Finite Group Databasebeta

← C42×D5×A4 #14513976

Subgroups — C42×D5×A4 #14513976

Order 1920.

1360 conjugacy classes of subgroups; only the 207 normal subgroups are shown.

normal subgroups only

This group has 1360 conjugacy classes of subgroups — too many to draw. Only its 207 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
1C2×C4×D5×A4C213yesmaximal
2C42×C5×A4C211yesmaximal, characteristic, complemented
3C4×A4×Dic5C213yesmaximal, complemented
4C22×C42×D5C311yesmaximal, characteristic, complemented, Hall
5C22×D5×A4C2211yescharacteristic
6C2×C4×C5×A4C2213yes—
7C2×A4×Dic5C2213yes—
8C4×D5×A4C4112yesdirect product factor
9C3×C42×D5—41nomaximal
10C2×C42×A4—51nomaximal, Hall
11C23×C4×D5C2×C313yes—
12C22×C42×C5C2×C311yescharacteristic, complemented
13C22×C4×Dic5C2×C313yescomplemented
14C2×C42×D5—31no—
15C2×C42×D5—31no—
16C2×C42×D5—33no—
17C2×C42×D5—33no—
18C22×C5×A4C2311yescharacteristic
19C2×D5×A4C2×C416yes—
20C2×C3×C4×D5—43no—
21C4×C5×A4C2×C416yescomplemented
22A4×Dic5C2×C416yescomplemented
23C3×C42×C5—41no—
24C3×C4×Dic5—43no—
25C22×C4×A4—53no—
26C42×A4—53no—
27C42×A4D511yescharacteristic, direct product factor
28C24×D5C22×C311yescharacteristic
29C23×C4×C5C22×C313yes—
30C23×Dic5C22×C313yes—
31C22×C4×D5—33no—
32C22×C4×D5—33no—
33C22×C4×D5—33no—
34C22×C4×D5—33no—
35C22×C4×D5—312no—
36C22×C4×D5C3×C4112yescomplemented
37C2×C42×C5—31no—
38C2×C42×C5—33no—
39C2×C4×Dic5—33no—
40C2×C4×Dic5—33no—
41C2×C4×Dic5—36no—
42C42×D5—32no—
43C42×D5—36no—
44C42×D5—36no—
45C42×D5—33no—
46C42×D5—31no—
47C42×D5—33no—
48C42×D5A411yescharacteristic, direct product factor
49C23×C42—51noSylow
50C22×C3×D5—41no—
51C2×C5×A4C22×C413yes—
52D5×A4C4214yesdirect product factor
53C2×C3×C4×C5—43no—
54C2×C3×Dic5—43no—
55C3×C4×D5—412no—
56C23×A4—51no—
57C2×C4×A4—53no—
58C2×C4×A4—512no—
59C2×C4×A4C2×D513yes—
60C2×C3×C42—201no—
61C24×C5C23×C311yescharacteristic
62C23×D5—31no—
63C23×D5—31no—
64C23×D5—36no—
65C23×D5C2×C3×C416yes—
66C22×C4×C5—33no—
67C22×C4×C5—33no—
68C22×C4×C5—36no—
69C22×C4×C5C2×C3×C416yescomplemented
70C22×Dic5—33no—
71C22×Dic5—36no—
72C22×Dic5—33no—
73C22×Dic5C2×C3×C416yescomplemented
74C2×C4×D5—312no—
75C2×C4×D5—312no—
76C2×C4×D5—312no—
77C2×C4×D5—36no—
78C2×C4×D5—33no—
79C2×C4×D5—33no—
80C2×C4×D5—33no—
81C2×C4×D5—312no—
82C2×C4×D5—312no—
83C2×C4×D5—312no—
84C2×C4×D5—312no—
85C2×C4×D5—312no—
86C2×C4×D5C2×A413yes—
87C42×C5—32no—
88C42×C5—33no—
89C42×C5C2×A411yescharacteristic, complemented
90C4×Dic5—36no—
91C4×Dic5—33no—
92C4×Dic5—36no—
93C4×Dic5C2×A413yescomplemented
94C24×C4—53no—
95C22×C42—53no—
96C22×C42—151no—
97C22×C42—151no—
98C22×C42—153no—
99C22×C42—153no—
100C22×C42C3×D511yescharacteristic, complemented
101C22×C3×C5—41no—
102C2×C3×D5—46no—
103C5×A4C2×C4211yescharacteristic, complemented
104C3×C4×C5—46no—
105C3×Dic5—46no—
106C22×A4—56no—
107C22×A4C22×D511yescharacteristic
108C22×C3×C4—203no—
109C4×A4—56no—
110C4×A4C4×D516yesdirect product factor
111C3×C42—41no—
112C3×C42—203no—
113C23×C5—33no—
114C23×C5—31no—
115C23×C5C22×C3×C413yes—
116C22×D5—36no—
117C22×D5—38no—
118C22×D5—31no—
119C22×D5—36no—
120C22×D5—36no—
121C22×D5—36no—
122C22×D5—312no—
123C22×D5C3×C4214yescomplemented
124C22×D5C22×A411yescharacteristic
125C2×C4×C5—36no—
126C2×C4×C5—33no—
127C2×C4×C5—36no—
128C2×C4×C5—36no—
129C2×C4×C5—36no—
130C2×C4×C5C22×A413yes—
131C2×Dic5—36no—
132C2×Dic5—33no—
133C2×Dic5—36no—
134C2×Dic5—36no—
135C2×Dic5—36no—
136C2×Dic5C22×A413yes—
137C4×D5—324no—
138C4×D5—312no—
139C4×D5—312no—
140C4×D5—312no—
141C4×D5C4×A4112yesdirect product factor
142C25—51no—
143C23×C4—53no—
144C23×C4—512no—
145C23×C4—153no—
146C23×C4—1512no—
147C23×C4—153no—
148C23×C4—153no—
149C23×C4—153no—
150C23×C4C2×C3×D513yes—
151C2×C42—31no—
152C2×C42—33no—
153C2×C42—51no—
154C2×C42—153no—
155C2×C42—153no—
156C2×C42—156no—
157C2×C42—152no—
158C2×C42—156no—
159C2×C42—153no—
160C2×C42—151no—
161C2×C42—156no—
162C2×C42—153no—
163C2×C3×C5—43no—
164C3×D5—44no—
165C23×C3—201no—
166C2×A4—54no—
167C2×A4C2×C4×D513yes—
168C2×C3×C4—43no—
169C2×C3×C4—2012no—
170C2×C3×C4—203no—
171C22×C5—33no—
172C22×C5—32no—
173C22×C5—33no—
174C22×C5—33no—
175C22×C5C2×C3×C4211yescharacteristic, complemented
176C22×C5C23×A411yescharacteristic
177C2×D5—312no—
178C2×D5—36no—
179C2×D5—312no—
180C2×D5—34no—
181C2×D5—34no—
182C2×D5C2×C4×A416yes—
183C4×C5—36no—
184C4×C5C2×C4×A416yescomplemented
185Dic5—36no—
186Dic5C2×C4×A416yescomplemented
187C24—56no—
188C24—151no—
189C24—151no—
190C24—156no—
191C24C22×C3×D511yescharacteristic
192C22×C4—33no—
193C22×C4—33no—
194C22×C4—36no—
195C22×C4—53no—
196C22×C4—56no—
197C22×C4—153no—
198C22×C4—1512no—
199C22×C4—1512no—
200C22×C4—153no—
201C22×C4—156no—
202C22×C4—1512no—
203C22×C4—1512no—
204C22×C4—1512no—
205C22×C4—1512no—
206C22×C4—1512no—
207C22×C4—1512no—
208C22×C4—153no—
209C22×C4—153no—
210C22×C4—153no—
211C22×C4—156no—
212C22×C4C3×C4×D516yescomplemented
213C42—32no—
214C42—33no—
215C42—53no—
216C42—156no—
217C42—156no—
218C42—153no—
219C42D5×A411yescharacteristic, direct product factor
220C3×C5—41noHall
221C22×C3—41no—
222C22×C3—206no—
223A4C42×D511yescharacteristic, direct product factor
224C3×C4—46no—
225C3×C4—206no—
226C2×C5—33no—
227C2×C5—31no—
228C2×C5C22×C4×A413yes—
229D5—34no—
230D5C42×A414yesdirect product factor
231C23—33no—
232C23—31no—
233C23—51no—
234C23—54no—
235C23—156no—
236C23—156no—
237C23—156no—
238C23—1512no—
239C23—156no—
240C23—158no—
241C23—151no—
242C23C2×C3×C4×D513yes—
243C2×C4—36no—
244C2×C4—33no—
245C2×C4—36no—
246C2×C4—36no—
247C2×C4—36no—
248C2×C4—53no—
249C2×C4—512no—
250C2×C4—1512no—
251C2×C4—1512no—
252C2×C4—1524no—
253C2×C4—156no—
254C2×C4—156no—
255C2×C4—156no—
256C2×C4—153no—
257C2×C4—1512no—
258C2×C4—156no—
259C2×C4C2×D5×A413yes—
260C2×C3—43no—
261C2×C3—204no—
262C5C2×C42×A411yescharacteristic, complemented, Sylow
263C22—33no—
264C22—32no—
265C22—33no—
266C22—33no—
267C22—56no—
268C22—154no—
269C22—1512no—
270C22—154no—
271C22—1512no—
272C22—156no—
273C22C3×C42×D511yescharacteristic, complemented
274C22C22×D5×A411yescharacteristic
275C4—36no—
276C4—56no—
277C4—156no—
278C4C4×D5×A416yesdirect product factor
279C3—41noSylow
280C2—31no—
281C2—33no—
282C2—54no—
283C2—154no—
284C2C2×C4×D5×A413yes—
subgroupG/H
center, hypercenterC42D5×A4
commutator, hypocenterC22×C5C2×C3×C42
FrattiniC22C22×D5×A4
FittingC22×C42×C5C2×C3
socle, cosocleC24×C5C23×C3
prime radicalC22×D5×A4C22
LCSG ▷ C22×C5
UCSC1 ◁ C42

Complements

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

NH ≅ G/Ntype
2. C42×C5×A4C2semidirect
3. C4×A4×Dic5C2semidirect
4. C22×C42×D5C3semidirect
8. C4×D5×A4C4direct (N × H)
12. C22×C42×C5C2×C3semidirect
13. C22×C4×Dic5C2×C3semidirect
21. C4×C5×A4C2×C4semidirect
22. A4×Dic5C2×C4semidirect
27. C42×A4D5direct (N × H)
36. C22×C4×D5C3×C4semidirect
48. C42×D5A4direct (N × H)
52. D5×A4C42direct (N × H)
69. C22×C4×C5C2×C3×C4semidirect
73. C22×Dic5C2×C3×C4semidirect
89. C42×C5C2×A4semidirect
93. C4×Dic5C2×A4semidirect
100. C22×C42C3×D5semidirect
103. C5×A4C2×C42semidirect
110. C4×A4C4×D5direct (N × H)
123. C22×D5C3×C42semidirect
141. C4×D5C4×A4direct (N × H)
175. C22×C5C2×C3×C42semidirect
184. C4×C5C2×C4×A4semidirect
186. Dic5C2×C4×A4semidirect
212. C22×C4C3×C4×D5semidirect
219. C42D5×A4direct (N × H)
223. A4C42×D5direct (N × H)
230. D5C42×A4direct (N × H)
262. C5C2×C42×A4semidirect
273. C22C3×C42×D5semidirect
278. C4C4×D5×A4direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×D5×A42
C42×C5×A42
C4×A4×Dic52
C22×C42×D53
C3×C42×D54
C2×C42×A45