Finite Group Databasebeta

← #14284385

Subgroups — #14284385

Order 1920.

392 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 94 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×#91388C211yesmaximal, characteristic
2#11752416C211yesmaximal, characteristic
3C3×#65757C211yesmaximal, characteristic
4#11746506C214yesmaximal, complemented
5#10604267—31nomaximal, Hall
6C2×C4⋊Dic15C411yescharacteristic
7C2×C5×C4⋊Dic3C411yescharacteristic
8C2×C3×C4×Dic5C2211yescharacteristic
9C2×Dic3⋊Dic5—21no—
10C2×#6669—21no—
11#91388—21no—
12#91388—21no—
13#91388C412yes—
14#91388C2212yes—
15#91241—21no—
16#91233—21no—
17#91231C2212yes—
18C3×C22⋊#170—21no—
19C3×#4004—21no—
20C3×#4002C2212yes—
21#70814—51nomaximal, Hall
22C2×#4036—31no—
23#65757—31no—
24#65757D311yescharacteristic
25#64870—34no—
26C22×C3×C4×C5C2×C411yescharacteristic
27C22×Dic15—21no—
28C22×C5×Dic3—21no—
29C22×C3×Dic5D411yescharacteristic
30C22×C3×Dic5D411yescharacteristic
31C2×C3⋊#170—22no—
32C2×C3×#170—22no—
33C4⋊Dic15—21no—
34C4⋊Dic15C2×C412yes—
35C5×C4⋊Dic3—21no—
36C5×C4⋊Dic3C2×C412yes—
37C3×C4×Dic5C2×C411yescharacteristic
38C3×C4×Dic5D411yescharacteristic
39C3×C4×Dic5D411yescharacteristic
40C3×C4×Dic5C2311yescharacteristic
41Dic3⋊Dic5—22no—
42Dic3⋊Dic5—22no—
43#6669—22no—
44#6669—22no—
45C2×#870—51no—
46C3×#432—51no—
47#4926—51no—
48#4465—54no—
49C2×C5×C4⋊C4—31no—
50C2×C4⋊Dic5—31no—
51C2×C4⋊Dic5—61no—
52C2×#683—61no—
53C2×C4×Dic5C2×D311yescharacteristic
54#4036—32no—
55#4036—32no—
56#4036—61no—
57#4036—61no—
58C22⋊#170—21no—
59C22⋊#170—61no—
60#4004—21no—
61#4004—61no—
62#4002—32no—
63#4002C2×D312yes—
64#1534—151noSylow
65C23×C3×C5C22⋊C411yescharacteristic
66C2×C3×C4×C5—22no—
67C2×C3×C4×C5C22⋊C411yescharacteristic
68C2×C3×C4×C5C22×C411yescharacteristic
69C2×Dic15—22no—
70C2×Dic15—42no—
71C2×C5×Dic3—22no—
72C2×C5×Dic3—42no—
73C2×C3×Dic5—41no—
74C2×C3×Dic5—41no—
75C2×C3×Dic5C22⋊C411yescharacteristic
76C2×C3×Dic5C22⋊C411yescharacteristic
77C2×C3×Dic5C2×D411yescharacteristic
78C2×C3×Dic5C2×D411yescharacteristic
79C3⋊#170—42no—
80C3×#170—42no—
81C2×C3×C42—51no—
82C2×C4⋊Dic3—51no—
83C2×C4⋊Dic3AGL(1,𝔽5)11yescharacteristic
84C2×Dic3⋊C4—101no—
85C2×Dic3⋊C4—101no—
86#870—52no—
87#870—52no—
88#870—101no—
89#870—101no—
90C3×C4⋊C8—101no—
91C3×C22⋊C8—101no—
92C3×#97—52no—
93#830—101no—
94C4⋊(C3⋊C8)—101no—
95#803—52no—
96C22×C4×C5—61no—
97C22×C4×C5C4×D311yescharacteristic
98C22×Dic5—61no—
99C22×Dic5D1211yescharacteristic
100C22×Dic5#6711yescharacteristic
101C2×#170—22no—
102C2×#170—62no—
103C5×C4⋊C4—32no—
104C5×C4⋊C4—61no—
105C4⋊Dic5—32no—
106C4⋊Dic5—61no—
107C4⋊Dic5—62no—
108C4⋊Dic5—62no—
109#683—62no—
110#683—62no—
111C4×Dic5C4×D311yescharacteristic
112C4×Dic5D1211yescharacteristic
113C4×Dic5#6711yescharacteristic
114C4×Dic5C22×D311yescharacteristic
115C2×#125—151no—
116#432—51no—
117#432—151no—
118#330—154no—
119C22×C3×C5—21no—
120C22×C3×C5—21no—
121C22×C3×C5#10112yes—
122C22×C3×C5C2×C22⋊C411yescharacteristic
123C3×C4×C5—21no—
124C3×C4×C5—21no—
125Dic15—42no—
126C3×Dic5—21no—
127C3×Dic5—21no—
128C3×Dic5—21no—
129C3×Dic5—21no—
130C5×Dic3—42no—
131C22×C3×C4—51no—
132C22×C3×C4—51no—
133C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
134C22×Dic3—21no—
135C22×Dic3—101no—
136C2×C3×C8—102no—
137C3×C42—51no—
138C3×C42—51no—
139C3×C42—51no—
140C3×C42—51no—
141C4⋊Dic3—21no—
142C4⋊Dic3—52no—
143C4⋊Dic3—101no—
144C4⋊Dic3C2×AGL(1,𝔽5)12yes—
145Dic3⋊C4—102no—
146Dic3⋊C4—102no—
147Dic3⋊C4—102no—
148Dic3⋊C4—102no—
149C2×C3⋊C8—102no—
150C23×C5(C2×D3)⋊C411yescharacteristic
151C2×C4×C5—22no—
152C2×C4×C5—62no—
153C2×C4×C5—122no—
154C2×C4×C5(C2×D3)⋊C411yescharacteristic
155C2×C4×C5C2×C4×D311yescharacteristic
156C2×Dic5—41no—
157C2×Dic5—41no—
158C2×Dic5—62no—
159C2×Dic5—122no—
160C2×Dic5(C2×D3)⋊C411yescharacteristic
161C2×Dic5(C2×D3)⋊C411yescharacteristic
162C2×Dic5C2×D1211yescharacteristic
163C2×Dic5C2×#6711yescharacteristic
164#170—42no—
165#170—122no—
166#125—152no—
167#125—152no—
168#125—301no—
169#125—301no—
170C2×C4⋊C4—31no—
171C2×C4⋊C4—151no—
172C2×C4⋊C4—301no—
173C2×C4⋊C4—301no—
174C2×C42—51no—
175C4⋊C8—101no—
176C4⋊C8—301no—
177C22⋊C8—101no—
178C22⋊C8—301no—
179#97—52no—
180#97—152no—
181C2×C3×C5—22no—
182C2×C3×C5C2×#10111yescharacteristic
183C2×C3×C5#42111yescharacteristic
184C2×C3×C5#42111yescharacteristic
185C23×C3C22⋊AGL(1,𝔽5)11yescharacteristic
186C2×C3×C4—22no—
187C2×C3×C4—51no—
188C2×C3×C4—51no—
189C2×C3×C4—51no—
190C2×C3×C4—51no—
191C2×C3×C4—201no—
192C2×C3×C4—201no—
193C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
194C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
195C2×Dic3—22no—
196C2×Dic3—42no—
197C2×Dic3—102no—
198C2×Dic3—202no—
199C3×C8—202no—
200C3⋊C8—202no—
201C22×C5—21no—
202C22×C5—21no—
203C22×C5#82412yes—
204C22×C5C2×(C2×D3)⋊C411yescharacteristic
205C4×C5—21no—
206C4×C5—21no—
207C4×C5—122no—
208Dic5—21no—
209Dic5—21no—
210Dic5—21no—
211Dic5—21no—
212Dic5—122no—
213C22×C4—51no—
214C22×C4—51no—
215C22×C4—61no—
216C22×C4—301no—
217C22×C4D3×AGL(1,𝔽5)11yescharacteristic
218C2×C8—102no—
219C2×C8—302no—
220C4⋊C4—32no—
221C4⋊C4—61no—
222C4⋊C4—152no—
223C4⋊C4—302no—
224C4⋊C4—302no—
225C4⋊C4—302no—
226C4⋊C4—302no—
227C4⋊C4—301no—
228C42—51no—
229C42—51no—
230C42—51no—
231C42—51no—
232C3×C5#153411yescharacteristic, complemented, Hall
233C22×C3—21no—
234C22×C3—21no—
235C22×C3#400512yes—
236C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
237C3×C4—21no—
238C3×C4—21no—
239C3×C4—101no—
240C3×C4—101no—
241C3×C4—101no—
242C3×C4—101no—
243Dic3—42no—
244Dic3—202no—
245C2×C5—22no—
246C2×C5#500511yescharacteristic
247C2×C5C2×#82411yescharacteristic
248C2×C5#513911yescharacteristic
249C23(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
250C2×C4—22no—
251C2×C4—51no—
252C2×C4—51no—
253C2×C4—51no—
254C2×C4—51no—
255C2×C4—62no—
256C2×C4—122no—
257C2×C4—201no—
258C2×C4—201no—
259C2×C4—302no—
260C2×C4—602no—
261C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
262C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
263C8—202no—
264C8—602no—
265C2×C3—22no—
266C2×C3C2×#400511yescharacteristic
267C2×C3#6576911yescharacteristic
268C2×C3#6578411yescharacteristic
269C5#7081411yescharacteristic, complemented, Sylow
270C22—21no—
271C22—21no—
272C22#9117512yes—
273C22C2×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
274C4—21no—
275C4—21no—
276C4—101no—
277C4—101no—
278C4—101no—
279C4—101no—
280C4—122no—
281C4—602no—
282C3#1060426711yescharacteristic, complemented, Sylow
283C2—22no—
284C2#1175171811yescharacteristic
285C2#1175172411yescharacteristic
286C2C2×#9117511yescharacteristic
subgroupG/H
centerC22C2×(C2×D3)⋊AGL(1,𝔽5)
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×C4C2×D3×AGL(1,𝔽5)
FittingC22×C3×C4×C5C2×C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC23×C3×C5C22⋊C4
cosocleC3×C4×Dic5C23
hypercenterC22×C4D3×AGL(1,𝔽5)
hypocenterC3×C5#1534
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
4. #11746506C2semidirect
232. C3×C5#1534semidirect
269. C5#70814semidirect
282. C3#10604267semidirect

Maximal subgroups

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

subgroupindex
C2×#913882
#117524162
C3×#657572
#117465062
#106042673
#708145