Finite Group Databasebeta

← #10606030⋊C3 #14512111

Subgroups — #10606030⋊C3 #14512111

Order 1920.

232 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 232 conjugacy classes of subgroups — too many to draw. Only its 37 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⋊(#126⋊C3)C211yesmaximal, characteristic
2C5×#383⋊C3C211yesmaximal, characteristic, complemented
3#65224⋊C3C211yesmaximal, characteristic, complemented
4#10606030C311yesmaximal, characteristic, complemented, Hall
5C4×D5×A4—41nomaximal
6C2×C5×C42⋊C3C2211yescharacteristic
7C5⋊(#126⋊C3)C412yescomplemented
8(#126⋊C3)⋊C4—51nomaximal, Hall
9C2×#4022C2×C311yescharacteristic
10C5×#383C2×C311yescharacteristic, complemented
11#65224C2×C311yescharacteristic, complemented
12#64959—31no—
13#64957—31no—
14#64944—31no—
15#64936—31no—
16C2×D5×A4—41no—
17C4×C5×A4—41no—
18A4×Dic5—41no—
19C5×C42⋊C3C2×C411yescharacteristic, complemented
20C2×#126⋊C3—51no—
21#384⋊C3—51no—
22#383⋊C3D511yescharacteristic, complemented
23C22×C4×D5A411yescharacteristic
24C2×C42×C5C22×C311yescharacteristic
25C2×#685—31no—
26C2×#685—31no—
27C2×C4⋊Dic5—31no—
28C2×C4⋊Dic5—31no—
29C2×#683—31no—
30C2×#683—31no—
31C2×C4×Dic5—31no—
32#4022—32no—
33#4022C3×C412yescomplemented
34C5×#95—31no—
35C5×#95—31no—
36#3963—31no—
37#3963—31no—
38#2383—51noSylow
39C2×C5×A4—41no—
40D5×A4—42no—
41C3×C4×D5—161no—
42C2×C4×A4—201no—
43#126⋊C3—52no—
44C2×C42⋊C3C2×D511yescharacteristic
45C23×D5C2×A411yescharacteristic
46C22×C4×C5—31no—
47C22×C4×C5—31no—
48C22×C4×C5C2×A411yescharacteristic
49C22×Dic5—31no—
50C22×Dic5—31no—
51C22×Dic5C2×A411yescharacteristic
52C2×C4×D5—121no—
53C42×C5—31no—
54C42×C5C2×C3×C411yescharacteristic, complemented
55#685—32no—
56#685—32no—
57#685—121no—
58C4⋊Dic5—121no—
59C4⋊Dic5—121no—
60#683—32no—
61#683—32no—
62#683—121no—
63C4×Dic5—121no—
64C2×#126—51no—
65#389—151no—
66#388—151no—
67#387—151no—
68#385—151no—
69#384—51no—
70#383C3×D511yescharacteristic, complemented
71C2×C3×D5—161no—
72C5×A4—41no—
73C3×C4×C5—161no—
74C3×Dic5—161no—
75C22×A4—201no—
76C4×A4—41no—
77C4×A4—201no—
78C42⋊C3C4×D511yescharacteristic, complemented
79C23×C5C22×A411yescharacteristic
80C22×D5—61no—
81C22×D5—61no—
82C22×D5C4×A412yes—
83C2×C4×C5—31no—
84C2×C4×C5—31no—
85C2×C4×C5—61no—
86C2×C4×C5—61no—
87C2×C4×C5—61no—
88C2×C4×C5—61no—
89C2×C4×C5—62no—
90C2×Dic5—32no—
91C2×Dic5—61no—
92C2×Dic5—61no—
93C2×Dic5—61no—
94C2×Dic5—61no—
95C2×Dic5—61no—
96C2×Dic5—61no—
97C4×D5—41no—
98C4×D5—121no—
99C23×C4—51no—
100#126—52no—
101#126—152no—
102C2×C4⋊C4—151no—
103C2×C4⋊C4—151no—
104C2×C4⋊C4—151no—
105C2×C4⋊C4—151no—
106C2×C22⋊C4—151no—
107C2×C22⋊C4—151no—
108C2×C42—151no—
109C2×C42C2×C3×D511yescharacteristic
110#95—31no—
111#95—31no—
112#95—151no—
113#95—151no—
114C2×C3×C5—161no—
115C3×D5—162no—
116C2×A4—41no—
117C2×A4—202no—
118C2×C3×C4—801no—
119C22×C5—31no—
120C22×C5—31no—
121C22×C5C2×C4×A411yescharacteristic
122C2×D5—41no—
123C2×D5—62no—
124C2×D5—121no—
125C4×C5—41no—
126C4×C5—61no—
127C4×C5—61no—
128C4×C5—121no—
129Dic5—41no—
130Dic5—62no—
131Dic5—121no—
132C24—51no—
133C22×C4—31no—
134C22×C4—31no—
135C22×C4—51no—
136C22×C4—151no—
137C22×C4—151no—
138C22×C4—601no—
139C22×C4D5×A411yescharacteristic
140C4⋊C4—152no—
141C4⋊C4—152no—
142C4⋊C4—601no—
143C4⋊C4—601no—
144C4⋊C4—601no—
145C22⋊C4—152no—
146C22⋊C4—152no—
147C22⋊C4—601no—
148C42—31no—
149C42—601no—
150C42C3×C4×D511yescharacteristic, complemented
151C3×C5—161noHall
152C22×C3—801no—
153A4—41no—
154C3×C4—161no—
155C3×C4—801no—
156C2×C5—31no—
157C2×C5—31no—
158C2×C5#560⋊C311yescharacteristic
159D5—42no—
160C23—52no—
161C23—301no—
162C23—301no—
163C23C2×D5×A411yescharacteristic
164C2×C4—31no—
165C2×C4—31no—
166C2×C4—61no—
167C2×C4—61no—
168C2×C4—61no—
169C2×C4—61no—
170C2×C4—62no—
171C2×C4—152no—
172C2×C4—201no—
173C2×C4—301no—
174C2×C4—301no—
175C2×C4—301no—
176C2×C4—301no—
177C2×C4—301no—
178C2×C4—301no—
179C2×C4—601no—
180C2×C3—161no—
181C2×C3—802no—
182C5(#126⋊C3)⋊C411yescharacteristic, complemented, Sylow
183C22—31no—
184C22—31no—
185C22—201no—
186C22—302no—
187C22—601no—
188C22C4×D5×A411yescharacteristic
189C4—41no—
190C4—61no—
191C4—61no—
192C4—121no—
193C4—201no—
194C4—302no—
195C4—601no—
196C3—161noSylow
197C2—31no—
198C2—31no—
199C2—202no—
200C2(#126⋊C3)⋊D511yescharacteristic
subgroupG/H
center, hypercenterC2(#126⋊C3)⋊D5
commutator, hypocenterC42×C5C2×C3×C4
FrattiniC23C2×D5×A4
FittingC5×#383C2×C3
socleC23×C5C22×A4
prime radicalC2×C5⋊(#126⋊C3)C2
cosocleC2×C42×C5C22×C3
LCSG ▷ C42×C5
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
2. C5×#383⋊C3C2semidirect
3. #65224⋊C3C2semidirect
4. #10606030C3semidirect
7. C5⋊(#126⋊C3)C4semidirect
10. C5×#383C2×C3semidirect
11. #65224C2×C3semidirect
19. C5×C42⋊C3C2×C4semidirect
22. #383⋊C3D5semidirect
33. #4022C3×C4semidirect
54. C42×C5C2×C3×C4semidirect
70. #383C3×D5semidirect
78. C42⋊C3C4×D5semidirect
150. C42C3×C4×D5semidirect
182. C5(#126⋊C3)⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×C5⋊(#126⋊C3)2
C5×#383⋊C32
#65224⋊C32
#106060303
C4×D5×A44
(#126⋊C3)⋊C45