Finite Group Databasebeta

← (#126⋊C3)⋊Dic5 #14512247

Subgroups — (#126⋊C3)⋊Dic5 #14512247

Order 1920.

232 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 232 conjugacy classes of subgroups — too many to draw. Only its 43 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⋊C3C211yesmaximal, characteristic
2#65226⋊C3C211yesmaximal, characteristic, complemented
3#65224⋊C3C211yesmaximal, characteristic, complemented
4#10614807C311yesmaximal, characteristic, complemented, Hall
5C2×A4×Dic5—41nomaximal
6C5×#126⋊C3C412yescomplemented
7C2×C5×C42⋊C3C2211yescharacteristic
8(#126⋊C3)⋊C4—51nomaximal, Hall
9C2×C5×#126C2×C311yescharacteristic
10#65274—31no—
11#65270—31no—
12#65240—31no—
13#65239—31no—
14#65226C2×C311yescharacteristic, complemented
15#65224C2×C311yescharacteristic, complemented
16C22×C5×A4—41no—
17A4×Dic5—41no—
18A4×Dic5—41no—
19C5×C42⋊C3C2×C411yescharacteristic, complemented
20C2×#126⋊C3D511yescharacteristic
21#384⋊C3—51no—
22#383⋊C3—51no—
23C23×Dic5A411yescharacteristic
24C5×#126—32no—
25C5×#126C3×C412yescomplemented
26C2×C5×C4⋊C4—31no—
27C2×C5×C22⋊C4—31no—
28C2×C42×C5C22×C311yescharacteristic
29C2×C22⋊Dic5—31no—
30C2×C4⋊Dic5—31no—
31C2×C4⋊Dic5—31no—
32C2×C4⋊Dic5—31no—
33C2×C4×Dic5—31no—
34#3963—31no—
35#3963—31no—
36#3963—31no—
37#3963—31no—
38#2383—51noSylow
39C2×C5×A4—42no—
40C2×C5×A4—41no—
41C2×C3×Dic5—161no—
42C2×C4×A4—201no—
43#126⋊C3Dic512yescomplemented
44C2×C42⋊C3C2×D511yescharacteristic
45C24×C5C2×A411yescharacteristic
46C22×C4×C5—31no—
47C22×C4×C5—31no—
48C22×Dic5—31no—
49C22×Dic5—31no—
50C22×Dic5—121no—
51C22×Dic5C2×A411yescharacteristic
52C22×Dic5C2×A411yescharacteristic
53C5×C4⋊C4—32no—
54C5×C4⋊C4—32no—
55C5×C22⋊C4—32no—
56C5×C22⋊C4—32no—
57C42×C5—31no—
58C42×C5C2×C3×C411yescharacteristic, complemented
59C22⋊Dic5—121no—
60C4⋊Dic5—121no—
61C4⋊Dic5—121no—
62C4⋊Dic5—121no—
63C4×Dic5—121no—
64C2×#126C3×D511yescharacteristic
65#389—151no—
66#388—151no—
67#387—151no—
68#385—151no—
69#384—51no—
70#383—51no—
71C22×C3×C5—161no—
72C5×A4—41no—
73C3×Dic5—161no—
74C3×Dic5—161no—
75C22×A4—41no—
76C4×A4—201no—
77C4×A4—201no—
78C42⋊C3C2×Dic511yescharacteristic, complemented
79C23×C5—61no—
80C23×C5—61no—
81C23×C5C4×A412yes—
82C23×C5C22×A411yescharacteristic
83C2×C4×C5—31no—
84C2×C4×C5—31no—
85C2×C4×C5—32no—
86C2×C4×C5—61no—
87C2×C4×C5—61no—
88C2×C4×C5—61no—
89C2×C4×C5—61no—
90C2×Dic5—41no—
91C2×Dic5—61no—
92C2×Dic5—61no—
93C2×Dic5—61no—
94C2×Dic5—61no—
95C2×Dic5—61no—
96C2×Dic5—61no—
97C2×Dic5—62no—
98C2×Dic5—121no—
99C23×C4—51no—
100#126—32no—
101#126C3×Dic512yescomplemented
102C2×C4⋊C4—31no—
103C2×C4⋊C4—151no—
104C2×C4⋊C4—151no—
105C2×C4⋊C4—151no—
106C2×C22⋊C4—31no—
107C2×C22⋊C4—151no—
108C2×C42—151no—
109C2×C42C2×C3×D511yescharacteristic
110#95—151no—
111#95—151no—
112#95—151no—
113#95—151no—
114C2×C3×C5—162no—
115C2×C3×C5—161no—
116C2×A4—42no—
117C2×A4—41no—
118C2×C3×C4—801no—
119C22×C5—31no—
120C22×C5—31no—
121C22×C5—41no—
122C22×C5—62no—
123C22×C5—121no—
124C22×C5C2×C4×A411yescharacteristic
125C4×C5—61no—
126C4×C5—61no—
127C4×C5—62no—
128Dic5—41no—
129Dic5—41no—
130Dic5—121no—
131Dic5—121no—
132C24D5×A411yescharacteristic
133C22×C4—31no—
134C22×C4—31no—
135C22×C4—51no—
136C22×C4—51no—
137C22×C4—151no—
138C22×C4—151no—
139C22×C4—601no—
140C4⋊C4—32no—
141C4⋊C4—32no—
142C4⋊C4—601no—
143C4⋊C4—601no—
144C4⋊C4—601no—
145C22⋊C4—32no—
146C22⋊C4—32no—
147C22⋊C4—601no—
148C42—31no—
149C42—601no—
150C42C2×C3×Dic511yescharacteristic, complemented
151C3×C5—161noHall
152C22×C3—161no—
153A4—41no—
154C3×C4—801no—
155C3×C4—801no—
156C2×C5—31no—
157C2×C5—31no—
158C2×C5—42no—
159C2×C5#560⋊C311yescharacteristic
160C23—61no—
161C23—61no—
162C23A4×Dic512yes—
163C23C2×D5×A411yescharacteristic
164C2×C4—31no—
165C2×C4—31no—
166C2×C4—32no—
167C2×C4—61no—
168C2×C4—61no—
169C2×C4—61no—
170C2×C4—61no—
171C2×C4—201no—
172C2×C4—301no—
173C2×C4—301no—
174C2×C4—301no—
175C2×C4—301no—
176C2×C4—301no—
177C2×C4—301no—
178C2×C4—302no—
179C2×C4—601no—
180C2×C3—162no—
181C2×C3—161no—
182C5(#126⋊C3)⋊C411yescharacteristic, complemented, Sylow
183C22—31no—
184C22—31no—
185C22—41no—
186C22—62no—
187C22—121no—
188C22C2×A4×Dic511yescharacteristic
189C4—61no—
190C4—61no—
191C4—62no—
192C4—201no—
193C4—201no—
194C4—601no—
195C4—601no—
196C3—161noSylow
197C2—31no—
198C2—31no—
199C2—42no—
200C2(#126⋊C3)⋊D511yescharacteristic
subgroupG/H
center, hypercenterC2(#126⋊C3)⋊D5
commutator, hypocenterC42×C5C2×C3×C4
FrattiniC23C2×D5×A4
FittingC2×C5×#126C2×C3
socleC23×C5C22×A4
prime radicalC2×C5×#126⋊C3C2
cosocleC2×C42×C5C22×C3
LCSG ▷ C42×C5
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
2. #65226⋊C3C2semidirect
3. #65224⋊C3C2semidirect
4. #10614807C3semidirect
6. C5×#126⋊C3C4semidirect
14. #65226C2×C3semidirect
15. #65224C2×C3semidirect
19. C5×C42⋊C3C2×C4semidirect
25. C5×#126C3×C4semidirect
43. #126⋊C3Dic5semidirect
58. C42×C5C2×C3×C4semidirect
78. C42⋊C3C2×Dic5semidirect
101. #126C3×Dic5semidirect
150. C42C2×C3×Dic5semidirect
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⋊C32
#65226⋊C32
#65224⋊C32
#106148073
C2×A4×Dic54
(#126⋊C3)⋊C45