Finite Group Databasebeta

← #10614849⋊C3 #14512250

Subgroups — #10614849⋊C3 #14512250

Order 1920.

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

normal subgroups only

This group has 290 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⋊(#127⋊C3)C211yesmaximal, characteristic, complemented
3#65226⋊C3C211yesmaximal, characteristic, complemented
4#10614849C311yesmaximal, characteristic, complemented, Hall
5A4×C22⋊D5—41nomaximal
6C5×#126⋊C3—21no—
7C2×C5×C42⋊C3C2211yescharacteristic
8C5⋊(#127⋊C3)—21no—
9#2818⋊C3—51nomaximal, Hall
10C2×C5×#126C2×C311yescharacteristic, complemented
11C2×#4020C2×C311yescharacteristic, complemented
12#65280—31no—
13#65280—31no—
14#65249—31no—
15#65249—31no—
16#65226C2×C311yescharacteristic, complemented
17C22×C5×A4—41no—
18C2×D5×A4—41no—
19A4×Dic5—41no—
20C5×C42⋊C3D411yescharacteristic, complemented
21C2×#127⋊C3—51no—
22C2×#126⋊C3D511yescharacteristic, complemented
23#383⋊C3—51no—
24C22×C22⋊D5—31no—
25C22×C22⋊D5A411yescharacteristic
26C22×D20—31no—
27C22×D20—31no—
28C5×#126—21no—
29C5×#126—61no—
30C2×C5×C4⋊C4—31no—
31C2×C5×C22⋊C4—31no—
32C2×C42×C5C22×C311yescharacteristic
33C2×#685—31no—
34C2×#685—31no—
35C2×#685—31no—
36C2×#685—31no—
37#4020—21no—
38#4020—61no—
39#3963—31no—
40#3963—31no—
41#2818—51noSylow
42C2×C5×A4—41no—
43C2×C5×A4—81no—
44D5×A4—81no—
45C3×C22⋊D5—161no—
46D4×A4—201no—
47#127⋊C3—101no—
48#126⋊C3—21no—
49C2×C42⋊C3C2×D511yescharacteristic
50C24×C5C2×A411yescharacteristic
51C23×D5—31no—
52C23×D5C2×A411yescharacteristic
53C22×C4×C5—31no—
54C22×C4×C5—31no—
55C2×C22⋊D5—121no—
56C2×C22⋊D5—121no—
57C2×C22⋊D5—121no—
58C2×C22⋊D5—121no—
59C22×Dic5—31no—
60C22×Dic5C2×A411yescharacteristic
61C2×D20—61no—
62C2×D20—61no—
63C2×D20—61no—
64C2×D20—61no—
65C2×D20—121no—
66C2×D20—121no—
67C2×D20—121no—
68C2×D20—121no—
69C5×C4⋊C4—61no—
70C5×C4⋊C4—61no—
71C5×C22⋊C4—61no—
72C5×C22⋊C4—61no—
73C42×C5—31no—
74C42×C5C3×D411yescharacteristic, complemented
75#685—121no—
76#685—121no—
77#685—121no—
78#685—121no—
79C2×#127—51no—
80C2×#126C3×D511yescharacteristic, complemented
81#394—151no—
82#394—151no—
83#392—151no—
84#392—151no—
85#383—51no—
86C22×C3×C5—161no—
87C2×C3×D5—161no—
88C5×A4—41no—
89C3×Dic5—161no—
90C22×A4—41no—
91C22×A4—201no—
92C4×A4—201no—
93C42⋊C3C22⋊D511yescharacteristic, complemented
94C23×C5—21no—
95C23×C5—61no—
96C23×C5—61no—
97C23×C5C22×A411yescharacteristic
98C22×D5—21no—
99C22×D5—61no—
100C22×D5—61no—
101C22×D5—61no—
102C22×D5—61no—
103C22×D5—61no—
104C22×D5—61no—
105C22×D5—61no—
106C22×D5—61no—
107C22×D5—61no—
108C2×C4×C5—31no—
109C2×C4×C5—31no—
110C2×C4×C5—61no—
111C2×C4×C5—61no—
112C2×C4×C5—61no—
113C2×C4×C5—61no—
114C2×C4×C5—61no—
115C22⋊D5—41no—
116C22⋊D5—121no—
117C22⋊D5—124no—
118C2×Dic5—61no—
119C2×Dic5—61no—
120C2×Dic5—61no—
121C2×Dic5—61no—
122D20—122no—
123D20—122no—
124D20—122no—
125D20—122no—
126C22×D4—51no—
127C22×D4—151no—
128C22×D4—151no—
129C22×D4—151no—
130#127—101no—
131#127—301no—
132#126—21no—
133#126—61no—
134C2×C4⋊C4—31no—
135C2×C22⋊C4—31no—
136C2×C22⋊C4—151no—
137C2×C22⋊C4—151no—
138C2×C22⋊C4—151no—
139C2×C22⋊C4—151no—
140C2×C42C2×C3×D511yescharacteristic
141#95—151no—
142#95—151no—
143C2×C3×C5—161no—
144C2×C3×C5—321no—
145C3×D5—321no—
146C2×A4—41no—
147C2×A4—81no—
148C2×A4—401no—
149C3×D4—801no—
150C22×C5—31no—
151C22×C5—31no—
152C22×C5—41no—
153C22×C5—121no—
154C22×C5—121no—
155C22×C5D4×A411yescharacteristic
156C2×D5—41no—
157C2×D5—121no—
158C2×D5—121no—
159C2×D5—121no—
160C2×D5—121no—
161C2×D5—121no—
162C2×D5—121no—
163C2×D5—121no—
164C2×D5—121no—
165C2×D5—121no—
166C4×C5—61no—
167C4×C5—61no—
168C4×C5—121no—
169Dic5—41no—
170Dic5—121no—
171C24—51no—
172C24—151no—
173C24D5×A411yescharacteristic
174C2×D4—301no—
175C2×D4—301no—
176C2×D4—301no—
177C2×D4—301no—
178C2×D4—601no—
179C2×D4—601no—
180C2×D4—601no—
181C2×D4—601no—
182C2×D4—601no—
183C2×D4—601no—
184C2×D4—601no—
185C2×D4—601no—
186C22×C4—31no—
187C22×C4—31no—
188C22×C4—51no—
189C22×C4—151no—
190C4⋊C4—61no—
191C4⋊C4—61no—
192C22⋊C4—61no—
193C22⋊C4—61no—
194C22⋊C4—601no—
195C22⋊C4—601no—
196C22⋊C4—601no—
197C22⋊C4—601no—
198C42—31no—
199C42C3×C22⋊D511yescharacteristic, complemented
200C3×C5—161noHall
201C22×C3—161no—
202C22×C3—801no—
203A4—41no—
204C3×C4—801no—
205C2×C5—31no—
206C2×C5—31no—
207C2×C5—81no—
208C2×C5#560⋊C311yescharacteristic
209D5—81no—
210D5—241no—
211C23—21no—
212C23—61no—
213C23—61no—
214C23—101no—
215C23—301no—
216C23—301no—
217C23—301no—
218C23—301no—
219C23—301no—
220C23—301no—
221C23—301no—
222C23—301no—
223C23—301no—
224C23C2×D5×A411yescharacteristic
225D4—201no—
226D4—602no—
227D4—602no—
228D4—602no—
229D4—602no—
230D4—601no—
231D4—604no—
232C2×C4—31no—
233C2×C4—31no—
234C2×C4—61no—
235C2×C4—61no—
236C2×C4—61no—
237C2×C4—61no—
238C2×C4—61no—
239C2×C4—301no—
240C2×C4—301no—
241C2×C4—301no—
242C2×C4—301no—
243C2×C3—161no—
244C2×C3—321no—
245C2×C3—1601no—
246C5#2818⋊C311yescharacteristic, complemented, Sylow
247C22—31no—
248C22—31no—
249C22—41no—
250C22—121no—
251C22—121no—
252C22—201no—
253C22—601no—
254C22—601no—
255C22—601no—
256C22—601no—
257C22—601no—
258C22—601no—
259C22—601no—
260C22—601no—
261C22—601no—
262C22A4×C22⋊D511yescharacteristic
263C4—61no—
264C4—61no—
265C4—121no—
266C4—201no—
267C4—601no—
268C3—161noSylow
269C2—31no—
270C2—31no—
271C2—81no—
272C2—401no—
273C2—1201no—
274C2(#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⋊(#127⋊C3)C2semidirect
3. #65226⋊C3C2semidirect
4. #10614849C3semidirect
10. C2×C5×#126C2×C3semidirect
11. C2×#4020C2×C3semidirect
16. #65226C2×C3semidirect
20. C5×C42⋊C3D4semidirect
22. C2×#126⋊C3D5semidirect
74. C42×C5C3×D4semidirect
80. C2×#126C3×D5semidirect
93. C42⋊C3C22⋊D5semidirect
199. C42C3×C22⋊D5semidirect
246. C5#2818⋊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⋊(#127⋊C3)2
#65226⋊C32
#106148493
A4×C22⋊D54
#2818⋊C35