Finite Group Databasebeta

← C2×D3×#4022 #14479748

Subgroups — C2×D3×#4022 #14479748

Order 1920.

2640 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91765C211yesmaximal, characteristic, complemented
2C2×C42×C5×D3C211yesmaximal, characteristic, complemented
3C2×C3×#4022C211yesmaximal, characteristic, complemented
4C2×D3×#685C213yesmaximal
5C2×D3×#683C213yesmaximal, complemented
6C2×#91380C213yesmaximal, complemented
7C2×#91363C213yesmaximal, complemented
8D3×#4022C2116yesmaximal, direct product factor
9C22×#4022—31nomaximal, Hall
10C23×D3×D5C2211yescharacteristic
11C22×C4×C5×D3C2213yes—
12C22×D3×Dic5C2213yes—
13C2×C3×C42×C5C2211yescharacteristic, complemented
14C2×#6714C2213yes—
15C2×#6712C2213yescomplemented
16#91765C2218yescomplemented
17C2×C4×C5×Dic3C2213yescomplemented
18C42×C5×D3C2218yescomplemented
19C2×C3×#685C2213yes—
20C2×C3×#683C2213yescomplemented
21C3×#4022C2218yescomplemented
22C2×#6669C2213yescomplemented
23C2×#6668C2213yescomplemented
24C2×#6667C2213yes—
25C2×#6665C2213yes—
26D3×#685C22124yes—
27D3×#683C22124yescomplemented
28#91380C22124yescomplemented
29#91363C22124yescomplemented
30C2×D3×#126—51nomaximal, Hall
31C22×C42×C5—31no—
32C22×#685—33no—
33C22×#683—33no—
34C2×#4022—33no—
35C2×#4022—33no—
36C2×#4022—316no—
37C2×#4022—31no—
38C2×#4022D311yescharacteristic, direct product factor
39C23×D15C2311yescharacteristic
40C23×C5×D3C2311yescharacteristic
41C23×C3×D5C2311yescharacteristic
42C22×D3×D5—212no—
43C22×D3×D5C2314yes—
44C22×C3×C4×C5C2313yes—
45C22×Dic15C2313yes—
46C22×C5×Dic3C2313yes—
47C2×C4×C5×D3—212no—
48C2×C4×C5×D3C23112yes—
49C22×C3×Dic5C2313yes—
50C2×D3×Dic5—212no—
51C2×D3×Dic5C23112yes—
52C3×C42×C5C2314yescomplemented
53#6714C23112yes—
54#6712C23112yescomplemented
55C4×C5×Dic3C23112yescomplemented
56C3×#685C23112yes—
57C3×#683C23112yescomplemented
58#6669C23112yescomplemented
59#6668C23112yescomplemented
60#6667C23112yes—
61#6665C23112yes—
62C2×C3×#126—51no—
63D3×#126—516no—
64C2×#898—53no—
65C2×D3×C4⋊C4—53no—
66C2×D3×C22⋊C4—53no—
67C2×#879—53no—
68C2×#876—51no—
69C2×C42×D3D511yescharacteristic, complemented
70C24×D5—31no—
71C23×C4×C5—33no—
72C23×Dic5—33no—
73C2×C42×C5—33no—
74C2×C42×C5—38no—
75C2×C42×C5C2×D311yescharacteristic, complemented
76C2×#685—33no—
77C2×#685—33no—
78C2×#685—33no—
79C2×#685—324no—
80C2×#685C2×D313yes—
81C2×#683—33no—
82C2×#683—33no—
83C2×#683—33no—
84C2×#683—324no—
85C2×#683C2×D313yescomplemented
86#4022—38no—
87#4022—324no—
88#4022—324no—
89#4022C2×D318yesdirect product factor
90C22×#126—151noSylow
91C23×C3×C5C2411yescharacteristic
92C22×D15—26no—
93C22×D15C2412yes—
94C22×C5×D3#41112yes—
95C22×C5×D3C2412yes—
96C22×C3×D5—26no—
97C22×C3×D5C2412yes—
98C2×D3×D5—224no—
99C2×D3×D5—416no—
100C2×C3×C4×C5—26no—
101C2×C3×C4×C5C2416yes—
102C2×Dic15—26no—
103C2×Dic15C2416yes—
104C2×C5×Dic3—26no—
105C2×C5×Dic3C2416yes—
106C4×C5×D3—224no—
107C2×C3×Dic5—26no—
108C2×C3×Dic5C2416yes—
109D3×Dic5—224no—
110C24×D3—51no—
111C22×C4×D3—53no—
112C22×C4×D3C2×D513yes—
113C3×#126—58no—
114C2×C3×C4⋊C4—53no—
115C2×C3×C22⋊C4—53no—
116C2×C3×C42C2×D511yescharacteristic, complemented
117C2×#217—53no—
118C2×(C2×D3)⋊C4—53no—
119C2×(C2×D3)⋊C4—53no—
120C2×C4⋊Dic3—53no—
121C2×Dic3⋊C4—53no—
122C2×Dic3⋊C4—53no—
123C2×C4×Dic3C2×D513yescomplemented
124#898—524no—
125D3×C4⋊C4—524no—
126D3×C22⋊C4—524no—
127#879—524no—
128#876—58no—
129C42×D3C2×D518yescomplemented
130C24×C5—31no—
131C23×D5—31no—
132C23×D5—34no—
133C23×D5—612no—
134C23×D5C22×D311yescharacteristic
135C22×C4×C5—33no—
136C22×C4×C5—312no—
137C22×C4×C5—612no—
138C22×C4×C5C22×D313yes—
139C22×Dic5—33no—
140C22×Dic5—312no—
141C22×Dic5—612no—
142C22×Dic5C22×D313yes—
143C42×C5—312no—
144C42×C5C22×D314yescomplemented
145#685—312no—
146#685—312no—
147#685—312no—
148#685C22×D3112yes—
149#683—312no—
150#683—312no—
151#683—312no—
152#683C22×D3112yescomplemented
153C2×#126—51no—
154C2×#126—153no—
155C2×#126—153no—
156C2×#126—1516no—
157C2×#126—151no—
158C22×C4⋊C4—153no—
159C22×C22⋊C4—153no—
160C22×C42—31no—
161C22×C3×C5C2×#4116yes—
162C22×C3×C5C2511yescharacteristic
163C2×D15—26no—
164C2×D15—44no—
165C2×C5×D3#126116yescomplemented
166C2×C5×D3C2×#41112yes—
167C2×C3×D5—26no—
168C2×C3×D5—44no—
169D3×D5—416no—
170C3×C4×C5—26no—
171Dic15—26no—
172C3×Dic5—26no—
173C5×Dic3—26no—
174C24×C3—51no—
175C23×D3—51no—
176C23×D3—54no—
177C23×D3—1012no—
178C23×D3C22×D511yescharacteristic
179C22×C3×C4—53no—
180C22×C3×C4C22×D513yes—
181C22×Dic3—53no—
182C22×Dic3C22×D513yes—
183C2×C4×D3—212no—
184C2×C4×D3—512no—
185C2×C4×D3—1012no—
186C2×C4×D3C22×D5112yes—
187C3×C4⋊C4—512no—
188C3×C22⋊C4—512no—
189C3×C42C22×D514yescomplemented
190#217—512no—
191(C2×D3)⋊C4—512no—
192(C2×D3)⋊C4—512no—
193C4⋊Dic3—512no—
194Dic3⋊C4—512no—
195Dic3⋊C4—512no—
196C4×Dic3C22×D5112yescomplemented
197C23×C5—312no—
198C23×C5—32no—
199C23×C5C23×D311yescharacteristic
200C22×D5—26no—
201C22×D5—32no—
202C22×D5—624no—
203C22×D5—66no—
204C22×D5—1216no—
205C22×D5C23×D312yes—
206C2×C4×C5—26no—
207C2×C4×C5—36no—
208C2×C4×C5—624no—
209C2×C4×C5—66no—
210C2×C4×C5C23×D316yes—
211C2×Dic5—26no—
212C2×Dic5—36no—
213C2×Dic5—624no—
214C2×Dic5—66no—
215C2×Dic5C23×D316yes—
216C25—151no—
217C23×C4—33no—
218C23×C4—153no—
219#126—58no—
220#126—1524no—
221#126—1524no—
222#126—158no—
223C2×C4⋊C4—53no—
224C2×C4⋊C4—1524no—
225C2×C4⋊C4—153no—
226C2×C4⋊C4—153no—
227C2×C4⋊C4—153no—
228C2×C22⋊C4—53no—
229C2×C22⋊C4—1524no—
230C2×C22⋊C4—153no—
231C2×C22⋊C4—153no—
232C2×C22⋊C4—153no—
233C2×C42—33no—
234C2×C42—38no—
235C2×C42D3×D511yescharacteristic, complemented
236C2×C3×C5C2×#12614yescomplemented
237C2×C3×C5C22×#4113yes—
238D15—42no—
239C3×D5—42no—
240C5×D3C2×#12618yescomplemented
241C23×C3—52no—
242C23×C3—106no—
243C23×C3C23×D511yescharacteristic
244C22×D3—52no—
245C22×D3—106no—
246C22×D3—1024no—
247C22×D3—2016no—
248C22×D3#709112yes—
249C22×D3C23×D512yes—
250C2×C3×C4—26no—
251C2×C3×C4—56no—
252C2×C3×C4—106no—
253C2×C3×C4C23×D516yes—
254C2×Dic3—26no—
255C2×Dic3—56no—
256C2×Dic3—106no—
257C2×Dic3C23×D516yes—
258C4×D3—224no—
259C4×D3—1024no—
260C22×C5—316no—
261C22×C5—312no—
262C22×C5D3×#4116yes—
263C22×C5C24×D311yescharacteristic
264C2×D5—26no—
265C2×D5—44no—
266C2×D5—66no—
267C2×D5—1216no—
268C2×D5—124no—
269C4×C5—26no—
270C4×C5—66no—
271Dic5—26no—
272Dic5—66no—
273C24—31no—
274C24—51no—
275C24—154no—
276C24—151no—
277C24—3012no—
278C22×C4—33no—
279C22×C4—312no—
280C22×C4—53no—
281C22×C4—612no—
282C22×C4—1512no—
283C22×C4—153no—
284C22×C4—3012no—
285C22×C4C2×D3×D513yes—
286C4⋊C4—512no—
287C4⋊C4—1512no—
288C4⋊C4—1512no—
289C4⋊C4—1512no—
290C22⋊C4—512no—
291C22⋊C4—1512no—
292C22⋊C4—1512no—
293C22⋊C4—1512no—
294C42—312no—
295C42C2×D3×D514yescomplemented
296C3×C5C22×#12611yescharacteristic, complemented, Hall
297C22×C3—106no—
298C22×C3—204no—
299C22×C3C2×#70916yes—
300C22×C3C24×D511yescharacteristic
301C2×D3—106no—
302C2×D3—204no—
303C2×D3—2016no—
304C2×D3#4022116yesdirect product factor
305C2×D3C2×#709112yes—
306C3×C4—26no—
307C3×C4—106no—
308Dic3—26no—
309Dic3—106no—
310C2×C5—38no—
311C2×C5D3×#12614yescomplemented
312C2×C5C2×D3×#4113yes—
313D5—42no—
314D5—122no—
315C23—312no—
316C23—32no—
317C23—52no—
318C23—106no—
319C23—152no—
320C23—3024no—
321C23—306no—
322C23—6016no—
323C23C22×D3×D511yescharacteristic
324C2×C4—26no—
325C2×C4—36no—
326C2×C4—56no—
327C2×C4—624no—
328C2×C4—66no—
329C2×C4—106no—
330C2×C4—156no—
331C2×C4—3024no—
332C2×C4—306no—
333C2×C4C22×D3×D516yes—
334C2×C3—202no—
335C2×C3C2×#402214yescomplemented
336C2×C3C22×#70913yes—
337D3—202no—
338D3C2×#402218yesdirect product factor
339C5C2×D3×#12611yescharacteristic, complemented, Sylow
340C22—316no—
341C22—312no—
342C22—106no—
343C22—204no—
344C22—306no—
345C22—6016no—
346C22—604no—
347C22D3×#70916yes—
348C22C23×D3×D511yescharacteristic
349C4—26no—
350C4—66no—
351C4—106no—
352C4—306no—
353C3C22×#402211yescharacteristic, complemented, Sylow
354C2—38no—
355C2—202no—
356C2—602no—
357C2D3×#402214yesdirect product factor
358C2C2×D3×#70913yes—
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC2×C3×C42×C5C22
socleC23×C3×C5C24
prime radicalC23×D3×D5C22
hypercenterC2×C42D3×D5
hypocenterC3×C5C22×#126
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C2×#91765C2semidirect
2. C2×C42×C5×D3C2semidirect
3. C2×C3×#4022C2semidirect
5. C2×D3×#683C2semidirect
6. C2×#91380C2semidirect
7. C2×#91363C2semidirect
8. D3×#4022C2direct (N × H)
13. C2×C3×C42×C5C22semidirect
15. C2×#6712C22semidirect
16. #91765C22semidirect
17. C2×C4×C5×Dic3C22semidirect
18. C42×C5×D3C22semidirect
20. C2×C3×#683C22semidirect
21. C3×#4022C22semidirect
22. C2×#6669C22semidirect
23. C2×#6668C22semidirect
27. D3×#683C22semidirect
28. #91380C22semidirect
29. #91363C22semidirect
38. C2×#4022D3direct (N × H)
52. C3×C42×C5C23semidirect
54. #6712C23semidirect
55. C4×C5×Dic3C23semidirect
57. C3×#683C23semidirect
58. #6669C23semidirect
59. #6668C23semidirect
69. C2×C42×D3D5semidirect
75. C2×C42×C5C2×D3semidirect
85. C2×#683C2×D3semidirect
89. #4022C2×D3direct (N × H)
116. C2×C3×C42C2×D5semidirect
123. C2×C4×Dic3C2×D5semidirect
129. C42×D3C2×D5semidirect
144. C42×C5C22×D3semidirect
152. #683C22×D3semidirect
165. C2×C5×D3#126semidirect
189. C3×C42C22×D5semidirect
196. C4×Dic3C22×D5semidirect
235. C2×C42D3×D5semidirect
236. C2×C3×C5C2×#126semidirect
240. C5×D3C2×#126semidirect
295. C42C2×D3×D5semidirect
296. C3×C5C22×#126semidirect
304. C2×D3#4022direct (N × H)
311. C2×C5D3×#126semidirect
335. C2×C3C2×#4022semidirect
338. D3C2×#4022direct (N × H)
339. C5C2×D3×#126semidirect
353. C3C22×#4022semidirect
357. C2D3×#4022direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#917652
C2×C42×C5×D32
C2×C3×#40222
C2×D3×#6852
C2×D3×#6832
C2×#913802
C2×#913632
D3×#40222
C22×#40223
C2×D3×#1265