Finite Group Databasebeta

← #14276950

Subgroups — #14276950

Order 1920.

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

normal subgroups only

This group has 328 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
1#11752416C211yesmaximal, characteristic
2C3×#65757C211yesmaximal, characteristic
3C4×#6668C211yesmaximal, characteristic
4#10598697—31nomaximal, Hall
5C2×C4×Dic15C411yescharacteristic
6C2×C4×C5×Dic3C411yescharacteristic
7C2×C3×C4×Dic5C2211yescharacteristic
8C2×#6668—21no—
9#91241—21no—
10#91233C412yescomplemented
11#91231—21no—
12C3×C22⋊#170—21no—
13C3×#4004—21no—
14C3×#4002C412yescomplemented
15#90994—21no—
16#67749—51nomaximal, Hall
17#65757—31no—
18#65757D311yescharacteristic
19C4×#683—31no—
20C22×C3×C4×C5C2×C411yescharacteristic
21C22×Dic15—21no—
22C22×C5×Dic3—21no—
23C22×C3×Dic5D411yescharacteristic
24C22×C3×Dic5D411yescharacteristic
25C2×C3⋊#170—22no—
26C2×C3×#170—22no—
27C4×Dic15—41no—
28C4×C5×Dic3—41no—
29C3×C4×Dic5C2×C411yescharacteristic
30C3×C4×Dic5C2×C411yescharacteristic
31C3×C4×Dic5D411yescharacteristic
32C3×C4×Dic5Q811yescharacteristic
33#6668—24no—
34C3×#432—51no—
35C4×C4⋊Dic3—51no—
36#4926—51no—
37C2×C42×C5—31no—
38C2×#683—61no—
39C2×C4×Dic5—31no—
40C2×C4×Dic5C2×D311yescharacteristic
41C22⋊#170—21no—
42C22⋊#170—61no—
43#4004—21no—
44#4004—32no—
45#4002—61no—
46#4002Dic312yescomplemented
47#3963—61no—
48#1285—151noSylow
49C23×C3×C5C22⋊C411yescharacteristic
50C2×C3×C4×C5—21no—
51C2×C3×C4×C5—21no—
52C2×C3×C4×C5C4211yescharacteristic
53C2×C3×C4×C5C4⋊C411yescharacteristic
54C2×Dic15—22no—
55C2×Dic15—41no—
56C2×Dic15—41no—
57C2×C5×Dic3—22no—
58C2×C5×Dic3—41no—
59C2×C5×Dic3—41no—
60C2×C3×Dic5—22no—
61C2×C3×Dic5—41no—
62C2×C3×Dic5C22⋊C411yescharacteristic
63C2×C3×Dic5C22⋊C411yescharacteristic
64C2×C3×Dic5C4⋊C411yescharacteristic
65C2×C3×Dic5C4⋊C411yescharacteristic
66C3⋊#170—42no—
67C3×#170—42no—
68C2×C3×C42—51no—
69C2×C4⋊Dic3—101no—
70C2×C4×Dic3—51no—
71C2×C4×Dic3AGL(1,𝔽5)11yescharacteristic
72C3×C4⋊C8—101no—
73C3×C22⋊C8—101no—
74C3×#97—52no—
75C3⋊#95—101no—
76#830—101no—
77C4⋊(C3⋊C8)—52no—
78#803—101no—
79C22×C4×C5—61no—
80C22×C4×C5C4×D311yescharacteristic
81C22×Dic5—61no—
82C22×Dic5D1211yescharacteristic
83C22×Dic5#6711yescharacteristic
84C2×#170—22no—
85C2×#170—62no—
86C42×C5—121no—
87#683—64no—
88C4×Dic5—121no—
89C4×Dic5Dic611yescharacteristic
90C4×Dic5C4×D311yescharacteristic
91C4×Dic5C2×Dic311yescharacteristic
92C4×Dic5#6711yescharacteristic
93#432—51no—
94#432—151no—
95C4×C4⋊C4—151no—
96C22×C3×C5—21no—
97C22×C3×C5—21no—
98C22×C3×C5#9511yescharacteristic
99C22×C3×C5#10011yescharacteristic
100C22×C3×C5#10111yescharacteristic
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—
120C4×Dic3—41no—
121C4×Dic3—201no—
122C2×C3⋊C8—102no—
123C23×C5(C2×D3)⋊C411yescharacteristic
124C2×C4×C5—21no—
125C2×C4×C5—21no—
126C2×C4×C5—62no—
127C2×C4×C5—121no—
128C2×C4×C5—121no—
129C2×C4×C5C4×Dic311yescharacteristic
130C2×C4×C5Dic3⋊C411yescharacteristic
131C2×Dic5—22no—
132C2×Dic5—41no—
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—122no—
142C2×C4⋊C4—301no—
143C2×C42—31no—
144C2×C42—51no—
145C2×C42—151no—
146C4⋊C8—101no—
147C4⋊C8—152no—
148C22⋊C8—101no—
149C22⋊C8—301no—
150#97—52no—
151#97—301no—
152#95—301no—
153C2×C3×C5—21no—
154C2×C3×C5—21no—
155C2×C3×C5H(3,ℤ/4)11yescharacteristic
156C2×C3×C5#33911yescharacteristic
157C2×C3×C5#34311yescharacteristic
158C23×C3C22⋊AGL(1,𝔽5)11yescharacteristic
159C2×C3×C4—21no—
160C2×C3×C4—21no—
161C2×C3×C4—51no—
162C2×C3×C4—51no—
163C2×C3×C4—51no—
164C2×C3×C4—51no—
165C2×C3×C4—102no—
166C2×C3×C4—201no—
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—202no—
177C22×C5—21no—
178C22×C5—21no—
179C22×C5#82311yescharacteristic
180C22×C5#82411yescharacteristic
181C22×C5C3⋊#9511yescharacteristic
182C4×C5—21no—
183C4×C5—21no—
184C4×C5—122no—
185Dic5—21no—
186Dic5—21no—
187Dic5—21no—
188Dic5—122no—
189Dic5#82512yes—
190C22×C4—51no—
191C22×C4—51no—
192C22×C4—61no—
193C22×C4—301no—
194C22×C4D3×AGL(1,𝔽5)11yescharacteristic
195C2×C8—102no—
196C2×C8—302no—
197C4⋊C4—304no—
198C42—51no—
199C42—51no—
200C42—51no—
201C42—51no—
202C42—121no—
203C42—601no—
204C3×C5#128511yescharacteristic, complemented, Hall
205C22×C3—21no—
206C22×C3—21no—
207C22×C3#400511yescharacteristic
208C22×C3(C2×AGL(1,𝔽5))⋊C411yescharacteristic
209C22×C3#401311yescharacteristic
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#453111yescharacteristic
221C2×C5#455411yescharacteristic
222C2×C5#455511yescharacteristic
223C23(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—51no—
227C2×C4—51no—
228C2×C4—51no—
229C2×C4—51no—
230C2×C4—62no—
231C2×C4—102no—
232C2×C4—121no—
233C2×C4—121no—
234C2×C4—201no—
235C2×C4—302no—
236C2×C4—601no—
237C2×C4—601no—
238C2×C4Dic3×AGL(1,𝔽5)11yescharacteristic
239C2×C4Dic3⋊AGL(1,𝔽5)11yescharacteristic
240C8—202no—
241C8—602no—
242C2×C3—21no—
243C2×C3—21no—
244C2×C3#6486211yescharacteristic
245C2×C3#6486311yescharacteristic
246C2×C3#6491911yescharacteristic
247C5#6774911yescharacteristic, complemented, Sylow
248C22—21no—
249C22—21no—
250C22(C2×AGL(1,𝔽5))⋊Dic311yescharacteristic
251C22#9117411yescharacteristic
252C22#9117511yescharacteristic
253C4—21no—
254C4—21no—
255C4—52no—
256C4—101no—
257C4—101no—
258C4—101no—
259C4—122no—
260C4—602no—
261C3#1059869711yescharacteristic, complemented, Sylow
262C2—21no—
263C2—21no—
264C2#1174651811yescharacteristic
265C2#1174652511yescharacteristic
266C2#1174657411yescharacteristic
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#1285
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
10. #91233C4semidirect
14. C3×#4002C4semidirect
46. #4002Dic3semidirect
204. C3×C5#1285semidirect
247. C5#67749semidirect
261. C3#10598697semidirect

Maximal subgroups

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

subgroupindex
#117524162
C3×#657572
C4×#66682
#105986973
#677495