Finite Group Databasebeta

← #10614851⋊C3 #14512248

Subgroups — #10614851⋊C3 #14512248

Order 1920.

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

normal subgroups only

This group has 274 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×D5×C42⋊C3C211yesmaximal, characteristic, complemented
3#65226⋊C3C211yesmaximal, characteristic, complemented
4#10614851C311yesmaximal, characteristic, complemented, Hall
5A4×C22⋊D5—41nomaximal
6C5×#126⋊C3—21no—
7C2×C5×C42⋊C3C2211yescharacteristic
8D5×C42⋊C3—21no—
9#2852⋊C3—51nomaximal, Hall
10C2×C5×#126C2×C311yescharacteristic, complemented
11C2×C42×D5C2×C311yescharacteristic, complemented
12#65278—31no—
13#65267—31no—
14#65245—31no—
15#65233—31no—
16#65226C2×C311yescharacteristic, complemented
17C22×C5×A4—41no—
18C2×D5×A4—41no—
19A4×Dic5—41no—
20C5×C42⋊C3D411yescharacteristic, complemented
21C2×#126⋊C3D511yescharacteristic, complemented
22C22×C42⋊C3—51no—
23#383⋊C3—51no—
24C22×C22⋊D5A411yescharacteristic
25C22×C4×D5—31no—
26C5×#126—21no—
27C5×#126—61no—
28C2×C5×C4⋊C4—31no—
29C2×C5×C22⋊C4—31no—
30C2×C42×C5C22×C311yescharacteristic
31C2×C22⋊Dic5—31no—
32C2×#685—31no—
33C2×#683—31no—
34C2×C4×Dic5—31no—
35C42×D5—21no—
36C42×D5—61no—
37#3963—31no—
38#3963—31no—
39#3963—31no—
40#3963—31no—
41#2852—51noSylow
42C2×C5×A4—41no—
43C2×C5×A4—81no—
44D5×A4—81no—
45C3×C22⋊D5—161no—
46D4×A4—201no—
47#126⋊C3—21no—
48C2×C42⋊C3—101no—
49C2×C42⋊C3C2×D511yescharacteristic
50C24×C5C2×A411yescharacteristic
51C23×D5C2×A411yescharacteristic
52C22×C4×C5—31no—
53C22×C4×C5—31no—
54C2×C22⋊D5—61no—
55C2×C22⋊D5—61no—
56C22×Dic5—31no—
57C22×Dic5—31no—
58C22×Dic5C2×A411yescharacteristic
59C2×C4×D5—62no—
60C2×C4×D5—61no—
61C2×C4×D5—61no—
62C2×C4×D5—61no—
63C2×C4×D5—61no—
64C5×C4⋊C4—61no—
65C5×C4⋊C4—61no—
66C5×C22⋊C4—61no—
67C5×C22⋊C4—61no—
68C42×C5—31no—
69C42×C5C3×D411yescharacteristic, complemented
70C22⋊Dic5—62no—
71#685—61no—
72#685—61no—
73#683—62no—
74C4×Dic5—61no—
75C4×Dic5—61no—
76C2×#126C3×D511yescharacteristic, complemented
77C22×C42—51no—
78#388—151no—
79#387—151no—
80#386—151no—
81#385—151no—
82#383—51no—
83C22×C3×C5—161no—
84C2×C3×D5—161no—
85C5×A4—41no—
86C3×Dic5—161no—
87C22×A4—41no—
88C22×A4—201no—
89C4×A4—201no—
90C42⋊C3C22⋊D511yescharacteristic, complemented
91C23×C5—21no—
92C23×C5—61no—
93C23×C5—61no—
94C23×C5C22×A411yescharacteristic
95C22×D5—21no—
96C22×D5—31no—
97C22×D5—31no—
98C22×D5—61no—
99C2×C4×C5—31no—
100C2×C4×C5—31no—
101C2×C4×C5—61no—
102C2×C4×C5—61no—
103C2×C4×C5—61no—
104C2×C4×C5—61no—
105C2×C4×C5—61no—
106C22⋊D5—41no—
107C22⋊D5—121no—
108C2×Dic5—32no—
109C2×Dic5—61no—
110C2×Dic5—61no—
111C2×Dic5—61no—
112C2×Dic5—61no—
113C2×Dic5—61no—
114C2×Dic5—61no—
115C4×D5—62no—
116C4×D5—62no—
117C4×D5—62no—
118C4×D5—62no—
119C22×D4—51no—
120C23×C4—151no—
121#126—21no—
122#126—61no—
123C2×C4⋊C4—31no—
124C2×C4⋊C4—151no—
125C2×C22⋊C4—31no—
126C2×C22⋊C4—151no—
127C2×C22⋊C4—151no—
128C2×C42—101no—
129C2×C42—151no—
130C2×C42—301no—
131C2×C42C2×C3×D511yescharacteristic
132#95—151no—
133#95—151no—
134#95—151no—
135#95—151no—
136C2×C3×C5—161no—
137C2×C3×C5—321no—
138C3×D5—321no—
139C2×A4—41no—
140C2×A4—81no—
141C2×A4—401no—
142C3×D4—801no—
143C22×C5—31no—
144C22×C5—31no—
145C22×C5—41no—
146C22×C5—121no—
147C22×C5—121no—
148C22×C5D4×A411yescharacteristic
149C2×D5—31no—
150C2×D5—61no—
151C2×D5—61no—
152C2×D5—61no—
153C2×D5—61no—
154C2×D5#126⋊C311yescharacteristic, complemented
155C4×C5—61no—
156C4×C5—61no—
157C4×C5—121no—
158Dic5—41no—
159Dic5—62no—
160Dic5—121no—
161C24—51no—
162C24D5×A411yescharacteristic
163C2×D4—301no—
164C2×D4—301no—
165C22×C4—31no—
166C22×C4—31no—
167C22×C4—51no—
168C22×C4—151no—
169C22×C4—151no—
170C22×C4—301no—
171C22×C4—301no—
172C22×C4—302no—
173C22×C4—301no—
174C22×C4—301no—
175C4⋊C4—61no—
176C4⋊C4—61no—
177C4⋊C4—302no—
178C22⋊C4—61no—
179C22⋊C4—61no—
180C22⋊C4—301no—
181C22⋊C4—301no—
182C22⋊C4—302no—
183C42—31no—
184C42—301no—
185C42—301no—
186C42C3×C22⋊D511yescharacteristic, complemented
187C3×C5—161noHall
188C22×C3—161no—
189C22×C3—801no—
190A4—41no—
191C3×C4—801no—
192C2×C5—31no—
193C2×C5—31no—
194C2×C5—81no—
195C2×C5C2×#126⋊C311yescharacteristic
196D5—21no—
197D5—61no—
198C23—21no—
199C23—61no—
200C23—61no—
201C23—101no—
202C23—151no—
203C23—151no—
204C23—301no—
205C23C2×D5×A411yescharacteristic
206D4—201no—
207D4—601no—
208C2×C4—31no—
209C2×C4—31no—
210C2×C4—61no—
211C2×C4—61no—
212C2×C4—61no—
213C2×C4—61no—
214C2×C4—61no—
215C2×C4—152no—
216C2×C4—302no—
217C2×C4—302no—
218C2×C4—302no—
219C2×C4—302no—
220C2×C4—301no—
221C2×C4—301no—
222C2×C4—301no—
223C2×C4—301no—
224C2×C4—301no—
225C2×C4—301no—
226C2×C3—161no—
227C2×C3—321no—
228C2×C3—1601no—
229C5#2852⋊C311yescharacteristic, complemented, Sylow
230C22—31no—
231C22—31no—
232C22—41no—
233C22—51no—
234C22—121no—
235C22—121no—
236C22—151no—
237C22—301no—
238C22—301no—
239C22—301no—
240C22—301no—
241C22A4×C22⋊D511yescharacteristic
242C4—61no—
243C4—61no—
244C4—121no—
245C4—201no—
246C4—302no—
247C4—601no—
248C3—161noSylow
249C2—31no—
250C2—31no—
251C2—81no—
252C2—101no—
253C2—301no—
254C2D5×#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×D5×C42⋊C3C2semidirect
3. #65226⋊C3C2semidirect
4. #10614851C3semidirect
10. C2×C5×#126C2×C3semidirect
11. C2×C42×D5C2×C3semidirect
16. #65226C2×C3semidirect
20. C5×C42⋊C3D4semidirect
21. C2×#126⋊C3D5semidirect
69. C42×C5C3×D4semidirect
76. C2×#126C3×D5semidirect
90. C42⋊C3C22⋊D5semidirect
154. C2×D5#126⋊C3semidirect
186. C42C3×C22⋊D5semidirect
229. C5#2852⋊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×D5×C42⋊C32
#65226⋊C32
#106148513
A4×C22⋊D54
#2852⋊C35