Finite Group Databasebeta

← #14282061

Subgroups — #14282061

Order 1920.

436 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 436 conjugacy classes of subgroups — too many to draw. Only its 106 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#11752506C211yesmaximal, characteristic
2C4×#6758C211yesmaximal, characteristic
3C3×#65680C211yesmaximal, characteristic
4#11746494C214yesmaximal, complemented
5#10604649—31nomaximal, Hall
6C2×#6758—21no—
7#91758C411yescharacteristic
8C5×#869C411yescharacteristic
9C3×C42×D5C2211yescharacteristic
10#91388—21no—
11#91360C412yes—
12#91359—21no—
13#91358—21no—
14#91333C2212yes—
15Dic5×Dic6—21no—
16#91231—21no—
17C4×C3⋊#170C2212yes—
18C3×#4003—21no—
19C3×C4⋊#170C2212yes—
20C3×C4×#170—21no—
21#70769—51nomaximal, Hall
22#66062—31no—
23#65680D311yescharacteristic
24C4×#700—31no—
25#64872—34no—
26C2×Dic30C2×C412yes—
27C2×C5×Dic6—21no—
28C2×C3×C4×D5C2×C411yescharacteristic
29C2×C3×C4×D5D411yescharacteristic
30C2×C3×C4×D5D411yescharacteristic
31C2×C3⋊#170—22no—
32#6758—24no—
33C2×C3×#170—22no—
34C3×C42×C5C2×C411yescharacteristic
35C4⋊Dic15—21no—
36C4⋊Dic15—21no—
37C5×C4⋊Dic3—21no—
38C5×C4⋊Dic3C2×C412yes—
39C3×C4×Dic5D411yescharacteristic
40C3×C4×Dic5D411yescharacteristic
41C3×C4×Dic5C2311yescharacteristic
42Dic3⋊Dic5—22no—
43#6669—22no—
44#6665—22no—
45Dic3×Dic5—22no—
46#5470—51no—
47C3×#431—51no—
48C4×#208—51no—
49#4484—54no—
50C2×#700—61no—
51C5×C4⋊Q8—31no—
52#4092—61no—
53Q8×Dic5—61no—
54#4043—32no—
55#4038—61no—
56#4036—61no—
57#4033—32no—
58C42×D5C2×D311yescharacteristic
59#4015—31no—
60#4003—21no—
61#4002—61no—
62C4⋊#170C2×D312yes—
63C4×#170—21no—
64C4×#170—32no—
65#1485—151noSylow
66C22×C3×D5C22⋊C411yescharacteristic
67C2×C3×C4×C5C22⋊C411yescharacteristic
68C2×C3×C4×C5C22⋊C411yescharacteristic
69C2×C3×C4×C5C22×C411yescharacteristic
70C2×Dic15—22no—
71Dic30—24no—
72C2×C5×Dic3—22no—
73C5×Dic6—42no—
74C2×C3×Dic5C22⋊C411yescharacteristic
75C2×C3×Dic5C2×D411yescharacteristic
76C2×C3×Dic5C2×D411yescharacteristic
77C3×C4×D5—22no—
78C3×C4×D5—22no—
79C3×C4×D5—22no—
80C3⋊#170—24no—
81C3×#170—42no—
82C2×C3×C42—51no—
83#926—101no—
84#924—52no—
85#924—101no—
86C2×#208—101no—
87#870—101no—
88#869—51no—
89#869AGL(1,𝔽5)11yescharacteristic
90C4×Dic6—52no—
91C4×Dic6—101no—
92C3×C4⋊C8—52no—
93C3×C22⋊C8—101no—
94C3×C4×C8—101no—
95#803—101no—
96C4×C3⋊C8—52no—
97C2×C5×Q8—61no—
98C2×C4×D5C4×D311yescharacteristic
99C2×C4×D5D1211yescharacteristic
100C2×C4×D5#6711yescharacteristic
101C2×Dic10—32no—
102C2×#170—22no—
103C2×#170—62no—
104#700—64no—
105C5×C4⋊C4—32no—
106C5×C4⋊C4—61no—
107C42×C5C4×D311yescharacteristic
108#685—62no—
109C4⋊Dic5—61no—
110C4⋊Dic5—61no—
111C4⋊Dic5—62no—
112#683—62no—
113C4×Dic5—62no—
114C4×Dic5D1211yescharacteristic
115C4×Dic5#6711yescharacteristic
116C4×Dic5C22×D311yescharacteristic
117#533—151no—
118#431—51no—
119C4×M16—151no—
120Q8⋊C8—154no—
121C22×C3×C5C2×C22⋊C411yescharacteristic
122C2×C3×D5—21no—
123C2×C3×D5—21no—
124C2×C3×D5—21no—
125C3×C4×C5—21no—
126C3×C4×C5#10412yes—
127C3×C4×C5#13112yes—
128Dic15—42no—
129C3×Dic5—21no—
130C3×Dic5—21no—
131C3×Dic5#13712yes—
132C5×Dic3—42no—
133C22×C3×C4—51no—
134C22×C3×C4—51no—
135C22×C3×C4—51no—
136C2×Dic6—21no—
137C2×Dic6—52no—
138C2×C3×C8—102no—
139C3×C42—51no—
140C3×C42—51no—
141C3×C42—51no—
142C3×C42C2×AGL(1,𝔽5)11yescharacteristic
143#217—102no—
144C4⋊Dic3—21no—
145C4⋊Dic3—101no—
146C4⋊Dic3—101no—
147C4⋊Dic3C2×AGL(1,𝔽5)12yes—
148Dic3⋊C4—102no—
149Dic3⋊C4—102no—
150C4×Dic3—102no—
151#208—104no—
152C2×C3⋊C8—102no—
153C22×D5(C2×D3)⋊C411yescharacteristic
154C5×Q8—122no—
155C2×C4×C5—62no—
156C2×C4×C5(C2×D3)⋊C411yescharacteristic
157C2×C4×C5(C2×D3)⋊C411yescharacteristic
158C2×C4×C5C2×C4×D311yescharacteristic
159C2×Dic5—62no—
160C2×Dic5(C2×D3)⋊C411yescharacteristic
161C2×Dic5C2×D1211yescharacteristic
162C2×Dic5C2×#6711yescharacteristic
163C4×D5—22no—
164C4×D5—22no—
165C4×D5—22no—
166Dic10—64no—
167#170—42no—
168#170—64no—
169C2×M16—301no—
170C4⋊Q8—31no—
171C4⋊Q8—151no—
172#125—301no—
173C22⋊Q8—152no—
174C22⋊Q8—301no—
175C4×Q8—152no—
176C4×Q8—301no—
177#117—301no—
178C2×C42—51no—
179C4⋊C8—52no—
180C22⋊C8—101no—
181#97—301no—
182C4×C8—101no—
183C4×C8—152no—
184C2×C3×C5#40811yescharacteristic
185C2×C3×C5#41911yescharacteristic
186C2×C3×C5C2×#10411yescharacteristic
187C3×D5—41no—
188C23×C3—51no—
189C2×C3×C4—51no—
190C2×C3×C4—51no—
191C2×C3×C4—51no—
192C2×C3×C4—102no—
193C2×C3×C4—102no—
194C2×C3×C4—102no—
195C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
196C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
197C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
198C2×Dic3—22no—
199C2×Dic3—102no—
200Dic6—42no—
201Dic6—104no—
202C3×C8—202no—
203C3⋊C8—104no—
204C22×C5C2×(C2×D3)⋊C411yescharacteristic
205C2×D5—21no—
206C2×D5—21no—
207C2×D5—21no—
208C4×C5—21no—
209C4×C5—122no—
210C4×C5#82512yes—
211C4×C5#90112yes—
212Dic5—21no—
213Dic5—21no—
214Dic5—122no—
215Dic5#95112yes—
216C2×Q8—61no—
217C2×Q8—152no—
218C22×C4—51no—
219C22×C4—51no—
220C22×C4—51no—
221M16—304no—
222C2×C8—102no—
223C2×C8—302no—
224C4⋊C4—32no—
225C4⋊C4—61no—
226C4⋊C4—302no—
227C4⋊C4—302no—
228C4⋊C4—301no—
229C4⋊C4—301no—
230C22⋊C4—302no—
231C42—51no—
232C42—51no—
233C42—51no—
234C42—302no—
235C42D3×AGL(1,𝔽5)11yescharacteristic
236C3×C5#148511yescharacteristic, complemented, Hall
237C22×C3—101no—
238C22×C3—101no—
239C22×C3—101no—
240C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
241C3×C4—21no—
242C3×C4—52no—
243C3×C4—101no—
244C3×C4—101no—
245C3×C4#400812yes—
246C3×C4#413312yes—
247Dic3—42no—
248Dic3—202no—
249C2×C5#500411yescharacteristic
250C2×C5#511011yescharacteristic
251C2×C5C2×#82511yescharacteristic
252D5—41no—
253C23—51no—
254Q8—122no—
255Q8—304no—
256C2×C4—51no—
257C2×C4—51no—
258C2×C4—51no—
259C2×C4—62no—
260C2×C4—102no—
261C2×C4—102no—
262C2×C4—102no—
263C2×C4—302no—
264C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
265C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
266C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
267C8—202no—
268C8—304no—
269C2×C3—201no—
270C2×C3C2×#400811yescharacteristic
271C2×C3#6578211yescharacteristic
272C2×C3#6578711yescharacteristic
273C5#7076911yescharacteristic, complemented, Sylow
274C22—101no—
275C22—101no—
276C22—101no—
277C22C2×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
278C4—21no—
279C4—52no—
280C4—101no—
281C4—101no—
282C4—122no—
283C4—602no—
284C4#9115512yes—
285C4#9191412yes—
286C3#1060464911yescharacteristic, complemented, Sylow
287C2—201no—
288C2#1175171111yescharacteristic
289C2C2×#9115511yescharacteristic
290C2#1175181311yescharacteristic
subgroupG/H
centerC22C2×(C2×D3)⋊AGL(1,𝔽5)
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×C4C2×D3×AGL(1,𝔽5)
FittingC3×C42×C5C2×C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×C3×D5C22⋊C4
cosocleC3×C4×Dic5C23
hypercenterC42D3×AGL(1,𝔽5)
hypocenterC3×C5#1485
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
4. #11746494C2semidirect
236. C3×C5#1485semidirect
273. C5#70769semidirect
286. C3#10604649semidirect

Maximal subgroups

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

subgroupindex
#117525062
C4×#67582
C3×#656802
#117464942
#106046493
#707695