Finite Group Databasebeta

← #10614835⋊C3 #14512249

Subgroups — #10614835⋊C3 #14512249

Order 1920.

252 conjugacy classes of subgroups; only the 32 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 32 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
3Dic5×C42⋊C3C211yesmaximal, characteristic, complemented
4#10614835C311yesmaximal, characteristic, complemented, Hall
5A4×C22⋊D5—41nomaximal
6C5×#126⋊C3—21no—
7C2×C5×C42⋊C3C2211yescharacteristic
8C5⋊(#126⋊C3)—21no—
9C4⋊(#126⋊C3)—51nomaximal, Hall
10C2×C5×#126C2×C311yescharacteristic, complemented
11C2×#4022C2×C311yescharacteristic, complemented
12#65279—31no—
13#65261—31no—
14#65246—31no—
15#65234—31no—
16C42×Dic5C2×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
23C4×C42⋊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×#683—31no—
34C2×#683—31no—
35C2×C4×Dic5—31no—
36C2×C4×Dic5—31no—
37#4022—21no—
38#4022—61no—
39#3963—32no—
40#2860—51noSylow
41C2×C5×A4—41no—
42C2×C5×A4—81no—
43D5×A4—81no—
44C3×C22⋊D5—161no—
45D4×A4—201no—
46#126⋊C3—21no—
47#126⋊C3—101no—
48C2×C42⋊C3C2×D511yescharacteristic
49C24×C5C2×A411yescharacteristic
50C23×D5C2×A411yescharacteristic
51C22×C4×C5—31no—
52C22×C4×C5—31no—
53C2×C22⋊D5—61no—
54C2×C22⋊D5—61no—
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—62no—
65#685—62no—
66#685—61no—
67#685—61no—
68#683—61no—
69#683—61no—
70#683—61no—
71#683—61no—
72C4×Dic5—61no—
73C4×Dic5—61no—
74C4×Dic5—62no—
75C2×#126—51no—
76C2×#126C3×D511yescharacteristic, complemented
77#390—151no—
78#389—151no—
79#388—151no—
80#388—151no—
81C43—51no—
82C22×C3×C5—161no—
83C2×C3×D5—161no—
84C5×A4—41no—
85C3×Dic5—161no—
86C22×A4—41no—
87C22×A4—201no—
88C4×A4—201no—
89C42⋊C3C22⋊D511yescharacteristic, complemented
90C23×C5—21no—
91C23×C5—61no—
92C23×C5—61no—
93C23×C5C22×A411yescharacteristic
94C22×D5—21no—
95C22×D5—61no—
96C22×D5—61no—
97C2×C4×C5—31no—
98C2×C4×C5—31no—
99C2×C4×C5—61no—
100C2×C4×C5—61no—
101C2×C4×C5—61no—
102C2×C4×C5—61no—
103C2×C4×C5—61no—
104C22⋊D5—41no—
105C22⋊D5—121no—
106C2×Dic5—31no—
107C2×Dic5—31no—
108C2×Dic5—32no—
109C2×Dic5—61no—
110C2×Dic5—61no—
111C2×Dic5—61no—
112C2×Dic5—61no—
113C2×Dic5—61no—
114C22×D4—51no—
115#126—21no—
116#126—61no—
117#126—101no—
118#126—301no—
119C2×C4⋊C4—31no—
120C2×C4⋊C4—151no—
121C2×C4⋊C4—151no—
122C2×C22⋊C4—31no—
123C2×C22⋊C4—151no—
124C2×C22⋊C4—151no—
125C2×C22⋊C4—151no—
126C2×C42—151no—
127C2×C42—151no—
128C2×C42C2×C3×D511yescharacteristic
129#95—152no—
130C2×C3×C5—161no—
131C2×C3×C5—321no—
132C3×D5—321no—
133C2×A4—41no—
134C2×A4—81no—
135C2×A4—401no—
136C3×D4—801no—
137C22×C5—31no—
138C22×C5—31no—
139C22×C5—41no—
140C22×C5—121no—
141C22×C5—121no—
142C22×C5D4×A411yescharacteristic
143C2×D5—41no—
144C2×D5—121no—
145C2×D5—121no—
146C4×C5—61no—
147C4×C5—61no—
148C4×C5—121no—
149Dic5—31no—
150Dic5—62no—
151Dic5—121no—
152Dic5#126⋊C311yescharacteristic, complemented
153C24—51no—
154C24D5×A411yescharacteristic
155C2×D4—301no—
156C2×D4—301no—
157C22×C4—31no—
158C22×C4—31no—
159C22×C4—51no—
160C22×C4—151no—
161C22×C4—151no—
162C4⋊C4—61no—
163C4⋊C4—61no—
164C4⋊C4—301no—
165C4⋊C4—301no—
166C4⋊C4—301no—
167C4⋊C4—301no—
168C22⋊C4—61no—
169C22⋊C4—61no—
170C22⋊C4—301no—
171C22⋊C4—301no—
172C22⋊C4—302no—
173C22⋊C4—302no—
174C42—31no—
175C42—301no—
176C42—301no—
177C42—302no—
178C42C3×C22⋊D511yescharacteristic, complemented
179C3×C5—161noHall
180C22×C3—161no—
181C22×C3—801no—
182A4—41no—
183C3×C4—801no—
184C2×C5—31no—
185C2×C5—31no—
186C2×C5—81no—
187C2×C5C2×#126⋊C311yescharacteristic
188D5—81no—
189C23—21no—
190C23—61no—
191C23—61no—
192C23—101no—
193C23—301no—
194C23—301no—
195C23C2×D5×A411yescharacteristic
196D4—201no—
197D4—601no—
198C2×C4—31no—
199C2×C4—31no—
200C2×C4—61no—
201C2×C4—61no—
202C2×C4—61no—
203C2×C4—61no—
204C2×C4—61no—
205C2×C4—151no—
206C2×C4—151no—
207C2×C4—152no—
208C2×C4—301no—
209C2×C4—301no—
210C2×C4—301no—
211C2×C4—301no—
212C2×C4—301no—
213C2×C3—161no—
214C2×C3—321no—
215C2×C3—1601no—
216C5C4⋊(#126⋊C3)11yescharacteristic, complemented, Sylow
217C22—31no—
218C22—31no—
219C22—41no—
220C22—121no—
221C22—121no—
222C22—201no—
223C22—601no—
224C22—601no—
225C22A4×C22⋊D511yescharacteristic
226C4—51no—
227C4—61no—
228C4—61no—
229C4—121no—
230C4—151no—
231C4—302no—
232C4—601no—
233C3—161noSylow
234C2—31no—
235C2—31no—
236C2—81no—
237C2—401no—
238C2D5×#126⋊C311yescharacteristic
subgroupG/H
center, hypercenterC2D5×#126⋊C3
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. Dic5×C42⋊C3C2semidirect
4. #10614835C3semidirect
10. C2×C5×#126C2×C3semidirect
11. C2×#4022C2×C3semidirect
16. C42×Dic5C2×C3semidirect
20. C5×C42⋊C3D4semidirect
22. C2×#126⋊C3D5semidirect
63. C42×C5C3×D4semidirect
76. C2×#126C3×D5semidirect
89. C42⋊C3C22⋊D5semidirect
152. Dic5#126⋊C3semidirect
178. C42C3×C22⋊D5semidirect
216. C5C4⋊(#126⋊C3)semidirect

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
Dic5×C42⋊C32
#106148353
A4×C22⋊D54
C4⋊(#126⋊C3)5