Finite Group Databasebeta

← Dic5×#126⋊C3 #14512246

Subgroups — Dic5×#126⋊C3 #14512246

Order 1920.

252 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 44 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
2Dic5×C42⋊C3C211yesmaximal, characteristic, complemented
3#65226⋊C3C211yesmaximal, characteristic, complemented
4Dic5×#126C311yesmaximal, characteristic, complemented, Hall
5C2×A4×Dic5—41nomaximal
6C5×#126⋊C3C412yescomplemented
7C2×C5×C42⋊C3C2211yescharacteristic
8C4×#126⋊C3—51nomaximal, Hall
9C2×C5×#126C2×C311yescharacteristic
10#65270—31no—
11C4⋊C4×Dic5—31no—
12#65240—31no—
13C22⋊C4×Dic5—31no—
14#65226C2×C311yescharacteristic, complemented
15C42×Dic5C2×C311yescharacteristic, complemented
16C22×C5×A4—41no—
17A4×Dic5—41no—
18A4×Dic5—41no—
19C5×C42⋊C3C2×C411yescharacteristic, complemented
20C2×#126⋊C3D511yescharacteristic
21#383⋊C3—51no—
22C4×C42⋊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—
38C4×#126—51noSylow
39C2×C5×A4—42no—
40C2×C5×A4—41no—
41C2×C3×Dic5—161no—
42C2×C4×A4—201no—
43#126⋊C3Dic512yesdirect product factor
44C2×C42⋊C3C2×D511yescharacteristic
45C24×C5C2×A411yescharacteristic
46C22×C4×C5—31no—
47C22×C4×C5—31no—
48C22×Dic5—31no—
49C22×Dic5—31no—
50C22×Dic5—61no—
51C22×Dic5—61no—
52C22×Dic5C2×A411yescharacteristic
53C22×Dic5C2×A411yescharacteristic
54C5×C4⋊C4—32no—
55C5×C4⋊C4—32no—
56C5×C22⋊C4—32no—
57C5×C22⋊C4—32no—
58C42×C5—31no—
59C42×C5C2×C3×C411yescharacteristic, complemented
60C22⋊Dic5—62no—
61C4⋊Dic5—62no—
62C4×Dic5—61no—
63C4×Dic5—61no—
64C4×Dic5—61no—
65C4×Dic5—61no—
66C4×Dic5—62no—
67C2×#126C3×D511yescharacteristic
68#388—151no—
69#387—151no—
70#383—51no—
71C4×C4⋊C4—151no—
72C4×C22⋊C4—151no—
73C43—51no—
74C22×C3×C5—161no—
75C5×A4—41no—
76C3×Dic5—161no—
77C3×Dic5—161no—
78C22×A4—41no—
79C4×A4—201no—
80C4×A4—201no—
81C42⋊C3C2×Dic511yescharacteristic, complemented
82C23×C5—61no—
83C23×C5—61no—
84C23×C5C4×A412yes—
85C23×C5C22×A411yescharacteristic
86C2×C4×C5—31no—
87C2×C4×C5—31no—
88C2×C4×C5—32no—
89C2×C4×C5—61no—
90C2×C4×C5—61no—
91C2×C4×C5—61no—
92C2×C4×C5—61no—
93C2×Dic5—31no—
94C2×Dic5—31no—
95C2×Dic5—32no—
96C2×Dic5—41no—
97C2×Dic5—61no—
98C2×Dic5—61no—
99C2×Dic5—61no—
100C2×Dic5—61no—
101C2×Dic5—61no—
102C2×Dic5—61no—
103C2×Dic5—121no—
104C23×C4—51no—
105#126—32no—
106#126C3×Dic512yescomplemented
107C2×C4⋊C4—31no—
108C2×C4⋊C4—151no—
109C2×C22⋊C4—31no—
110C2×C22⋊C4—151no—
111C2×C42—151no—
112C2×C42—151no—
113C2×C42—151no—
114C2×C42C2×C3×D511yescharacteristic
115#95—151no—
116#95—151no—
117#95—151no—
118#95—151no—
119C2×C3×C5—162no—
120C2×C3×C5—161no—
121C2×A4—42no—
122C2×A4—41no—
123C2×C3×C4—801no—
124C22×C5—31no—
125C22×C5—31no—
126C22×C5—41no—
127C22×C5—62no—
128C22×C5—121no—
129C22×C5C2×C4×A411yescharacteristic
130C4×C5—61no—
131C4×C5—61no—
132C4×C5—62no—
133Dic5—31no—
134Dic5—41no—
135Dic5—62no—
136Dic5—121no—
137Dic5#126⋊C311yescharacteristic, direct product factor
138C24D5×A411yescharacteristic
139C22×C4—31no—
140C22×C4—31no—
141C22×C4—51no—
142C22×C4—51no—
143C22×C4—151no—
144C22×C4—151no—
145C22×C4—301no—
146C22×C4—301no—
147C4⋊C4—32no—
148C4⋊C4—32no—
149C4⋊C4—302no—
150C22⋊C4—32no—
151C22⋊C4—32no—
152C22⋊C4—302no—
153C42—31no—
154C42—301no—
155C42—301no—
156C42—301no—
157C42—301no—
158C42—302no—
159C42C2×C3×Dic511yescharacteristic, complemented
160C3×C5—161noHall
161C22×C3—161no—
162A4—41no—
163C3×C4—801no—
164C3×C4—801no—
165C2×C5—31no—
166C2×C5—31no—
167C2×C5—42no—
168C2×C5C2×#126⋊C311yescharacteristic
169C23—61no—
170C23—61no—
171C23A4×Dic512yes—
172C23C2×D5×A411yescharacteristic
173C2×C4—31no—
174C2×C4—31no—
175C2×C4—32no—
176C2×C4—61no—
177C2×C4—61no—
178C2×C4—61no—
179C2×C4—61no—
180C2×C4—151no—
181C2×C4—151no—
182C2×C4—152no—
183C2×C4—201no—
184C2×C4—301no—
185C2×C4—301no—
186C2×C4—301no—
187C2×C4—301no—
188C2×C4—301no—
189C2×C4—301no—
190C2×C4—601no—
191C2×C3—162no—
192C2×C3—161no—
193C5C4×#126⋊C311yescharacteristic, complemented, Sylow
194C22—31no—
195C22—31no—
196C22—41no—
197C22—62no—
198C22—121no—
199C22C2×A4×Dic511yescharacteristic
200C4—51no—
201C4—61no—
202C4—61no—
203C4—62no—
204C4—151no—
205C4—201no—
206C4—302no—
207C4—601no—
208C3—161noSylow
209C2—31no—
210C2—31no—
211C2—42no—
212C2D5×#126⋊C311yescharacteristic
subgroupG/H
center, hypercenterC2D5×#126⋊C3
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. Dic5×C42⋊C3C2semidirect
3. #65226⋊C3C2semidirect
4. Dic5×#126C3semidirect
6. C5×#126⋊C3C4semidirect
14. #65226C2×C3semidirect
15. C42×Dic5C2×C3semidirect
19. C5×C42⋊C3C2×C4semidirect
25. C5×#126C3×C4semidirect
43. #126⋊C3Dic5direct (N × H)
59. C42×C5C2×C3×C4semidirect
81. C42⋊C3C2×Dic5semidirect
106. #126C3×Dic5semidirect
137. Dic5#126⋊C3direct (N × H)
159. C42C2×C3×Dic5semidirect
193. C5C4×#126⋊C3semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#126⋊C32
Dic5×C42⋊C32
#65226⋊C32
Dic5×#1263
C2×A4×Dic54
C4×#126⋊C35