Finite Group Databasebeta

← C2×Dic5×C42⋊C3 #14512204

Subgroups — C2×Dic5×C42⋊C3 #14512204

Order 1920.

504 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 52 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
1C22×C5×C42⋊C3C211yesmaximal, characteristic
2Dic5×C42⋊C3C212yesmaximal, direct product factor
3C2×C42×Dic5C311yesmaximal, characteristic, complemented, Hall
4C2×A4×Dic5—41nomaximal
5C2×C5×C42⋊C3C412yescomplemented
6C2×C5×C42⋊C3C2211yescharacteristic
7C2×C4×C42⋊C3—51nomaximal, Hall
8C22×C42×C5C2×C311yescharacteristic
9C22×C4×Dic5—31no—
10C22×C4×Dic5—31no—
11C42×Dic5—32no—
12C42×Dic5C2×C312yescomplemented
13C22×C5×A4—41no—
14A4×Dic5—42no—
15C5×C42⋊C3C2×C411yescharacteristic, complemented
16C22×C42⋊C3D511yescharacteristic
17C4×C42⋊C3—52no—
18C23×C4×C5—31no—
19C23×Dic5—31no—
20C23×Dic5A411yescharacteristic
21C2×C42×C5—32no—
22C2×C42×C5—31no—
23C2×C42×C5C3×C412yescomplemented
24C2×C42×C5C22×C311yescharacteristic
25C2×C4×Dic5—38no—
26C2×C4×Dic5—32no—
27C2×C4×Dic5—34no—
28C2×C4×Dic5—32no—
29C2×C4×Dic5—32no—
30C2×C4×Dic5—32no—
31C2×C4×Dic5—32no—
32C2×C4×Dic5—32no—
33C2×C43—51noSylow
34C2×C5×A4—42no—
35C2×C5×A4—41no—
36C2×C3×Dic5—161no—
37C2×C4×A4—201no—
38C2×C42⋊C3Dic512yesdirect product factor
39C2×C42⋊C3C2×D511yescharacteristic
40C24×C5C2×A411yescharacteristic
41C22×C4×C5—34no—
42C22×C4×C5—32no—
43C22×C4×C5—32no—
44C22×C4×C5—32no—
45C22×C4×C5—32no—
46C22×C4×C5—31no—
47C22×C4×C5—31no—
48C22×Dic5—38no—
49C22×Dic5—32no—
50C22×Dic5—32no—
51C22×Dic5—32no—
52C22×Dic5—31no—
53C22×Dic5—31no—
54C22×Dic5—32no—
55C22×Dic5C2×A412yes—
56C42×C5—32no—
57C42×C5—31no—
58C42×C5—32no—
59C42×C5C2×C3×C411yescharacteristic, complemented
60C4×Dic5—38no—
61C4×Dic5—38no—
62C4×Dic5—34no—
63C4×Dic5—34no—
64C4×Dic5—34no—
65C4×Dic5—34no—
66C22×C42—151no—
67C22×C42—151no—
68C22×C42C3×D511yescharacteristic
69C43—52no—
70C43—152no—
71C22×C3×C5—161no—
72C5×A4—41no—
73C3×Dic5—162no—
74C22×A4—41no—
75C4×A4—202no—
76C42⋊C3C2×Dic511yescharacteristic, direct product factor
77C23×C5—32no—
78C23×C5—31no—
79C23×C5—31no—
80C23×C5C4×A412yes—
81C23×C5C22×A411yescharacteristic
82C2×C4×C5—32no—
83C2×C4×C5—32no—
84C2×C4×C5—32no—
85C2×C4×C5—32no—
86C2×C4×C5—34no—
87C2×C4×C5—34no—
88C2×C4×C5—34no—
89C2×C4×C5—34no—
90C2×C4×C5—31no—
91C2×C4×C5—32no—
92C2×C4×C5—31no—
93C2×Dic5—38no—
94C2×Dic5—34no—
95C2×Dic5—38no—
96C2×Dic5—38no—
97C2×Dic5—32no—
98C2×Dic5—31no—
99C2×Dic5—32no—
100C2×Dic5—32no—
101C2×Dic5—32no—
102C2×Dic5C42⋊C311yescharacteristic, direct product factor
103C23×C4—31no—
104C23×C4—51no—
105C23×C4—151no—
106C2×C42—31no—
107C2×C42—32no—
108C2×C42—152no—
109C2×C42—152no—
110C2×C42—152no—
111C2×C42—152no—
112C2×C42—152no—
113C2×C42—158no—
114C2×C42—154no—
115C2×C42—152no—
116C2×C42C3×Dic512yescomplemented
117C2×C42C2×C3×D511yescharacteristic
118C2×C3×C5—162no—
119C2×C3×C5—161no—
120C2×A4—42no—
121C2×A4—41no—
122C2×C3×C4—801no—
123C22×C5—31no—
124C22×C5—32no—
125C22×C5—32no—
126C22×C5—32no—
127C22×C5—32no—
128C22×C5—31no—
129C22×C5—31no—
130C22×C5C2×C42⋊C311yescharacteristic
131C22×C5C2×C4×A411yescharacteristic
132C4×C5—32no—
133C4×C5—32no—
134C4×C5—34no—
135Dic5—38no—
136Dic5—32no—
137Dic5C2×C42⋊C312yesdirect product factor
138C24D5×A411yescharacteristic
139C22×C4—34no—
140C22×C4—32no—
141C22×C4—32no—
142C22×C4—32no—
143C22×C4—32no—
144C22×C4—31no—
145C22×C4—31no—
146C22×C4—52no—
147C22×C4—151no—
148C22×C4—158no—
149C22×C4—152no—
150C22×C4—152no—
151C22×C4—152no—
152C22×C4—152no—
153C22×C4—151no—
154C42—32no—
155C42—31no—
156C42—32no—
157C42—154no—
158C42—154no—
159C42—158no—
160C42—158no—
161C42—154no—
162C42—154no—
163C42C2×C3×Dic511yescharacteristic, complemented
164C3×C5—161noHall
165C22×C3—161no—
166A4—41no—
167C3×C4—802no—
168C2×C5—31no—
169C2×C5—31no—
170C2×C5—32no—
171C2×C5C4×C42⋊C312yescomplemented
172C2×C5C22×C42⋊C311yescharacteristic
173C23—32no—
174C23—31no—
175C23—31no—
176C23A4×Dic512yes—
177C23C2×D5×A411yescharacteristic
178C2×C4—32no—
179C2×C4—32no—
180C2×C4—32no—
181C2×C4—32no—
182C2×C4—34no—
183C2×C4—34no—
184C2×C4—34no—
185C2×C4—34no—
186C2×C4—31no—
187C2×C4—32no—
188C2×C4—31no—
189C2×C4—51no—
190C2×C4—152no—
191C2×C4—152no—
192C2×C4—158no—
193C2×C4—154no—
194C2×C4—158no—
195C2×C4—158no—
196C2×C4—152no—
197C2×C4—151no—
198C2×C4—152no—
199C2×C3—162no—
200C2×C3—161no—
201C5C2×C4×C42⋊C311yescharacteristic, complemented, Sylow
202C22—31no—
203C22—32no—
204C22—32no—
205C22—32no—
206C22—32no—
207C22—31no—
208C22—31no—
209C22D5×C42⋊C311yescharacteristic
210C22C2×A4×Dic511yescharacteristic
211C4—32no—
212C4—32no—
213C4—34no—
214C4—52no—
215C4—158no—
216C4—152no—
217C3—161noSylow
218C2—31no—
219C2—31no—
220C2—32no—
221C2Dic5×C42⋊C312yesdirect product factor
222C2C2×D5×C42⋊C311yescharacteristic
subgroupG/H
center, hypercenterC22D5×C42⋊C3
commutator, hypocenterC42×C5C2×C3×C4
FrattiniC23C2×D5×A4
FittingC22×C42×C5C2×C3
socleC24×C5C2×A4
prime radicalC22×C5×C42⋊C3C2
cosocleC2×C42×C5C22×C3
LCSG ▷ C42×C5
UCSC1 ◁ C22

Complements

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

NH ≅ G/Ntype
2. Dic5×C42⋊C3C2direct (N × H)
3. C2×C42×Dic5C3semidirect
5. C2×C5×C42⋊C3C4semidirect
12. C42×Dic5C2×C3semidirect
15. C5×C42⋊C3C2×C4semidirect
23. C2×C42×C5C3×C4semidirect
38. C2×C42⋊C3Dic5direct (N × H)
59. C42×C5C2×C3×C4semidirect
76. C42⋊C3C2×Dic5direct (N × H)
102. C2×Dic5C42⋊C3direct (N × H)
116. C2×C42C3×Dic5semidirect
137. Dic5C2×C42⋊C3direct (N × H)
163. C42C2×C3×Dic5semidirect
171. C2×C5C4×C42⋊C3semidirect
201. C5C2×C4×C42⋊C3semidirect
221. C2Dic5×C42⋊C3direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C5×C42⋊C32
Dic5×C42⋊C32
C2×C42×Dic53
C2×A4×Dic54
C2×C4×C42⋊C35