Finite Group Databasebeta

← #14282444

Subgroups — #14282444

Order 1920.

464 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 464 conjugacy classes of subgroups — too many to draw. Only its 126 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×D5⋊(C3⋊C8)C211yesmaximal, characteristic
3C3×#65681C211yesmaximal, characteristic
4#11746492C214yesmaximal, complemented
5#10604651—31nomaximal, Hall
6C2×D5⋊(C3⋊C8)—21no—
7C2×C3×#700—21no—
8#91758C411yescharacteristic
9C5×#869C411yescharacteristic
10C3×C42×D5C2211yescharacteristic
11#91388—21no—
12#91360—21no—
13#91359C412yes—
14#91358—21no—
15#91333—21no—
16Dic5×Dic6C2212yes—
17C4×C3⋊#170—21no—
18C4×C3⋊#170C2212yes—
19C3×C4⋊#170—21no—
20C3×C4⋊#170C2212yes—
21#70501—51nomaximal, Hall
22#66062—31no—
23#65681D311yescharacteristic
24C4×D5⋊C8—31no—
25Q8⋊#170—34no—
26C2×Dic30—21no—
27C2×C5×Dic6C2×C412yes—
28C2×C3×C4×D5C2×C411yescharacteristic
29C2×C3×C4×D5D411yescharacteristic
30C2×C3×C4×D5D411yescharacteristic
31C2×C3⋊#170—22no—
32D5⋊(C3⋊C8)—24no—
33C2×C3×#170—22no—
34C3×#700—42no—
35C3×C42×C5C2×C411yescharacteristic
36C4⋊Dic15—21no—
37C4⋊Dic15C2×C412yes—
38C5×C4⋊Dic3—21no—
39C5×C4⋊Dic3—21no—
40C3×C4×Dic5D411yescharacteristic
41C3×C4×Dic5D411yescharacteristic
42C3×C4×Dic5C2311yescharacteristic
43Dic3⋊Dic5—22no—
44#6669—22no—
45#6665—22no—
46Dic3×Dic5—22no—
47#5470—51no—
48C3×#423—51no—
49C2×C4×C3⋊C8—51no—
50#4484—54no—
51C2×#700—21no—
52C2×D5⋊C8—61no—
53C5×C4⋊Q8—31no—
54#4092—32no—
55Q8×Dic5—32no—
56#4043—61no—
57#4038—61no—
58#4036—61no—
59#4033—61no—
60C42×D5C2×D311yescharacteristic
61#4015—31no—
62C4⋊#170—21no—
63C4⋊#170C2×D312yes—
64C4×#170—32no—
65C4×#170—61no—
66#1493—151noSylow
67C22×C3×D5C22⋊C411yescharacteristic
68C2×C3×C4×C5C22⋊C411yescharacteristic
69C2×C3×C4×C5C22⋊C411yescharacteristic
70C2×C3×C4×C5C22×C411yescharacteristic
71C2×Dic15—22no—
72Dic30—42no—
73C2×C5×Dic3—22no—
74C5×Dic6—24no—
75C2×C3×Dic5C22⋊C411yescharacteristic
76C2×C3×Dic5C2×D411yescharacteristic
77C2×C3×Dic5C2×D411yescharacteristic
78C3×C4×D5—22no—
79C3×C4×D5—22no—
80C3×C4×D5SD1612yes—
81C3×C4×D5Q1612yes—
82C3⋊#170—24no—
83C3×#170—42no—
84C2×C3×M16—101no—
85C2×C3×C42—51no—
86#926—101no—
87#924—52no—
88#924—101no—
89C22×C3⋊C8—101no—
90#870—101no—
91#869—51no—
92#869AGL(1,𝔽5)11yescharacteristic
93C4×Dic6—52no—
94C4×Dic6—101no—
95C3×C4⋊C8—52no—
96C3×C4⋊C8—101no—
97C4×C3⋊C8—52no—
98C4×C3⋊C8—101no—
99C2×C5×Q8—32no—
100C2×C4×D5C4×D311yescharacteristic
101C2×C4×D5D1211yescharacteristic
102C2×C4×D5#6711yescharacteristic
103C2×Dic10—61no—
104C2×#170—22no—
105C2×#170—62no—
106#700—42no—
107D5⋊C8—64no—
108C5×C4⋊C4—61no—
109C5×C4⋊C4—61no—
110C42×C5C4×D311yescharacteristic
111#685—62no—
112C4⋊Dic5—32no—
113C4⋊Dic5—61no—
114C4⋊Dic5—62no—
115#683—62no—
116C4×Dic5—62no—
117C4×Dic5D1211yescharacteristic
118C4×Dic5#6711yescharacteristic
119C4×Dic5C22×D311yescharacteristic
120#533—151no—
121#423—51no—
122C2×C4×C8—151no—
123Q8⋊C8—154no—
124C22×C3×C5C2×C22⋊C411yescharacteristic
125C2×C3×D5—21no—
126C2×C3×D5—21no—
127C2×C3×D5#10312yes—
128C3×C4×C5#10312yes—
129C3×C4×C5#10412yes—
130C3×C4×C5#13112yes—
131Dic15—42no—
132C3×Dic5—21no—
133C3×Dic5—21no—
134C3×Dic5C2×SD1611yescharacteristic
135C3×Dic5C2×Q1611yescharacteristic
136C5×Dic3—42no—
137C22×C3×C4—51no—
138C22×C3×C4—51no—
139C22×C3×C4—51no—
140C2×Dic6—101no—
141C2×Dic6C2×AGL(1,𝔽5)12yes—
142C3×M16—202no—
143C2×C3×C8—102no—
144C3×C42—51no—
145C3×C42—51no—
146C3×C42—51no—
147C3×C42C2×AGL(1,𝔽5)11yescharacteristic
148#217—102no—
149C4⋊Dic3—21no—
150C4⋊Dic3—21no—
151C4⋊Dic3—52no—
152C4⋊Dic3—101no—
153Dic3⋊C4—102no—
154Dic3⋊C4—102no—
155C4×Dic3—102no—
156C2×C3⋊C8—102no—
157C2×C3⋊C8—104no—
158C22×D5(C2×D3)⋊C411yescharacteristic
159C5×Q8—64no—
160C2×C4×C5—62no—
161C2×C4×C5(C2×D3)⋊C411yescharacteristic
162C2×C4×C5(C2×D3)⋊C411yescharacteristic
163C2×C4×C5C2×C4×D311yescharacteristic
164C2×Dic5—62no—
165C2×Dic5(C2×D3)⋊C411yescharacteristic
166C2×Dic5C2×D1211yescharacteristic
167C2×Dic5C2×#6711yescharacteristic
168C4×D5—22no—
169C4×D5—22no—
170C4×D5#21412yes—
171C4×D5#21612yes—
172Dic10—122no—
173#170—42no—
174#170—64no—
175C2×M16—101no—
176C22×C8—301no—
177C4⋊Q8—31no—
178C4⋊Q8—151no—
179#125—301no—
180C22⋊Q8—152no—
181C22⋊Q8—301no—
182C4×Q8—152no—
183C4×Q8—301no—
184#117—301no—
185C2×C42—51no—
186C4⋊C8—52no—
187C4⋊C8—101no—
188C4×C8—152no—
189C4×C8—301no—
190C2×C3×C5#40811yescharacteristic
191C2×C3×C5C2×#10311yescharacteristic
192C2×C3×C5C2×#10411yescharacteristic
193C3×D5—22no—
194C23×C3—51no—
195C2×C3×C4—51no—
196C2×C3×C4—52no—
197C2×C3×C4—52no—
198C2×C3×C4—51no—
199C2×C3×C4—51no—
200C2×C3×C4—102no—
201C2×C3×C4—102no—
202C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
203C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
204C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
205C2×Dic3—22no—
206C2×Dic3—102no—
207Dic6—24no—
208Dic6—202no—
209C3×C8—202no—
210C3⋊C8—104no—
211C22×C5C2×(C2×D3)⋊C411yescharacteristic
212C2×D5—21no—
213C2×D5—21no—
214C2×D5#81012yes—
215C4×C5—122no—
216C4×C5#81012yes—
217C4×C5#82512yes—
218C4×C5#90712yes—
219Dic5—21no—
220Dic5—21no—
221Dic5—122no—
222Dic5C2×#21411yescharacteristic
223Dic5C2×#21611yescharacteristic
224C2×Q8—32no—
225C2×Q8—301no—
226C22×C4—51no—
227C22×C4—51no—
228C22×C4—51no—
229M16—202no—
230C2×C8—102no—
231C2×C8—302no—
232C2×C8—304no—
233C4⋊C4—61no—
234C4⋊C4—61no—
235C4⋊C4—152no—
236C4⋊C4—302no—
237C4⋊C4—302no—
238C4⋊C4—301no—
239C22⋊C4—302no—
240C42—51no—
241C42—51no—
242C42—51no—
243C42—302no—
244C42D3×AGL(1,𝔽5)11yescharacteristic
245C3×C5#149311yescharacteristic, complemented, Hall
246C22×C3—52no—
247C22×C3—101no—
248C22×C3—101no—
249C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
250C3×C4—51no—
251C3×C4—51no—
252C3×C4—101no—
253C3×C4—101no—
254C3×C4#400912yes—
255C3×C4#401012yes—
256C3×C4#413112yes—
257Dic3—42no—
258Dic3—202no—
259C2×C5C2×#81011yescharacteristic
260C2×C5#512911yescharacteristic
261C2×C5C2×#82511yescharacteristic
262D5—22no—
263C23—51no—
264Q8—64no—
265Q8—602no—
266C2×C4—51no—
267C2×C4—52no—
268C2×C4—52no—
269C2×C4—51no—
270C2×C4—51no—
271C2×C4—62no—
272C2×C4—102no—
273C2×C4—102no—
274C2×C4—302no—
275C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
276C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
277C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
278C8—202no—
279C8—304no—
280C2×C3—102no—
281C2×C3#6577611yescharacteristic
282C2×C3C2×#400911yescharacteristic
283C2×C3C2×#401011yescharacteristic
284C5#7050111yescharacteristic, complemented, Sylow
285C22—52no—
286C22—101no—
287C22—101no—
288C22C2×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
289C4—51no—
290C4—51no—
291C4—101no—
292C4—101no—
293C4—122no—
294C4—602no—
295C4#9115312yes—
296C4#9115712yes—
297C4#9191312yes—
298C3#1060465111yescharacteristic, complemented, Sylow
299C2—102no—
300C2C2×#9115311yescharacteristic
301C2C2×#9115711yescharacteristic
302C2#1175181111yescharacteristic
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#1493
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. #11746492C2semidirect
245. C3×C5#1493semidirect
284. C5#70501semidirect
298. C3#10604651semidirect

Maximal subgroups

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

subgroupindex
#117525062
C4×D5⋊(C3⋊C8)2
C3×#656812
#117464922
#106046513
#705015