Finite Group Databasebeta

← #10606029⋊C3 #14512110

Subgroups — #10606029⋊C3 #14512110

Order 1920.

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

normal subgroups only

This group has 296 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⋊(#127⋊C3)C211yesmaximal, characteristic
2C5×#383⋊C3C211yesmaximal, characteristic, complemented
3#65226⋊C3C211yesmaximal, characteristic, complemented
4#10606029C311yesmaximal, characteristic, complemented, Hall
5C4×D5×A4—41nomaximal
6C2×C5×C42⋊C3C2211yescharacteristic
7C5⋊(#127⋊C3)C412yescomplemented
8#2380⋊C3—51nomaximal, Hall
9C2×#4020C2×C311yescharacteristic
10C5×#383C2×C311yescharacteristic, complemented
11#65226C2×C311yescharacteristic, complemented
12#64954—31no—
13#64954—31no—
14#64954—31no—
15#64954—31no—
16C2×D5×A4—41no—
17C4×C5×A4—41no—
18A4×Dic5—41no—
19C5×C42⋊C3C2×C411yescharacteristic, complemented
20C2×#127⋊C3—51no—
21#383⋊C3—51no—
22#383⋊C3D511yescharacteristic, complemented
23C22×D20—31no—
24C22×D20—31no—
25C22×C4×D5—31no—
26C22×C4×D5A411yescharacteristic
27C2×C42×C5C22×C311yescharacteristic
28C2×#685—31no—
29C2×#685—31no—
30C2×#685—31no—
31C2×#685—31no—
32#4020—32no—
33#4020C3×C412yescomplemented
34C5×#95—31no—
35C5×#95—31no—
36#3963—31no—
37#3963—31no—
38#2380—51noSylow
39C2×C5×A4—41no—
40D5×A4—42no—
41C3×C4×D5—161no—
42C2×C4×A4—201no—
43#127⋊C3—52no—
44C2×C42⋊C3C2×D511yescharacteristic
45C23×D5—31no—
46C23×D5C2×A411yescharacteristic
47C22×C4×C5—31no—
48C22×C4×C5—31no—
49C22×C4×C5C2×A411yescharacteristic
50C22×Dic5—31no—
51C22×Dic5C2×A411yescharacteristic
52C2×D20—32no—
53C2×D20—32no—
54C2×D20—32no—
55C2×D20—32no—
56C2×D20—121no—
57C2×D20—121no—
58C2×D20—121no—
59C2×D20—121no—
60C2×C4×D5—121no—
61C2×C4×D5—121no—
62C2×C4×D5—121no—
63C2×C4×D5—121no—
64C42×C5—31no—
65C42×C5C2×C3×C411yescharacteristic, complemented
66#685—121no—
67#685—121no—
68#685—121no—
69#685—121no—
70C2×#127—51no—
71#386—151no—
72#386—151no—
73#386—151no—
74#386—151no—
75#383—51no—
76#383C3×D511yescharacteristic, complemented
77C2×C3×D5—161no—
78C5×A4—41no—
79C3×C4×C5—161no—
80C3×Dic5—161no—
81C22×A4—201no—
82C4×A4—41no—
83C4×A4—201no—
84C42⋊C3C4×D511yescharacteristic, complemented
85C23×C5C22×A411yescharacteristic
86C22×D5—32no—
87C22×D5—61no—
88C22×D5—61no—
89C22×D5—61no—
90C22×D5—61no—
91C22×D5—61no—
92C22×D5—61no—
93C22×D5—61no—
94C22×D5—61no—
95C22×D5C4×A412yes—
96C2×C4×C5—31no—
97C2×C4×C5—31no—
98C2×C4×C5—61no—
99C2×C4×C5—61no—
100C2×C4×C5—61no—
101C2×C4×C5—61no—
102C2×C4×C5—61no—
103C2×C4×C5—61no—
104C2×Dic5—61no—
105C2×Dic5—61no—
106C2×Dic5—61no—
107C2×Dic5—61no—
108D20—122no—
109D20—122no—
110D20—122no—
111D20—122no—
112C4×D5—41no—
113C4×D5—121no—
114C4×D5—124no—
115C22×D4—151no—
116C22×D4—151no—
117C23×C4—51no—
118C23×C4—151no—
119#127—52no—
120#127—152no—
121C2×C22⋊C4—151no—
122C2×C22⋊C4—151no—
123C2×C22⋊C4—151no—
124C2×C22⋊C4—151no—
125C2×C42C2×C3×D511yescharacteristic
126#95—31no—
127#95—31no—
128#95—151no—
129#95—151no—
130C2×C3×C5—161no—
131C3×D5—162no—
132C2×A4—41no—
133C2×A4—202no—
134C2×C3×C4—801no—
135C22×C5—31no—
136C22×C5—31no—
137C22×C5C2×C4×A411yescharacteristic
138C2×D5—41no—
139C2×D5—62no—
140C2×D5—62no—
141C2×D5—62no—
142C2×D5—62no—
143C2×D5—121no—
144C2×D5—121no—
145C2×D5—121no—
146C2×D5—121no—
147C2×D5—121no—
148C4×C5—41no—
149C4×C5—61no—
150C4×C5—61no—
151C4×C5—121no—
152Dic5—41no—
153Dic5—121no—
154C24—51no—
155C24—151no—
156C2×D4—152no—
157C2×D4—152no—
158C2×D4—152no—
159C2×D4—152no—
160C2×D4—601no—
161C2×D4—601no—
162C2×D4—601no—
163C2×D4—601no—
164C22×C4—31no—
165C22×C4—31no—
166C22×C4—51no—
167C22×C4—151no—
168C22×C4—601no—
169C22×C4—601no—
170C22×C4—601no—
171C22×C4—601no—
172C22×C4D5×A411yescharacteristic
173C22⋊C4—601no—
174C22⋊C4—601no—
175C22⋊C4—601no—
176C22⋊C4—601no—
177C42—31no—
178C42C3×C4×D511yescharacteristic, complemented
179C3×C5—161noHall
180C22×C3—801no—
181A4—41no—
182C3×C4—161no—
183C3×C4—801no—
184C2×C5—31no—
185C2×C5—31no—
186C2×C5#560⋊C311yescharacteristic
187D5—42no—
188D5—122no—
189C23—52no—
190C23—152no—
191C23—301no—
192C23—301no—
193C23—301no—
194C23—301no—
195C23—301no—
196C23—301no—
197C23—301no—
198C23—301no—
199C23C2×D5×A411yescharacteristic
200D4—602no—
201D4—602no—
202D4—602no—
203D4—602no—
204C2×C4—31no—
205C2×C4—31no—
206C2×C4—61no—
207C2×C4—61no—
208C2×C4—61no—
209C2×C4—61no—
210C2×C4—61no—
211C2×C4—61no—
212C2×C4—201no—
213C2×C4—301no—
214C2×C4—301no—
215C2×C4—301no—
216C2×C4—301no—
217C2×C4—601no—
218C2×C4—604no—
219C2×C3—161no—
220C2×C3—802no—
221C5#2380⋊C311yescharacteristic, complemented, Sylow
222C22—31no—
223C22—31no—
224C22—201no—
225C22—302no—
226C22—302no—
227C22—302no—
228C22—302no—
229C22—601no—
230C22—601no—
231C22—601no—
232C22—601no—
233C22—601no—
234C22C4×D5×A411yescharacteristic
235C4—41no—
236C4—61no—
237C4—61no—
238C4—121no—
239C4—201no—
240C4—601no—
241C3—161noSylow
242C2—31no—
243C2—31no—
244C2—202no—
245C2—602no—
246C2(#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⋊(#127⋊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. #65226⋊C3C2semidirect
4. #10606029C3semidirect
7. C5⋊(#127⋊C3)C4semidirect
10. C5×#383C2×C3semidirect
11. #65226C2×C3semidirect
19. C5×C42⋊C3C2×C4semidirect
22. #383⋊C3D5semidirect
33. #4020C3×C4semidirect
65. C42×C5C2×C3×C4semidirect
76. #383C3×D5semidirect
84. C42⋊C3C4×D5semidirect
178. C42C3×C4×D5semidirect
221. C5#2380⋊C3semidirect

Maximal subgroups

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

subgroupindex
C2×C5⋊(#127⋊C3)2
C5×#383⋊C32
#65226⋊C32
#106060293
C4×D5×A44
#2380⋊C35