Finite Group Databasebeta

← #14277267

Subgroups — #14277267

Order 1920.

344 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 84 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
1C4×#6762C211yesmaximal, characteristic
2C3×#65759C211yesmaximal, characteristic
3#11748635C211yesmaximal, characteristic
4#10598510—31nomaximal, Hall
5C2×#6762—21no—
6C2×C3×C4×Dic5C2211yescharacteristic
7C2×Dic3×Dic5—21no—
8#91231C412yescomplemented
9C4×C3⋊#170—21no—
10C3×C22⋊#170—21no—
11C3×#4002—21no—
12C3×C4⋊#170C412yescomplemented
13#91115C411yescharacteristic
14C5×C3⋊#95C411yescharacteristic
15#90994—21no—
16#67748—51nomaximal, Hall
17#65759D311yescharacteristic
18C4×#704—31no—
19#64937—31no—
20C22×C3×C4×C5C2×C411yescharacteristic
21C22×Dic15—21no—
22C22×C5×Dic3—21no—
23C22×C3×Dic5D411yescharacteristic
24C22×C3×Dic5D411yescharacteristic
25#6762—22no—
26#6762—22no—
27C2×C3⋊#170—22no—
28C2×C3×#170—22no—
29C3×C4×Dic5C2×C411yescharacteristic
30C3×C4×Dic5C2×C411yescharacteristic
31C3×C4×Dic5D411yescharacteristic
32C3×C4×Dic5Q811yescharacteristic
33Dic3×Dic5—24no—
34C3×#432—51no—
35#4932—51no—
36C4×#208—51no—
37C2×#704—61no—
38C2×C4×Dic5—61no—
39C2×C4×Dic5C2×D311yescharacteristic
40C22⋊#170—21no—
41#4002—21no—
42#4002—32no—
43C4⋊#170Dic312yescomplemented
44C4×#170—61no—
45C5×#95—31no—
46#3963—31no—
47#3963—61no—
48#1300—151noSylow
49C23×C3×C5C22⋊C411yescharacteristic
50C2×C3×C4×C5—41no—
51C2×C3×C4×C5C4211yescharacteristic
52C2×C3×C4×C5C4⋊C411yescharacteristic
53C2×Dic15—22no—
54C2×Dic15—41no—
55C2×Dic15—41no—
56C2×C5×Dic3—22no—
57C2×C5×Dic3—41no—
58C2×C5×Dic3—41no—
59C2×C3×Dic5—21no—
60C2×C3×Dic5—21no—
61C2×C3×Dic5—22no—
62C2×C3×Dic5C22⋊C411yescharacteristic
63C2×C3×Dic5C22⋊C411yescharacteristic
64C2×C3×Dic5C4⋊C411yescharacteristic
65C2×C3×Dic5C4⋊C411yescharacteristic
66C3⋊#170—24no—
67C3×#170—42no—
68C2×C3×C42—51no—
69C2×C4×Dic3—101no—
70C2×#208—101no—
71C3×C4⋊C8—52no—
72C3×C22⋊C8—101no—
73C3×#97—101no—
74C3⋊#95—51no—
75C3⋊#95—101no—
76C3⋊#95AGL(1,𝔽5)11yescharacteristic
77#803—52no—
78C4×C3⋊C8—101no—
79C22×C4×C5—61no—
80C22×C4×C5C4×D311yescharacteristic
81C22×Dic5—61no—
82C22×Dic5D1211yescharacteristic
83C22×Dic5#6711yescharacteristic
84#704—62no—
85#704—62no—
86C2×#170—22no—
87C2×#170—62no—
88C4×Dic5—64no—
89C4×Dic5Dic611yescharacteristic
90C4×Dic5C4×D311yescharacteristic
91C4×Dic5C2×Dic311yescharacteristic
92C4×Dic5#6711yescharacteristic
93#432—51no—
94C4×M16—151no—
95#376—151no—
96C22×C3×C5—21no—
97C22×C3×C5—21no—
98C22×C3×C5#9511yescharacteristic
99C22×C3×C5#10411yescharacteristic
100C22×C3×C5#10411yescharacteristic
101C3×C4×C5—21no—
102C3×C4×C5—21no—
103Dic15—42no—
104C3×Dic5—21no—
105C3×Dic5—21no—
106C3×Dic5—21no—
107C3×Dic5#10412yes—
108C5×Dic3—42no—
109C22×C3×C4—51no—
110C22×C3×C4—51no—
111C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
112C22×Dic3—21no—
113C22×Dic3—101no—
114C2×C3×C8—102no—
115C3×C42—51no—
116C3×C42—51no—
117C3×C42—51no—
118C3×C42—51no—
119C4×Dic3—104no—
120#208—102no—
121#208—102no—
122C2×C3⋊C8—102no—
123C23×C5(C2×D3)⋊C411yescharacteristic
124C2×C4×C5—41no—
125C2×C4×C5—62no—
126C2×C4×C5—121no—
127C2×C4×C5—121no—
128C2×C4×C5C4×Dic311yescharacteristic
129C2×C4×C5Dic3⋊C411yescharacteristic
130C2×Dic5—21no—
131C2×Dic5—21no—
132C2×Dic5—22no—
133C2×Dic5—62no—
134C2×Dic5—121no—
135C2×Dic5—121no—
136C2×Dic5Dic3⋊C411yescharacteristic
137C2×Dic5C4⋊Dic311yescharacteristic
138C2×Dic5(C2×D3)⋊C411yescharacteristic
139C2×Dic5#21711yescharacteristic
140#170—42no—
141#170—64no—
142C2×M16—301no—
143C2×C42—51no—
144C2×C42—301no—
145C4⋊C8—52no—
146C22⋊C8—101no—
147#97—101no—
148#97—152no—
149C4×C8—301no—
150#95—31no—
151#95—151no—
152#95—301no—
153C2×C3×C5—21no—
154C2×C3×C5—21no—
155C2×C3×C5#33911yescharacteristic
156C2×C3×C5#33911yescharacteristic
157C2×C3×C5#34411yescharacteristic
158C23×C3C22⋊AGL(1,𝔽5)11yescharacteristic
159C2×C3×C4—41no—
160C2×C3×C4—51no—
161C2×C3×C4—51no—
162C2×C3×C4—51no—
163C2×C3×C4—51no—
164C2×C3×C4—102no—
165C2×C3×C4—101no—
166C2×C3×C4—101no—
167C2×C3×C4C4×AGL(1,𝔽5)11yescharacteristic
168C2×C3×C4C4⋊AGL(1,𝔽5)11yescharacteristic
169C2×Dic3—22no—
170C2×Dic3—41no—
171C2×Dic3—41no—
172C2×Dic3—102no—
173C2×Dic3—201no—
174C2×Dic3—201no—
175C3×C8—202no—
176C3⋊C8—104no—
177C22×C5—21no—
178C22×C5—21no—
179C22×C5#82511yescharacteristic
180C22×C5#82511yescharacteristic
181C22×C5C3⋊#9511yescharacteristic
182C4×C5—21no—
183C4×C5—21no—
184C4×C5—122no—
185Dic5—21no—
186Dic5—21no—
187Dic5—21no—
188Dic5—122no—
189Dic5#83712yes—
190C22×C4—51no—
191C22×C4—51no—
192C22×C4—61no—
193C22×C4—301no—
194C22×C4D3×AGL(1,𝔽5)11yescharacteristic
195M16—302no—
196M16—302no—
197C2×C8—102no—
198C2×C8—302no—
199C42—51no—
200C42—51no—
201C42—51no—
202C42—51no—
203C42—304no—
204C3×C5#130011yescharacteristic, complemented, Hall
205C22×C3—21no—
206C22×C3—21no—
207C22×C3(C2×AGL(1,𝔽5))⋊C411yescharacteristic
208C22×C3#400811yescharacteristic
209C22×C3#401011yescharacteristic
210C3×C4—21no—
211C3×C4—21no—
212C3×C4—52no—
213C3×C4—101no—
214C3×C4—101no—
215C3×C4—101no—
216Dic3—42no—
217Dic3—202no—
218C2×C5—21no—
219C2×C5—21no—
220C2×C5#453211yescharacteristic
221C2×C5#455511yescharacteristic
222C2×C5#455611yescharacteristic
223C23(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
224C2×C4—41no—
225C2×C4—51no—
226C2×C4—51no—
227C2×C4—51no—
228C2×C4—51no—
229C2×C4—62no—
230C2×C4—102no—
231C2×C4—101no—
232C2×C4—101no—
233C2×C4—121no—
234C2×C4—121no—
235C2×C4—302no—
236C2×C4—601no—
237C2×C4—601no—
238C2×C4Dic3×AGL(1,𝔽5)11yescharacteristic
239C2×C4Dic3⋊AGL(1,𝔽5)11yescharacteristic
240C8—202no—
241C8—304no—
242C2×C3—21no—
243C2×C3—21no—
244C2×C3#6486211yescharacteristic
245C2×C3#6486711yescharacteristic
246C2×C3#6487511yescharacteristic
247C5#6774811yescharacteristic, complemented, Sylow
248C22—21no—
249C22—21no—
250C22#9115511yescharacteristic
251C22#9115711yescharacteristic
252C22(C2×AGL(1,𝔽5))⋊Dic311yescharacteristic
253C4—21no—
254C4—21no—
255C4—52no—
256C4—101no—
257C4—101no—
258C4—101no—
259C4—122no—
260C4—602no—
261C3#1059851011yescharacteristic, complemented, Sylow
262C2—21no—
263C2—21no—
264C2#1174652311yescharacteristic
265C2#1174652411yescharacteristic
266C2#1174657511yescharacteristic
subgroupG/H
centerC22(C2×AGL(1,𝔽5))⋊Dic3
commutatorC2×C3×C4×C5C42
Frattini, hypercenterC22×C4D3×AGL(1,𝔽5)
FittingC22×C3×C4×C5C2×C4
socleC22×C3×C5#95
prime radicalC23×C3×C5C22⋊C4
cosocleC2×C3×C4×Dic5C22
hypocenterC3×C5#1300
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
8. #91231C4semidirect
12. C3×C4⋊#170C4semidirect
43. C4⋊#170Dic3semidirect
204. C3×C5#1300semidirect
247. C5#67748semidirect
261. C3#10598510semidirect

Maximal subgroups

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

subgroupindex
C4×#67622
C3×#657592
#117486352
#105985103
#677485