—
257C22×D3C22×Dic5112yes—
258C22×D3C23×D516yes—
259C3×Q8C22×Dic5116yescomplemented
260C2×C3×C4—54no—
261C2×C3×C4—52no—
262C2×C3×C4—56no—
263C2×C3×C4—106no—
264C2×C3×C4C22×Dic5112yes—
265C2×C3×C4C23×D516yes—
266C2×Dic3—54no—
267C2×Dic3—52no—
268C2×Dic3—56no—
269C2×Dic3—106no—
270C2×Dic3C22×Dic514yes—
271C2×Dic3C23×D512yes—
272D12C22×Dic5148yescomplemented
273C4×D3—1024no—
274C4×D3—1024no—
275C4×D3C22×Dic5148yescomplemented
276C22×C5—312no—
277C22×C5—66no—
278C22×C5—66no—
279C22×C5—624no—
280C22×C5C22×C4×D312yes—
281C22×C5C2×#23912yes—
282C22×C5D3×#4112yes—
283C22×C5C24×D311yescharacteristic
284C4×C5—34no—
285C4×C5C22×C4×D3112yes—
286Dic5—26no—
287Dic5—34no—
288Dic5—66no—
289Dic5C2×#23914yesdirect product factor
290C24—33no—
291#41—364no—
292C2×Q8D3×Dic518yescomplemented
293C2×Q8C2×D3×D514yes—
294C2×D4—324no—
295C2×D4—312no—
296C22×C4—31no—
297C22×C4—324no—
298C22×C4—312no—
299C22×C4—51no—
300C22×C4—53no—
301C22×C4—1512no—
302C22×C4—1512no—
303C22×C4—151no—
304C22×C4—153no—
305C22×C4—3012no—
306C22×C4—3012no—
307C22×C4C2×D3×D513yes—
308C4⋊C4—512no—
309C4⋊C4—1512no—
310C22⋊C4—1524no—
311C42—512no—
312C42—154no—
313C42—1512no—
314C42—1512no—
315C3×C5C2×C4×#4111yescharacteristic, complemented, Hall
316C22×C3D5×#4112yes—
317C22×C3D5×#4112yes—
318C22×C3C23×Dic512yes—
319C22×C3C24×D511yescharacteristic
320C2×D3—224no—
321C2×D3—26no—
322C2×D3—26no—
323C2×D3C23×Dic5112yes—
324C3×C4—54no—
325C3×C4—106no—
326C3×C4C23×Dic5112yes—
327Dic3—54no—
328Dic3—106no—
329Dic3C23×Dic514yes—
330C2×C5—612no—
331C2×C5C4×#23914yescomplemented
332C2×C5C23×C4×D311yescharacteristic
333C2×C5C22×#23911yescharacteristic
334C2×C5C2×D3×#4111yescharacteristic
335C23—312no—
336C23—36no—
337C23—66no—
338C23—66no—
339C23C22×D3×D511yescharacteristic
340Q8C2×D3×Dic5116yescomplemented
341D4—348no—
342C2×C4—34no—
343C2×C4—32no—
344C2×C4—348no—
345C2×C4—54no—
346C2×C4—52no—
347C2×C4—56no—
348C2×C4—106no—
349C2×C4—154no—
350C2×C4—152no—
351C2×C4—156no—
352C2×C4—3024no—
353C2×C4—3024no—
354C2×C4—306no—
355C2×C4C2×D3×Dic5112yes—
356C2×C4C22×D3×D516yes—
357C2×C3#41×Dic514yescomplemented
358C2×C3C2×D5×#4111yescharacteristic
359C2×C3C2×D5×#4111yescharacteristic
360C2×C3C24×Dic511yescharacteristic
361D3—212no—
362C5C2×C4×#23911yescharacteristic, complemented, Sylow
363C22—312no—
364C22—624no—
365C22—66no—
366C22—66no—
367C22D5×#23912yes—
368C22#9203412yes—
369C22C22×D3×Dic512yes—
370C22C23×D3×D511yescharacteristic
371C4—34no—
372C4—54no—
373C4—106no—
374C4—154no—
375C4—306no—
376C4C22×D3×Dic5112yes—
377C3C2×#41×Dic511yescharacteristic, complemented, Sylow
378C2—612no—
379C2Dic5×#23914yesdirect product factor
380C2C2×D5×#23911yescharacteristic
381C2C2×#9203411yescharacteristic
382C2C23×D3×Dic511yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutatorC2×C3×C5C24×C4
FrattiniC22C23×D3×D5
FittingC22×C3×C5×Q8C22
socleC23×C3×C5C24
prime radicalC22×C5×#239C2
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×C3×Q8×Dic5C2semidirect
4. Dic5×#239C2direct (N × H)
5. C2×#91435C2semidirect
6. C2×Dic5×D12C2semidirect
7. C2×C4×D3×Dic5C2semidirect
8. C2×#91338C2semidirect
11. C2×C5×#239C4semidirect
17. Q8×Dic15C22semidirect
20. C3×Q8×Dic5C22semidirect
26. #91435C22semidirect
27. Dic5×D12C22semidirect
28. C4×D3×Dic5C22semidirect
29. #91338C22semidirect
34. C2×Q8×Dic5D3semidirect
40. C2×C3×C5×Q8C2×C4semidirect
46. C5×#239C2×C4semidirect
47. C2×C5×D12C2×C4semidirect
49. C2×C4×C5×D3C2×C4semidirect
81. Q8×Dic5C2×D3semidirect
98. C3×C5×Q8C22×C4semidirect
102. C2×Dic15#41semidirect
107. C5×D12C22×C4semidirect
108. C4×C5×D3C22×C4semidirect
110. C2×C3×Dic5#41semidirect
116. C2×#239Dic5direct (N × H)
137. C2×C5×Q8C4×D3semidirect
178. Dic15C2×#41semidirect
180. C3×Dic5C2×#41semidirect
183. C2×C3×Q8C2×Dic5semidirect
191. #239C2×Dic5direct (N × H)
192. C2×D12C2×Dic5semidirect
198. C2×C4×D3C2×Dic5semidirect
212. C5×Q8C2×C4×D3semidirect
226. C2×Dic5#239direct (N × H)
249. C2×C3×C5C4×#41semidirect
259. C3×Q8C22×Dic5semidirect
272. D12C22×Dic5semidirect
275. C4×D3C22×Dic5semidirect
289. Dic5C2×#239direct (N × H)
292. C2×Q8D3×Dic5semidirect
315. C3×C5C2×C4×#41semidirect
331. C2×C5C4×#239semidirect
340. Q8C2×D3×Dic5semidirect
357. C2×C3#41×Dic5semidirect
362. C5C2×C4×#239semidirect
377. C3C2×#41×Dic5semidirect
379. C2Dic5×#239direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C5×#2392
C2×Q8×Dic152
C2×C3×Q8×Dic52
Dic5×#2392
C2×#914352
C2×Dic5×D122
C2×C4×D3×Dic52
C2×#913382
C2×#41×Dic53
C2×C4×#2395