Finite Group Databasebeta

← #14513562

Subgroups — #14513562

Order 1920.

658 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 658 conjugacy classes of subgroups — too many to draw. Only its 59 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×#4150⋊C3C211yesmaximal, characteristic, complemented
2C2×C5×#986C211yesmaximal, characteristic, complemented
3#11752143C211yesmaximal, characteristic, complemented
4#11751613C214yesmaximal, complemented
5#10615679—31nomaximal, Hall
6C2×C5×#41⋊C3C2211yescharacteristic
7#4150⋊C3—22no—
8C2×D5×SL(2,𝔽3)C2212yescomplemented
9C5×#986—22no—
10C2×C5×GL(2,𝔽3)C2212yes—
11#91463—41nomaximal
12#91184C2212yescomplemented
13#85540—51nomaximal, Hall
14C2×#4150D311yescharacteristic, complemented
15C2×C5×AGL(1,ℤ/8)—31no—
16#66139—31no—
17C22×#687—31no—
18#65522—31no—
19#65459—34no—
20#65447—34no—
21#65418—31no—
22#65409—31no—
23C2×C5×D12—41no—
24C2×C3×D20—41no—
25C5×#41⋊C3D412yescomplemented
26C2×C5×SL(2,𝔽3)C2311yescharacteristic
27C2×#1201—44no—
28D5×SL(2,𝔽3)—22no—
29C5×GL(2,𝔽3)—22no—
30C4×Dic15—41no—
31C2×2−1+4⋊C3—51no—
32C2×#986D511yescharacteristic, complemented
33#5424—51no—
34#5421—54no—
35C2×C5×#41C2×D311yescharacteristic
36C22×C5×D4—31no—
37#4150—22no—
38#4150—62no—
39C2×Q8×D5C2×D312yes—
40C2×#711—32no—
41C2×#709—31no—
42C22×Dic10—31no—
43C5×AGL(1,ℤ/8)—62no—
44C5×AGL(1,ℤ/8)—62no—
45C2×C5×SD16—32no—
46C2×C5×D8—32no—
47C2×C5×M16—31no—
48#4099—62no—
49#4086—61no—
50#4084—34no—
51#4082—61no—
52C2×#687—34no—
53C2×#687—64no—
54#4072—31no—
55C22×#168—31no—
56#3967—32no—
57#3964—32no—
58#3952—34no—
59#3948—34no—
60#3010—151noSylow
61C22×C5×D3—42no—
62C22×C3×D5—42no—
63C2×C3×C4×C5—41no—
64C2×Dic15—42no—
65C5×D12—82no—
66C3×D20—82no—
67C5×SL(2,𝔽3)C2×D411yescharacteristic
68#1201—88no—
692−1+4⋊C3—102no—
70C2×#41⋊C3C2×D511yescharacteristic
71C22×SL(2,𝔽3)—52no—
72#986—22no—
73C2×GL(2,𝔽3)C2×D512yes—
74#940—201no—
75#859—52no—
76C24×C5—61no—
77C5×#41—32no—
78C5×#41#6712yescomplemented
79C2×C5×Q8C22×D311yescharacteristic
80C2×C5×D4—31no—
81C2×C5×D4—32no—
82C2×C5×D4—62no—
83C2×C5×D4—62no—
84C2×C5×D4—61no—
85C22×C4×C5—31no—
86C2×C22⋊D5—32no—
87C2×C22⋊D5—64no—
88C22×Dic5—61no—
89Q8×D5—22no—
90Q8×D5—62no—
91#711—64no—
92#711—64no—
93#709—62no—
94#709—62no—
95C2×D20S411yescharacteristic
96C2×C4×D5—32no—
97C2×Dic10—32no—
98C2×Dic10—34no—
99C2×Dic10—31no—
100C2×Dic10—62no—
101C5×SD16—62no—
102C5×SD16—62no—
103C5×D8—64no—
104C5×M16—62no—
105C2×C5×C8—32no—
106C22⋊Dic5—64no—
107C22⋊Dic5—61no—
108#687—68no—
109C4⋊Dic5—32no—
110C4×Dic5—61no—
111C2×#168—32no—
112C2×#168—62no—
113C2×2−1+4—51no—
114C2×AGL(1,ℤ/8)—31no—
115C22×SD16—151no—
116#535—151no—
117#449—154no—
118#448—154no—
119#419—151no—
120#416—151no—
121#408—151no—
122C22×C3×C5—41no—
123C2×C5×D3—82no—
124C2×C5×D3—84no—
125C2×C3×D5—82no—
126C2×C3×D5—84no—
127C3×C4×C5—42no—
128Dic15—44no—
129C2×C3×D4—201no—
130C2×#67—204no—
131C2×D12—41no—
132#41⋊C3C22⋊D512yescomplemented
133C2×SL(2,𝔽3)—102no—
134C2×SL(2,𝔽3)C22×D511yescharacteristic
135GL(2,𝔽3)—22no—
136C4×Dic3—201no—
137C23×C5—31no—
138C23×C5—62no—
139C23×C5—122no—
140C23×C5—242no—
141C22×D5C2×S412yes—
142C5×Q8—31no—
143C5×Q8C2×#6711yescharacteristic
144C5×D4—32no—
145C5×D4—61no—
146C5×D4—62no—
147C5×D4—62no—
148C5×D4—122no—
149C2×C4×C5—31no—
150C2×C4×C5—32no—
151C2×C4×C5—32no—
152C2×C4×C5C2×S411yescharacteristic
153C22⋊D5—64no—
154C22⋊D5—244no—
155C2×Dic5—32no—
156C2×Dic5—64no—
157C2×Dic5—62no—
158D20—22no—
159C4×D5—62no—
160C4×D5—62no—
161Dic10—34no—
162Dic10—62no—
163Dic10—62no—
164C5×C8—62no—
165#168—62no—
1662−1+4—102no—
1672−1+4—302no—
168C2×#41—151no—
169C2×#41—152no—
170C2×#41D3×D511yescharacteristic
171C22×Q8—52no—
172C22×Q8—151no—
173C22×D4—31no—
174AGL(1,ℤ/8)—62no—
175AGL(1,ℤ/8)—62no—
176C2×SD16—32no—
177C2×SD16—154no—
178C2×SD16—304no—
179C2×D8—32no—
180C2×M16—31no—
181C22×C8—151no—
182#127—301no—
183#124—301no—
184#121—154no—
185#120—302no—
186#117—151no—
187#103—154no—
188#103—152no—
189#102—152no—
190C22⋊C8—154no—
191C2×C3×C5—42no—
192C2×C3×C5—41no—
193C3×D5—162no—
194C5×D3—162no—
195C23×C3—202no—
196C22×D3—42no—
197C3×D4—402no—
198C2×C3×C4—41no—
199#67—408no—
200C2×Dic3—202no—
201D12—82no—
202SL(2,𝔽3)C2×C22⋊D511yescharacteristic
203C22×C5—32no—
204C22×C5—62no—
205C22×C5—124no—
206C22×C5—122no—
207C22×C5—244no—
208C22×C5C22×S411yescharacteristic
209C2×D5—24no—
210C2×D5—22no—
211C4×C5—31no—
212C4×C5—31no—
213C4×C5GL(2,ℤ/4)12yes—
214Dic5—62no—
215Dic5—122no—
216C24—61no—
217#41—32no—
218#41—302no—
219#41—302no—
220#41—304no—
221#41—304no—
222#41#120112yescomplemented
223C2×Q8—102no—
224C2×Q8—152no—
225C2×Q8—154no—
226C2×Q8—151no—
227C2×Q8—302no—
228C2×Q8—302no—
229C2×Q8C2×D3×D511yescharacteristic
230C2×D4—31no—
231C2×D4—32no—
232C2×D4—51no—
233C2×D4—62no—
234C2×D4—62no—
235C2×D4—61no—
236C2×D4—152no—
237C2×D4—304no—
238C22×C4—31no—
239C22×C4—152no—
240C22×C4—301no—
241SD16—62no—
242SD16—62no—
243SD16—308no—
244D8—64no—
245M16—62no—
246C2×C8—32no—
247C2×C8—152no—
248C2×C8—302no—
249C4⋊C4—152no—
250C22⋊C4—304no—
251C22⋊C4—301no—
252C42—301no—
253C3×C5—41noHall
254C22×C3—41no—
255C22×C3—404no—
256C22×C3—402no—
257C2×D3—82no—
258C2×D3—84no—
259C3×C4—42no—
260Dic3—204no—
261C2×C5—62no—
262C2×C5—242no—
263C2×C5#592612yes—
264C2×C5C2×GL(2,ℤ/4)11yescharacteristic
265D5—42no—
266C23—31no—
267C23—52no—
268C23—62no—
269C23—122no—
270C23—242no—
271Q8—31no—
272Q8—154no—
273Q8—302no—
274Q8—302no—
275Q8C2×#120111yescharacteristic
276D4—32no—
277D4—61no—
278D4—62no—
279D4—62no—
280D4—102no—
281D4—122no—
282D4—304no—
283D4—1204no—
284C2×C4—31no—
285C2×C4—32no—
286C2×C4—32no—
287C2×C4—152no—
288C2×C4—302no—
289C2×C4—302no—
290C2×C4—304no—
291C2×C4—302no—
292C2×C4D5×S411yescharacteristic
293C8—62no—
294C8—302no—
295C2×C3—42no—
296C2×C3—41no—
297C2×C3—802no—
298D3—162no—
299C5#8554011yescharacteristic, complemented, Sylow
300C22—32no—
301C22—62no—
302C22—104no—
303C22—102no—
304C22—124no—
305C22—122no—
306C22—244no—
307C22C2×D5×S411yescharacteristic
308C4—31no—
309C4—31no—
310C4—302no—
311C4—602no—
312C4#9190412yes—
313C3—41noSylow
314C2—62no—
315C2—202no—
316C2—242no—
317C2#1175678612yes—
318C2C2×#9190411yescharacteristic
subgroupG/H
center, FrattiniC22C2×D5×S4
commutator, cosocleC2×C5×SL(2,𝔽3)C23
FittingC2×C5×#41C2×D3
socleC22×C5C22×S4
hypercenterC2×C4D5×S4
hypocenterC5×SL(2,𝔽3)C2×D4
LCSG ▷ C2×C5×SL(2,𝔽3) ▷ C5×SL(2,𝔽3)
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. C2×#4150⋊C3C2semidirect
2. C2×C5×#986C2semidirect
3. #11752143C2semidirect
4. #11751613C2semidirect
8. C2×D5×SL(2,𝔽3)C22semidirect
12. #91184C22semidirect
14. C2×#4150D3semidirect
25. C5×#41⋊C3D4semidirect
32. C2×#986D5semidirect
78. C5×#41#67semidirect
132. #41⋊C3C22⋊D5semidirect
222. #41#1201semidirect
299. C5#85540semidirect

Maximal subgroups

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

subgroupindex
C2×#4150⋊C32
C2×C5×#9862
#117521432
#117516132
#106156793
#914634
#855405