Finite Group Databasebeta

← C5×A4×C4⋊Q8 #14511331

Subgroups — C5×A4×C4⋊Q8 #14511331

Order 1920.

768 conjugacy classes of subgroups; only the 156 normal subgroups are shown.

normal subgroups only

This group has 768 conjugacy classes of subgroups — too many to draw. Only its 156 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×C5×Q8×A4C212yesmaximal
2C5×A4×C4⋊C4C214yesmaximal
3C42×C5×A4C211yesmaximal, characteristic
4C22×C5×C4⋊Q8C311yesmaximal, characteristic, complemented, Hall
5C5×Q8×A4—24no—
6C2×C4×C5×A4C2214yes—
7C2×C4×C5×A4C2211yescharacteristic
8C2×C4×C5×A4C2212yes—
9C3×C5×C4⋊Q8—41nomaximal
10A4×C4⋊Q8C511yesmaximal, characteristic, direct product factor, Hall
11C23×C5×Q8C2×C312yes—
12C2×C5×C4⋊Q8—31no—
13C2×C5×C4⋊Q8—31no—
14C2×C5×C4⋊Q8—34no—
15C2×C5×C4⋊Q8—32no—
16C22×C5×C4⋊C4C2×C314yes—
17C22×C42×C5C2×C311yescharacteristic
18C22×C5×A4C2311yescharacteristic
19C2×C3×C5×Q8—42no—
20C4×C5×A4—24no—
21C4×C5×A4D412yes—
22C4×C5×A4Q814yescomplemented
23C3×C5×C4⋊C4—44no—
24C3×C42×C5—41no—
25C2×Q8×A4C2×C512yes—
26A4×C4⋊C4C2×C514yes—
27C42×A4C2×C511yescharacteristic
28C22×C5×Q8—24no—
29C22×C5×Q8—32no—
30C22×C5×Q8—34no—
31C22×C5×Q8—32no—
32C22×C5×Q8—64no—
33C23×C4×C5C22×C314yes—
34C23×C4×C5C22×C311yescharacteristic
35C23×C4×C5C22×C312yes—
36C5×C4⋊Q8—38no—
37C5×C4⋊Q8—32no—
38C5×C4⋊Q8—34no—
39C5×C4⋊Q8—32no—
40C5×C4⋊Q8—34no—
41C5×C4⋊Q8—31no—
42C5×C4⋊Q8A411yescharacteristic, direct product factor
43C2×C5×C4⋊C4—34no—
44C2×C5×C4⋊C4—34no—
45C2×C5×C4⋊C4—38no—
46C2×C42×C5—31no—
47C2×C42×C5—32no—
48C2×C42×C5—31no—
49C22×C4⋊Q8C3×C511yescharacteristic, complemented, Sylow
50C2×C5×A4C2×D411yescharacteristic
51C2×C5×A4C2×Q812yes—
52C3×C5×Q8—84no—
53C2×C3×C4×C5—42no—
54C2×C3×C4×C5—41no—
55C2×C3×C4×C5—44no—
56Q8×A4—24no—
57C2×C4×A4C22×C514yes—
58C2×C4×A4C22×C511yescharacteristic
59C2×C4×A4C22×C512yes—
60C3×C4⋊Q8—41no—
61C24×C5C23×C311yescharacteristic
62C2×C5×Q8—34no—
63C2×C5×Q8—34no—
64C2×C5×Q8—32no—
65C2×C5×Q8—64no—
66C2×C5×Q8—64no—
67C2×C5×Q8—64no—
68C2×C5×Q8—68no—
69C2×C5×Q8—64no—
70C2×C5×Q8—68no—
71C2×C5×Q8C2×A412yes—
72C22×C4×C5—24no—
73C22×C4×C5—32no—
74C22×C4×C5—31no—
75C22×C4×C5—32no—
76C22×C4×C5—31no—
77C22×C4×C5—34no—
78C22×C4×C5—32no—
79C22×C4×C5—34no—
80C22×C4×C5—34no—
81C22×C4×C5—64no—
82C22×C4×C5C3×D412yes—
83C22×C4×C5C3×Q814yescomplemented
84C5×C4⋊C4—38no—
85C5×C4⋊C4—38no—
86C5×C4⋊C4—34no—
87C5×C4⋊C4C2×A414yes—
88C42×C5—32no—
89C42×C5—31no—
90C42×C5—32no—
91C42×C5C2×A411yescharacteristic
92C23×Q8C2×C3×C512yes—
93C2×C4⋊Q8—31no—
94C2×C4⋊Q8—31no—
95C2×C4⋊Q8—34no—
96C2×C4⋊Q8—32no—
97C22×C4⋊C4C2×C3×C514yes—
98C22×C42C2×C3×C511yescharacteristic
99C22×C3×C5—41no—
100C5×A4C4⋊Q811yescharacteristic, direct product factor
101C3×C4×C5—42no—
102C3×C4×C5—44no—
103C3×C4×C5—84no—
104C22×A4C23×C511yescharacteristic
105C2×C3×Q8—42no—
106C4×A4—24no—
107C4×A4C5×D412yes—
108C4×A4C5×Q814yescomplemented
109C3×C4⋊C4—44no—
110C3×C42—41no—
111C23×C5—31no—
112C23×C5—32no—
113C23×C5—31no—
114C23×C5C2×C3×D411yescharacteristic
115C23×C5C2×C3×Q812yes—
116C5×Q8—24no—
117C5×Q8—68no—
118C5×Q8—68no—
119C5×Q8—64no—
120C2×C4×C5—34no—
121C2×C4×C5—32no—
122C2×C4×C5—32no—
123C2×C4×C5—31no—
124C2×C4×C5—32no—
125C2×C4×C5—32no—
126C2×C4×C5—34no—
127C2×C4×C5—34no—
128C2×C4×C5—32no—
129C2×C4×C5—34no—
130C2×C4×C5—34no—
131C2×C4×C5—64no—
132C2×C4×C5—64no—
133C2×C4×C5—64no—
134C2×C4×C5—64no—
135C2×C4×C5C22×A414yes—
136C2×C4×C5C22×A411yescharacteristic
137C2×C4×C5C22×A412yes—
138C22×Q8—24no—
139C22×Q8—32no—
140C22×Q8—34no—
141C22×Q8—32no—
142C22×Q8—64no—
143C23×C4C22×C3×C514yes—
144C23×C4C22×C3×C511yescharacteristic
145C23×C4C22×C3×C512yes—
146C4⋊Q8—38no—
147C4⋊Q8—32no—
148C4⋊Q8—34no—
149C4⋊Q8—32no—
150C4⋊Q8—34no—
151C4⋊Q8—31no—
152C4⋊Q8C5×A411yescharacteristic, direct product factor
153C2×C4⋊C4—34no—
154C2×C4⋊C4—34no—
155C2×C4⋊C4—38no—
156C2×C42—31no—
157C2×C42—32no—
158C2×C42—31no—
159C2×C3×C5—41no—
160C2×C3×C5—42no—
161C2×A4C2×C5×D411yescharacteristic
162C2×A4C2×C5×Q812yes—
163C3×Q8—84no—
164C2×C3×C4—42no—
165C2×C3×C4—41no—
166C2×C3×C4—44no—
167C22×C5—31no—
168C22×C5—32no—
169C22×C5—32no—
170C22×C5—31no—
171C22×C5—31no—
172C22×C5—32no—
173C22×C5—32no—
174C22×C5C3×C4⋊Q811yescharacteristic, complemented
175C22×C5C23×A411yescharacteristic
176C4×C5—24no—
177C4×C5—32no—
178C4×C5—34no—
179C4×C5—64no—
180C4×C5D4×A412yes—
181C4×C5Q8×A414yescomplemented
182C24C23×C3×C511yescharacteristic
183C2×Q8—34no—
184C2×Q8—34no—
185C2×Q8—32no—
186C2×Q8—64no—
187C2×Q8—64no—
188C2×Q8—64no—
189C2×Q8—68no—
190C2×Q8—64no—
191C2×Q8—68no—
192C2×Q8C2×C5×A412yes—
193C22×C4—24no—
194C22×C4—32no—
195C22×C4—31no—
196C22×C4—32no—
197C22×C4—31no—
198C22×C4—32no—
199C22×C4—34no—
200C22×C4—34no—
201C22×C4—34no—
202C22×C4—64no—
203C22×C4C3×C5×D412yes—
204C22×C4C3×C5×Q814yescomplemented
205C4⋊C4—38no—
206C4⋊C4—38no—
207C4⋊C4—34no—
208C4⋊C4C2×C5×A414yes—
209C42—32no—
210C42—31no—
211C42—32no—
212C42C2×C5×A411yescharacteristic
213C3×C5—41noHall
214C22×C3—41no—
215A4C5×C4⋊Q811yescharacteristic, direct product factor
216C3×C4—42no—
217C3×C4—44no—
218C3×C4—84no—
219C2×C5—31no—
220C2×C5—32no—
221C2×C5—31no—
222C2×C5C2×D4×A411yescharacteristic
223C2×C5C2×Q8×A412yes—
224C23—31no—
225C23—32no—
226C23—31no—
227C23C2×C3×C5×D411yescharacteristic
228C23C2×C3×C5×Q812yes—
229Q8—24no—
230Q8—68no—
231Q8—68no—
232Q8—64no—
233C2×C4—32no—
234C2×C4—34no—
235C2×C4—32no—
236C2×C4—31no—
237C2×C4—32no—
238C2×C4—32no—
239C2×C4—34no—
240C2×C4—34no—
241C2×C4—32no—
242C2×C4—34no—
243C2×C4—34no—
244C2×C4—64no—
245C2×C4—64no—
246C2×C4—64no—
247C2×C4—64no—
248C2×C4C22×C5×A414yes—
249C2×C4C22×C5×A411yescharacteristic
250C2×C4C22×C5×A412yes—
251C2×C3—41no—
252C2×C3—42no—
253C5A4×C4⋊Q811yescharacteristic, direct product factor, Sylow
254C22—31no—
255C22—32no—
256C22—32no—
257C22—31no—
258C22—31no—
259C22—32no—
260C22—32no—
261C22C3×C5×C4⋊Q811yescharacteristic, complemented
262C22C23×C5×A411yescharacteristic
263C4—24no—
264C4—32no—
265C4—34no—
266C4—64no—
267C4C5×D4×A412yes—
268C4C5×Q8×A414yescomplemented
269C3—41noSylow
270C2—31no—
271C2—31no—
272C2—32no—
273C2C2×C5×D4×A411yescharacteristic
274C2C2×C5×Q8×A412yes—
subgroupG/H
centerC22×C5C23×A4
commutator, cosocleC24C23×C3×C5
FrattiniC22C23×C5×A4
FittingC22×C5×C4⋊Q8C3
socleC24×C5C23×C3
prime radicalC22×C5×A4C23
hypercenterC5×C4⋊Q8A4
hypocenterC22C3×C5×C4⋊Q8
LCSG ▷ C24 ▷ C22
UCSC1 ◁ C22×C5 ◁ C5×C4⋊Q8

Complements

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

NH ≅ G/Ntype
4. C22×C5×C4⋊Q8C3semidirect
10. A4×C4⋊Q8C5direct (N × H)
22. C4×C5×A4Q8semidirect
42. C5×C4⋊Q8A4direct (N × H)
49. C22×C4⋊Q8C3×C5semidirect
83. C22×C4×C5C3×Q8semidirect
100. C5×A4C4⋊Q8direct (N × H)
108. C4×A4C5×Q8semidirect
152. C4⋊Q8C5×A4direct (N × H)
174. C22×C5C3×C4⋊Q8semidirect
181. C4×C5Q8×A4semidirect
204. C22×C4C3×C5×Q8semidirect
215. A4C5×C4⋊Q8direct (N × H)
253. C5A4×C4⋊Q8direct (N × H)
261. C22C3×C5×C4⋊Q8semidirect
268. C4C5×Q8×A4semidirect

Maximal subgroups

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

subgroupindex
C2×C5×Q8×A42
C5×A4×C4⋊C42
C42×C5×A42
C22×C5×C4⋊Q83
C3×C5×C4⋊Q84
A4×C4⋊Q85