Finite Group Databasebeta

← C22×C4⋊(C5⋊S4) #14514591

Subgroups — C22×C4⋊(C5⋊S4) #14514591

Order 1920.

2582 conjugacy classes of subgroups; only the 213 normal subgroups are shown.

normal subgroups only

This group has 2582 conjugacy classes of subgroups — too many to draw. Only its 213 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
1C23×C5⋊S4C212yesmaximal, complemented
2C22×C4×C5×A4C211yesmaximal, characteristic, complemented
3C2×C4⋊(C5⋊S4)C2112yesmaximal, direct product factor
4C22×#4076—31nomaximal, Hall
5C23×C5×A4C2211yescharacteristic
6C22×C5⋊S4—28no—
7C22×C5⋊S4C22112yescomplemented
8C22×D60—41nomaximal
9C2×C4×C5×A4C2216yescomplemented
10C4⋊(C5⋊S4)C22116yesdirect product factor
11C22×C4⋊S4—51nomaximal, Hall
12C24×C4×C5D311yescharacteristic, complemented
13C23×C22⋊D5—32no—
14C23×D20—31no—
15C2×#4076—312no—
16C2×#4076—312no—
17C22×#685—32no—
18C22×C4⋊Dic5—31no—
19C23×D15—42no—
20C22×C5×A4D414yescomplemented
21C22×C5×A4C2313yes—
22C2×C5⋊S4—224no—
23C2×C5⋊S4C2318yescomplemented
24C22×C3×C4×C5—41no—
25C2×D60—412no—
26C4×C5×A4C2314yescomplemented
27C23×S4—52no—
28C22×C4×A4D511yescharacteristic, complemented
29C2×C4⋊S4—512no—
30C25×C5C2×D311yescharacteristic
31C24×D5—32no—
32C23×C4×C5—31no—
33C23×C4×C5—31no—
34C23×C4×C5—36no—
35C23×C4×C5C2×D316yescomplemented
36C22×C22⋊D5—312no—
37C22×C22⋊D5—312no—
38C22×C22⋊D5—68no—
39C22×C22⋊D5—68no—
40C23×Dic5—32no—
41C22×D20—312no—
42C22×D20—61no—
43C22×D20—66no—
44C22×D20—61no—
45#4076—348no—
46#4076—316no—
47C2×#685—324no—
48C2×C4⋊Dic5—312no—
49C22×#121—151noSylow
50C23×C3×C5—41no—
51C22×D15—412no—
52C22×D15—88no—
53C2×C5×A4C2×D416yescomplemented
54C2×C5×A4C2411yescharacteristic
55C5⋊S4—28no—
56C2×C3×C4×C5—46no—
57D60—416no—
58C23×A4C2×D511yescharacteristic
59C22×S4—512no—
60C22×S4—108no—
61C22×D12—201no—
62C2×C4×A4C2×D516yescomplemented
63C4⋊S4—516no—
64C24×C5—31no—
65C24×C5—33no—
66C24×C5—34no—
67C24×C5D1214yescomplemented
68C24×C5C22×D313yes—
69C23×D5—312no—
70C23×D5—66no—
71C23×D5—68no—
72C23×D5—68no—
73C23×D5—62no—
74C22×C4×C5—31no—
75C22×C4×C5—36no—
76C22×C4×C5—36no—
77C22×C4×C5—36no—
78C22×C4×C5—312no—
79C22×C4×C5—64no—
80C22×C4×C5—63no—
81C22×C4×C5S411yescharacteristic, complemented
82C22×C4×C5C22×D314yescomplemented
83C2×C22⋊D5—324no—
84C2×C22⋊D5—38no—
85C2×C22⋊D5—648no—
86C2×C22⋊D5—624no—
87C2×C22⋊D5—624no—
88C22×Dic5—312no—
89C22×Dic5—68no—
90C2×D20—316no—
91C2×D20—612no—
92C2×D20—624no—
93C2×D20—612no—
94#685—332no—
95C4⋊Dic5—316no—
96C23×D4—151no—
97C23×D4—152no—
98C24×C4D1511yescharacteristic, complemented
99C2×#121—1512no—
100C2×#121—1512no—
101C22×C4⋊C4—151no—
102C22×C22⋊C4—152no—
103C22×C3×C5—44no—
104C22×C3×C5—43no—
105C2×D15—48no—
106C2×D15—824no—
107C5×A4C22×D411yescharacteristic, complemented
108C3×C4×C5—44no—
109C23×D3—202no—
110C22×A4D2014yescomplemented
111C22×A4C22×D513yes—
112C2×S4—58no—
113C2×S4—1024no—
114C22×C3×C4—41no—
115C2×D12—2012no—
116C4×A4C22×D514yescomplemented
117C23×C5—34no—
118C23×C5—34no—
119C23×C5—33no—
120C23×C5—33no—
121C23×C5—33no—
122C23×C5—312no—
123C23×C5—36no—
124C23×C5—61no—
125C23×C5—66no—
126C23×C5C2×D1216yescomplemented
127C23×C5C2×S411yescharacteristic
128C23×C5C23×D311yescharacteristic
129C22×D5—38no—
130C22×D5—612no—
131C22×D5—624no—
132C22×D5—624no—
133C22×D5—612no—
134C22×D5—1224no—
135C22×D5—128no—
136C2×C4×C5—36no—
137C2×C4×C5—34no—
138C2×C4×C5—312no—
139C2×C4×C5—34no—
140C2×C4×C5—66no—
141C2×C4×C5C2×S416yescomplemented
142C22⋊D5—648no—
143C22⋊D5—68no—
144C22⋊D5—68no—
145C2×Dic5—38no—
146C2×Dic5—624no—
147D20—616no—
148D20—616no—
149C25—152no—
150C25C2×D1511yescharacteristic
151C22×D4—1512no—
152C22×D4—1512no—
153C22×D4—1512no—
154C22×D4—301no—
155C22×D4—306no—
156C22×D4—308no—
157C22×D4—308no—
158C22×D4—301no—
159C23×C4—31no—
160C23×C4—31no—
161C23×C4—36no—
162C23×C4—152no—
163C23×C4C2×D1516yescomplemented
164#121—1548no—
165#121—1516no—
166C2×C4⋊C4—1512no—
167C2×C22⋊C4—1524no—
168C2×C3×C5—46no—
169C2×C3×C5—41no—
170D15—88no—
171C23×C3—41no—
172C22×D3—2012no—
173C22×D3—408no—
174C2×A4C2×D2016yescomplemented
175C2×A4C23×D511yescharacteristic
176S4—108no—
177C2×C3×C4—46no—
178D12—2016no—
179C22×C5—36no—
180C22×C5—31no—
181C22×C5—36no—
182C22×C5—36no—
183C22×C5—312no—
184C22×C5—31no—
185C22×C5—33no—
186C22×C5—63no—
187C22×C5—64no—
188C22×C5C4⋊S414yescomplemented
189C22×C5C22×D1211yescharacteristic, complemented
190C22×C5C22×S413yes—
191C2×D5—68no—
192C2×D5—68no—
193C2×D5—68no—
194C2×D5—1224no—
195C2×D5—1224no—
196C4×C5—34no—
197C4×C5C22×S414yescomplemented
198Dic5—68no—
199C24—31no—
200C24—33no—
201C24—34no—
202C24—1512no—
203C24—308no—
204C24—306no—
205C24—308no—
206C24—302no—
207C24D6014yescomplemented
208C24C22×D1513yes—
209C2×D4—1516no—
210C2×D4—1524no—
211C2×D4—158no—
212C2×D4—3012no—
213C2×D4—3024no—
214C2×D4—3048no—
215C2×D4—3024no—
216C2×D4—3024no—
217C2×D4—3012no—
218C22×C4—31no—
219C22×C4—36no—
220C22×C4—36no—
221C22×C4—36no—
222C22×C4—312no—
223C22×C4—64no—
224C22×C4—63no—
225C22×C4—1512no—
226C22×C4—308no—
227C22×C4C5⋊S411yescharacteristic, complemented
228C22×C4C22×D1514yescomplemented
229C4⋊C4—1516no—
230C22⋊C4—1532no—
231C3×C5—41noHall
232C22×C3—44no—
233C22×C3—43no—
234C2×D3—208no—
235C2×D3—4024no—
236A4C22×D2011yescharacteristic, complemented
237C3×C4—44no—
238C2×C5—31no—
239C2×C5—31no—
240C2×C5—36no—
241C2×C5C2×C4⋊S416yescomplemented
242C2×C5C23×S411yescharacteristic
243D5—128no—
244C23—34no—
245C23—34no—
246C23—33no—
247C23—33no—
248C23—33no—
249C23—312no—
250C23—36no—
251C23—61no—
252C23—66no—
253C23—158no—
254C23—3024no—
255C23—3012no—
256C23—3024no—
257C23—3012no—
258C23—6024no—
259C23—608no—
260C23C2×D6016yescomplemented
261C23C2×C5⋊S411yescharacteristic
262C23C23×D1511yescharacteristic
263D4—3016no—
264D4—3048no—
265D4—308no—
266D4—308no—
267D4—3016no—
268C2×C4—36no—
269C2×C4—34no—
270C2×C4—312no—
271C2×C4—34no—
272C2×C4—66no—
273C2×C4—158no—
274C2×C4—3024no—
275C2×C4C2×C5⋊S416yescomplemented
276C2×C3—46no—
277C2×C3—41no—
278D3—408no—
279C5C22×C4⋊S411yescharacteristic, complemented, Sylow
280C22—36no—
281C22—31no—
282C22—36no—
283C22—36no—
284C22—312no—
285C22—31no—
286C22—33no—
287C22—63no—
288C22—64no—
289C22—308no—
290C22—308no—
291C22—308no—
292C22—6024no—
293C22—6024no—
294C22C4⋊(C5⋊S4)14yesdirect product factor
295C22C22×D6011yescharacteristic, complemented
296C22C22×C5⋊S413yes—
297C4—34no—
298C4—308no—
299C4C22×C5⋊S414yescomplemented
300C3—41noSylow
301C2—31no—
302C2—31no—
303C2—36no—
304C2—608no—
305C2C2×C4⋊(C5⋊S4)16yesdirect product factor
306C2C23×C5⋊S411yescharacteristic
subgroupG/H
centerC23C2×C5⋊S4
commutator, cosocleC2×C5×A4C24
FrattiniC2C23×C5⋊S4
FittingC24×C4×C5D3
socleC25×C5C2×D3
hypercenterC22×C4C5⋊S4
hypocenterC5×A4C22×D4
LCSG ▷ C2×C5×A4 ▷ C5×A4
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. C23×C5⋊S4C2semidirect
2. C22×C4×C5×A4C2semidirect
3. C2×C4⋊(C5⋊S4)C2direct (N × H)
7. C22×C5⋊S4C22semidirect
9. C2×C4×C5×A4C22semidirect
10. C4⋊(C5⋊S4)C22direct (N × H)
12. C24×C4×C5D3semidirect
20. C22×C5×A4D4semidirect
23. C2×C5⋊S4C23semidirect
26. C4×C5×A4C23semidirect
28. C22×C4×A4D5semidirect
35. C23×C4×C5C2×D3semidirect
53. C2×C5×A4C2×D4semidirect
62. C2×C4×A4C2×D5semidirect
67. C24×C5D12semidirect
81. C22×C4×C5S4semidirect
82. C22×C4×C5C22×D3semidirect
98. C24×C4D15semidirect
107. C5×A4C22×D4semidirect
110. C22×A4D20semidirect
116. C4×A4C22×D5semidirect
126. C23×C5C2×D12semidirect
141. C2×C4×C5C2×S4semidirect
163. C23×C4C2×D15semidirect
174. C2×A4C2×D20semidirect
188. C22×C5C4⋊S4semidirect
189. C22×C5C22×D12semidirect
197. C4×C5C22×S4semidirect
207. C24D60semidirect
227. C22×C4C5⋊S4semidirect
228. C22×C4C22×D15semidirect
236. A4C22×D20semidirect
241. C2×C5C2×C4⋊S4semidirect
260. C23C2×D60semidirect
275. C2×C4C2×C5⋊S4semidirect
279. C5C22×C4⋊S4semidirect
294. C22C4⋊(C5⋊S4)direct (N × H)
295. C22C22×D60semidirect
299. C4C22×C5⋊S4semidirect
305. C2C2×C4⋊(C5⋊S4)direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C5⋊S42
C22×C4×C5×A42
C2×C4⋊(C5⋊S4)2
C22×#40763
C22×D604
C22×C4⋊S45