Finite Group Databasebeta

← #10614850⋊C3 #14512251

Subgroups — #10614850⋊C3 #14512251

Order 1920.

232 conjugacy classes of subgroups; only the 31 normal subgroups are shown.

normal subgroups only

This group has 232 conjugacy classes of subgroups — too many to draw. Only its 31 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, complemented
2C2×C5⋊(#126⋊C3)C211yesmaximal, characteristic, complemented
3#65224⋊C3C211yesmaximal, characteristic, complemented
4#10614850C311yesmaximal, characteristic, complemented, Hall
5A4×C22⋊D5—41nomaximal
6C5×#126⋊C3—21no—
7C2×C5×C42⋊C3C2211yescharacteristic
8C5⋊(#126⋊C3)—21no—
9#2823⋊C3—51nomaximal, Hall
10C2×C5×#126C2×C311yescharacteristic, complemented
11C2×#4022C2×C311yescharacteristic, complemented
12#65283—31no—
13#65273—31no—
14#65250—31no—
15#65237—31no—
16#65224C2×C311yescharacteristic, complemented
17C22×C5×A4—41no—
18C2×D5×A4—41no—
19A4×Dic5—41no—
20C5×C42⋊C3D411yescharacteristic, complemented
21C2×#126⋊C3—51no—
22C2×#126⋊C3D511yescharacteristic, complemented
23#384⋊C3—51no—
24C22×C22⋊D5A411yescharacteristic
25C5×#126—21no—
26C5×#126—61no—
27C2×C5×C4⋊C4—31no—
28C2×C5×C22⋊C4—31no—
29C2×C42×C5C22×C311yescharacteristic
30C2×C22⋊Dic5—31no—
31C2×#685—31no—
32C2×#685—31no—
33C2×C4⋊Dic5—31no—
34C2×C4⋊Dic5—31no—
35C2×#683—31no—
36C2×#683—31no—
37#4022—21no—
38#4022—61no—
39#3963—31no—
40#3963—31no—
41#2823—51noSylow
42C2×C5×A4—41no—
43C2×C5×A4—81no—
44D5×A4—81no—
45C3×C22⋊D5—161no—
46D4×A4—201no—
47#126⋊C3—21no—
48#126⋊C3—101no—
49C2×C42⋊C3C2×D511yescharacteristic
50C24×C5C2×A411yescharacteristic
51C23×D5C2×A411yescharacteristic
52C22×C4×C5—31no—
53C22×C4×C5—31no—
54C2×C22⋊D5—121no—
55C22×Dic5—31no—
56C22×Dic5—31no—
57C22×Dic5C2×A411yescharacteristic
58C5×C4⋊C4—61no—
59C5×C4⋊C4—61no—
60C5×C22⋊C4—61no—
61C5×C22⋊C4—61no—
62C42×C5—31no—
63C42×C5C3×D411yescharacteristic, complemented
64C22⋊Dic5—121no—
65#685—61no—
66#685—61no—
67#685—121no—
68C4⋊Dic5—121no—
69C4⋊Dic5—121no—
70#683—61no—
71#683—61no—
72#683—121no—
73C2×#126—51no—
74C2×#126C3×D511yescharacteristic, complemented
75#398—151no—
76#396—151no—
77#396—151no—
78#394—151no—
79#384—51no—
80C22×C3×C5—161no—
81C2×C3×D5—161no—
82C5×A4—41no—
83C3×Dic5—161no—
84C22×A4—41no—
85C22×A4—201no—
86C4×A4—201no—
87C42⋊C3C22⋊D511yescharacteristic, complemented
88C23×C5—21no—
89C23×C5—61no—
90C23×C5—61no—
91C23×C5C22×A411yescharacteristic
92C22×D5—21no—
93C22×D5—61no—
94C22×D5—61no—
95C2×C4×C5—31no—
96C2×C4×C5—31no—
97C2×C4×C5—61no—
98C2×C4×C5—61no—
99C2×C4×C5—61no—
100C2×C4×C5—61no—
101C2×C4×C5—61no—
102C22⋊D5—41no—
103C22⋊D5—121no—
104C2×Dic5—61no—
105C2×Dic5—61no—
106C2×Dic5—61no—
107C2×Dic5—61no—
108C2×Dic5—61no—
109C2×Dic5—61no—
110C2×Dic5—61no—
111C22×D4—51no—
112#126—21no—
113#126—61no—
114#126—101no—
115#126—301no—
116C2×C4⋊C4—31no—
117C2×C4⋊C4—151no—
118C2×C4⋊C4—151no—
119C2×C4⋊C4—151no—
120C2×C4⋊C4—151no—
121C2×C22⋊C4—31no—
122C2×C22⋊C4—151no—
123C2×C22⋊C4—151no—
124C2×C22⋊C4—151no—
125C2×C42C2×C3×D511yescharacteristic
126#95—151no—
127#95—151no—
128C2×C3×C5—161no—
129C2×C3×C5—321no—
130C3×D5—321no—
131C2×A4—41no—
132C2×A4—81no—
133C2×A4—401no—
134C3×D4—801no—
135C22×C5—31no—
136C22×C5—31no—
137C22×C5—41no—
138C22×C5—121no—
139C22×C5—121no—
140C22×C5D4×A411yescharacteristic
141C2×D5—41no—
142C2×D5—121no—
143C2×D5—121no—
144C4×C5—61no—
145C4×C5—61no—
146C4×C5—121no—
147Dic5—41no—
148Dic5—121no—
149Dic5—121no—
150C24—51no—
151C24D5×A411yescharacteristic
152C2×D4—601no—
153C22×C4—31no—
154C22×C4—31no—
155C22×C4—51no—
156C22×C4—151no—
157C22×C4—151no—
158C4⋊C4—61no—
159C4⋊C4—61no—
160C4⋊C4—301no—
161C4⋊C4—301no—
162C4⋊C4—601no—
163C4⋊C4—601no—
164C4⋊C4—601no—
165C22⋊C4—61no—
166C22⋊C4—61no—
167C22⋊C4—301no—
168C22⋊C4—301no—
169C22⋊C4—601no—
170C22⋊C4—601no—
171C42—31no—
172C42C3×C22⋊D511yescharacteristic, complemented
173C3×C5—161noHall
174C22×C3—161no—
175C22×C3—801no—
176A4—41no—
177C3×C4—801no—
178C2×C5—31no—
179C2×C5—31no—
180C2×C5—81no—
181C2×C5#560⋊C311yescharacteristic
182D5—81no—
183C23—21no—
184C23—61no—
185C23—61no—
186C23—101no—
187C23—301no—
188C23—301no—
189C23C2×D5×A411yescharacteristic
190D4—201no—
191D4—601no—
192C2×C4—31no—
193C2×C4—31no—
194C2×C4—61no—
195C2×C4—61no—
196C2×C4—61no—
197C2×C4—61no—
198C2×C4—61no—
199C2×C4—301no—
200C2×C4—301no—
201C2×C4—301no—
202C2×C4—301no—
203C2×C4—301no—
204C2×C4—301no—
205C2×C4—301no—
206C2×C3—161no—
207C2×C3—321no—
208C2×C3—1601no—
209C5#2823⋊C311yescharacteristic, complemented, Sylow
210C22—31no—
211C22—31no—
212C22—41no—
213C22—121no—
214C22—121no—
215C22—201no—
216C22—601no—
217C22—601no—
218C22A4×C22⋊D511yescharacteristic
219C4—61no—
220C4—61no—
221C4—121no—
222C4—201no—
223C4—601no—
224C4—601no—
225C3—161noSylow
226C2—31no—
227C2—31no—
228C2—81no—
229C2—401no—
230C2(#126⋊C3)⋊D511yescharacteristic
subgroupG/H
center, hypercenterC2(#126⋊C3)⋊D5
commutator, cosocleC2×C42×C5C22×C3
FrattiniC23C2×D5×A4
FittingC2×C5×#126C2×C3
socleC23×C5C22×A4
hypocenterC42×C5C3×D4
LCSG ▷ C2×C42×C5 ▷ C42×C5
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. C2×C5×#126⋊C3C2semidirect
2. C2×C5⋊(#126⋊C3)C2semidirect
3. #65224⋊C3C2semidirect
4. #10614850C3semidirect
10. C2×C5×#126C2×C3semidirect
11. C2×#4022C2×C3semidirect
16. #65224C2×C3semidirect
20. C5×C42⋊C3D4semidirect
22. C2×#126⋊C3D5semidirect
63. C42×C5C3×D4semidirect
74. C2×#126C3×D5semidirect
87. C42⋊C3C22⋊D5semidirect
172. C42C3×C22⋊D5semidirect
209. C5#2823⋊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
C2×C5⋊(#126⋊C3)2
#65224⋊C32
#106148503
A4×C22⋊D54
#2823⋊C35