Finite Group Databasebeta

← C2×#65224⋊C3 #14512205

Subgroups — C2×#65224⋊C3 #14512205

Order 1920.

376 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 49 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
2#65224⋊C3C212yesmaximal, direct product factor
3C2×#65224C311yesmaximal, characteristic, complemented, Hall
4C2×A4×Dic5—41nomaximal
5C2×C5×C42⋊C3C412yescomplemented
6C2×C5×C42⋊C3C2211yescharacteristic
7C2×#384⋊C3—51nomaximal, Hall
8C22×C42×C5C2×C311yescharacteristic
9C22×C4⋊Dic5—31no—
10C22×C4⋊Dic5—31no—
11#65224—32no—
12#65224C2×C312yescomplemented
13C22×C5×A4—41no—
14A4×Dic5—42no—
15C5×C42⋊C3C2×C411yescharacteristic, complemented
16C22×C42⋊C3D511yescharacteristic
17#384⋊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—32no—
26C2×C4⋊Dic5—32no—
27C2×C4⋊Dic5—32no—
28C2×C4⋊Dic5—32no—
29C2×C4⋊Dic5—62no—
30C2×C4⋊Dic5—62no—
31C2×C4⋊Dic5—62no—
32C2×C4⋊Dic5—62no—
33C2×#384—51noSylow
34C2×C5×A4—42no—
35C2×C5×A4—41no—
36C2×C3×Dic5—161no—
37C2×C4×A4—201no—
38C2×C42⋊C3Dic512yescomplemented
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—32no—
49C22×Dic5—61no—
50C22×Dic5—62no—
51C22×Dic5—61no—
52C22×Dic5—61no—
53C22×Dic5—62no—
54C22×Dic5—61no—
55C22×Dic5C2×A412yes—
56C42×C5—32no—
57C42×C5—31no—
58C42×C5—32no—
59C42×C5C2×C3×C411yescharacteristic, complemented
60C4⋊Dic5—64no—
61C4⋊Dic5—64no—
62C4⋊Dic5—64no—
63C4⋊Dic5—64no—
64C22×C4⋊C4—151no—
65C22×C4⋊C4—151no—
66C22×C42C3×D511yescharacteristic
67#384—52no—
68#384—152no—
69C22×C3×C5—161no—
70C5×A4—41no—
71C3×Dic5—162no—
72C22×A4—41no—
73C4×A4—202no—
74C42⋊C3C2×Dic511yescharacteristic, complemented
75C23×C5—31no—
76C23×C5—32no—
77C23×C5—31no—
78C23×C5C4×A412yes—
79C23×C5C22×A411yescharacteristic
80C2×C4×C5—32no—
81C2×C4×C5—32no—
82C2×C4×C5—34no—
83C2×C4×C5—34no—
84C2×C4×C5—32no—
85C2×C4×C5—32no—
86C2×C4×C5—34no—
87C2×C4×C5—34no—
88C2×C4×C5—31no—
89C2×C4×C5—32no—
90C2×C4×C5—31no—
91C2×Dic5—41no—
92C2×Dic5—62no—
93C2×Dic5—62no—
94C2×Dic5—64no—
95C2×Dic5—121no—
96C2×Dic5—121no—
97C2×Dic5—122no—
98C2×Dic5—121no—
99C23×C4—31no—
100C23×C4—51no—
101C23×C4—151no—
102C2×C4⋊C4—152no—
103C2×C4⋊C4—152no—
104C2×C4⋊C4—152no—
105C2×C4⋊C4—152no—
106C2×C4⋊C4—302no—
107C2×C4⋊C4—302no—
108C2×C4⋊C4—302no—
109C2×C4⋊C4—302no—
110C2×C42—31no—
111C2×C42—32no—
112C2×C42C3×Dic512yescomplemented
113C2×C42C2×C3×D511yescharacteristic
114C2×C3×C5—162no—
115C2×C3×C5—161no—
116C2×A4—42no—
117C2×A4—41no—
118C2×C3×C4—801no—
119C22×C5—32no—
120C22×C5—31no—
121C22×C5—32no—
122C22×C5—32no—
123C22×C5—32no—
124C22×C5—31no—
125C22×C5—31no—
126C22×C5#127⋊C311yescharacteristic
127C22×C5C2×C4×A411yescharacteristic
128C4×C5—32no—
129C4×C5—32no—
130C4×C5—34no—
131Dic5—42no—
132Dic5—122no—
133C24D5×A411yescharacteristic
134C22×C4—32no—
135C22×C4—32no—
136C22×C4—34no—
137C22×C4—32no—
138C22×C4—32no—
139C22×C4—31no—
140C22×C4—31no—
141C22×C4—52no—
142C22×C4—152no—
143C22×C4—301no—
144C22×C4—302no—
145C22×C4—301no—
146C22×C4—301no—
147C22×C4—302no—
148C22×C4—301no—
149C4⋊C4—304no—
150C4⋊C4—304no—
151C4⋊C4—304no—
152C4⋊C4—304no—
153C42—32no—
154C42—31no—
155C42—32no—
156C42C2×C3×Dic511yescharacteristic, complemented
157C3×C5—161noHall
158C22×C3—161no—
159A4—41no—
160C3×C4—802no—
161C2×C5—31no—
162C2×C5—32no—
163C2×C5—31no—
164C2×C5#384⋊C312yescomplemented
165C2×C5C2×#127⋊C311yescharacteristic
166C23—31no—
167C23—32no—
168C23—31no—
169C23A4×Dic512yes—
170C23C2×D5×A411yescharacteristic
171C2×C4—32no—
172C2×C4—32no—
173C2×C4—34no—
174C2×C4—34no—
175C2×C4—32no—
176C2×C4—32no—
177C2×C4—34no—
178C2×C4—34no—
179C2×C4—31no—
180C2×C4—32no—
181C2×C4—31no—
182C2×C4—201no—
183C2×C4—302no—
184C2×C4—302no—
185C2×C4—304no—
186C2×C4—601no—
187C2×C4—601no—
188C2×C4—602no—
189C2×C4—601no—
190C2×C3—162no—
191C2×C3—161no—
192C5C2×#384⋊C311yescharacteristic, complemented, Sylow
193C22—32no—
194C22—31no—
195C22—32no—
196C22—32no—
197C22—32no—
198C22—31no—
199C22—31no—
200C22C5⋊(#127⋊C3)11yescharacteristic
201C22C2×A4×Dic511yescharacteristic
202C4—32no—
203C4—32no—
204C4—34no—
205C4—202no—
206C4—602no—
207C3—161noSylow
208C2—31no—
209C2—32no—
210C2—31no—
211C2#65224⋊C312yesdirect product factor
212C2C2×C5⋊(#127⋊C3)11yescharacteristic
subgroupG/H
center, hypercenterC22C5⋊(#127⋊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. #65224⋊C3C2direct (N × H)
3. C2×#65224C3semidirect
5. C2×C5×C42⋊C3C4semidirect
12. #65224C2×C3semidirect
15. C5×C42⋊C3C2×C4semidirect
23. C2×C42×C5C3×C4semidirect
38. C2×C42⋊C3Dic5semidirect
59. C42×C5C2×C3×C4semidirect
74. C42⋊C3C2×Dic5semidirect
112. C2×C42C3×Dic5semidirect
156. C42C2×C3×Dic5semidirect
164. C2×C5#384⋊C3semidirect
192. C5C2×#384⋊C3semidirect
211. C2#65224⋊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
#65224⋊C32
C2×#652243
C2×A4×Dic54
C2×#384⋊C35