Finite Group Databasebeta

← #14512640

Subgroups — #14512640

Order 1920.

394 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 51 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
1C4×C5⋊(#41⋊C3)C211yesmaximal, characteristic
2#11752110C211yesmaximal, characteristic, complemented
3C5×C4⋊#226C211yesmaximal, characteristic, complemented
4#11751594C212yesmaximal, complemented
5#11751590C212yesmaximal
6#10612190—31nomaximal, Hall
7C2×C5⋊(#41⋊C3)C2211yescharacteristic
8C2×C5×#226C2212yes—
9C4×C5×SL(2,𝔽3)C2211yescharacteristic
10#91388—41nomaximal
11Dic5×SL(2,𝔽3)C2211yescharacteristic
12#91184C2212yes—
13#85338—51nomaximal, Hall
14#66062—31no—
15C4×#713D311yescharacteristic
16C5×#462—31no—
17#65476—32no—
18#65473—32no—
19#65372—31no—
20#65310—31no—
21#65131—31no—
22#65124—31no—
23#65106—32no—
24#65104—32no—
25C2×C5×SL(2,𝔽3)C2311yescharacteristic
26C5⋊(#41⋊C3)—21no—
27C5×#226—22no—
28C4⋊Dic15—41no—
29C5×C4⋊Dic3—41no—
30C3×C4×Dic5—41no—
31Dic3⋊Dic5—42no—
32#6669—42no—
33C4×#41⋊C3—51no—
34#5425—52no—
35#5391—51no—
36C4⋊#226D511yescharacteristic, complemented
37#5388—52no—
38C2×#713C2×D311yescharacteristic
39C2×C5×Q16—32no—
40C5×C4⋊Q8—31no—
41C4×C5×Q8C2×D311yescharacteristic
42#4092—32no—
43Q8×Dic5—32no—
44Q8×Dic5C2×D311yescharacteristic
45C2×#688—32no—
46#4043—61no—
47#4039—31no—
48#4038—31no—
49#4038—61no—
50#4036—61no—
51#4033—61no—
52C4×D20—31no—
53C42×D5—31no—
54#4015—31no—
55C5×C4⋊C8—31no—
56C5×#103—32no—
57#3967—32no—
58#3967—32no—
59#3953—32no—
60#3952—32no—
61#3949—32no—
62#3947—32no—
63#3939—32no—
64C4⋊#168—31no—
65#3116—151noSylow
66C2×C3×C4×C5—41no—
67C2×Dic15—42no—
68C2×C5×Dic3—42no—
69C2×C3×Dic5—41no—
70C2×C3×Dic5—41no—
71C5×SL(2,𝔽3)#4111yescharacteristic
72C2×#41⋊C3—51no—
73C2×#226C2×D512yes—
74#870—201no—
75C4×SL(2,𝔽3)—51no—
76C4×SL(2,𝔽3)C2×D511yescharacteristic
77#859—52no—
78C2×C5×Q8—32no—
79C2×C5×Q8C22×D311yescharacteristic
80#713—21no—
81#713—61no—
82C2×D20—31no—
83C2×C4×D5—31no—
84C2×C4×D5—31no—
85C2×C4×D5—31no—
86C2×Dic10—61no—
87C5×Q16—62no—
88C5×Q16—62no—
89C2×C5×C8—32no—
90C5×C4⋊C4—31no—
91C5×C4⋊C4—61no—
92C5×C4⋊C4—61no—
93C42×C5—31no—
94#688—64no—
95#685—61no—
96#685—62no—
97C4⋊Dic5—31no—
98C4⋊Dic5—32no—
99C4⋊Dic5—61no—
100C4⋊Dic5—62no—
101#683—62no—
102C4×Dic5—31no—
103C4×Dic5—31no—
104C4×Dic5—62no—
105C4×Dic5S411yescharacteristic
106C2×#168—32no—
107#533—151no—
108C4×#41—51no—
109#485—152no—
110#477—151no—
111#476—151no—
112#462—31no—
113#461—151no—
114#452—152no—
115#441—152no—
116#440—152no—
117#432—151no—
118C22×C3×C5—41no—
119C3×C4×C5—42no—
120Dic15—82no—
121C3×Dic5—81no—
122C3×Dic5—81no—
123C5×Dic3—82no—
124#41⋊C3—101no—
125C2×SL(2,𝔽3)C22×D511yescharacteristic
126#226—22no—
127C3×C42—201no—
128C4⋊Dic3—41no—
129C4⋊Dic3—201no—
130Dic3⋊C4—202no—
131Dic3⋊C4—202no—
132C22×D5—31no—
133C5×Q8—31no—
134C5×Q8—62no—
135C5×Q8—62no—
136C5×Q8#23511yescharacteristic
137C2×C4×C5—31no—
138C2×C4×C5—31no—
139C2×C4×C5—62no—
140C2×C4×C5C2×S411yescharacteristic
141C2×Dic5—31no—
142C2×Dic5—62no—
143C2×Dic5C2×S411yescharacteristic
144C2×Dic5C2×S411yescharacteristic
145D20—32no—
146D20—61no—
147C4×D5—61no—
148C4×D5—61no—
149C4×D5—62no—
150C4×D5—121no—
151Dic10—122no—
152C5×C8—62no—
153#168—62no—
154C2×#41—51no—
155C2×Q16—32no—
156C2×SD16—152no—
157C4⋊Q8—31no—
158C4⋊Q8—151no—
159#125—301no—
160C22⋊Q8—152no—
161C22⋊Q8—301no—
162C4×Q8—51no—
163C4×Q8—152no—
164C4×Q8—301no—
165C4×Q8D3×D511yescharacteristic
166C4×D4—151no—
167C4×D4—151no—
168#117—151no—
169#117—301no—
170C2×C42—151no—
171#107—152no—
172#106—152no—
173C4⋊C8—31no—
174C4⋊C8—151no—
175#103—32no—
176#103—152no—
177#103—152no—
178#102—152no—
179C22⋊C8—152no—
180#97—152no—
181C2×C3×C5—41no—
182C2×C3×C5—41no—
183C2×C3×C5—41no—
184C2×C3×C4—41no—
185C2×C3×C4—201no—
186C2×C3×C4—201no—
187C2×Dic3—42no—
188C2×Dic3—202no—
189SL(2,𝔽3)#71111yescharacteristic
190C22×C5C22×S411yescharacteristic
191C2×D5—61no—
192C2×D5—61no—
193C2×D5—61no—
194C4×C5—31no—
195C4×C5—31no—
196C4×C5—61no—
197C4×C5—122no—
198C4×C5#98412yes—
199Dic5—21no—
200Dic5—21no—
201Dic5—61no—
202Dic5—122no—
203#41—101no—
204#41—301no—
205C2×Q8—32no—
206C2×Q8—301no—
207C2×Q8C2×D3×D511yescharacteristic
208C2×D4—151no—
209C22×C4—151no—
210C22×C4—151no—
211C22×C4—151no—
212Q16—62no—
213Q16—62no—
214SD16—304no—
215C2×C8—32no—
216C2×C8—152no—
217C4⋊C4—31no—
218C4⋊C4—61no—
219C4⋊C4—61no—
220C4⋊C4—151no—
221C4⋊C4—152no—
222C4⋊C4—302no—
223C4⋊C4—302no—
224C4⋊C4—301no—
225C22⋊C4—301no—
226C22⋊C4—302no—
227C42—31no—
228C42—51no—
229C42—151no—
230C42—151no—
231C42—302no—
232C3×C5—41noHall
233C22×C3—41no—
234C3×C4—42no—
235C3×C4—401no—
236C3×C4—401no—
237Dic3—82no—
238Dic3—402no—
239C2×C5#591211yescharacteristic
240C2×C5C2×#98411yescharacteristic
241C2×C5#592311yescharacteristic
242D5—121no—
243C23—151no—
244Q8—31no—
245Q8—62no—
246Q8—62no—
247Q8—602no—
248Q8#677211yescharacteristic
249D4—152no—
250D4—301no—
251C2×C4—31no—
252C2×C4—31no—
253C2×C4—51no—
254C2×C4—51no—
255C2×C4—62no—
256C2×C4—151no—
257C2×C4—301no—
258C2×C4—301no—
259C2×C4—302no—
260C2×C4—302no—
261C2×C4—601no—
262C2×C4D5×S411yescharacteristic
263C8—62no—
264C8—302no—
265C2×C3—41no—
266C2×C3—41no—
267C2×C3—41no—
268C5#8533811yescharacteristic, complemented, Sylow
269C22—301no—
270C22—301no—
271C22—301no—
272C22C2×D5×S411yescharacteristic
273C4—31no—
274C4—31no—
275C4—61no—
276C4—101no—
277C4—101no—
278C4—122no—
279C4—301no—
280C4—602no—
281C4#9189112yes—
282C3—41noSylow
283C2—601no—
284C2#1175675311yescharacteristic
285C2C2×#9189111yescharacteristic
286C2#1175678211yescharacteristic
subgroupG/H
center, FrattiniC22C2×D5×S4
commutator, cosocleC2×C5×SL(2,𝔽3)C23
FittingC4×C5×Q8C2×D3
socleC22×C5C22×S4
prime radicalC2×C5⋊(#41⋊C3)C22
hypercenterC2×C4D5×S4
hypocenterC5×SL(2,𝔽3)#41
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
2. #11752110C2semidirect
3. C5×C4⋊#226C2semidirect
4. #11751594C2semidirect
36. C4⋊#226D5semidirect
268. C5#85338semidirect

Maximal subgroups

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

subgroupindex
C4×C5⋊(#41⋊C3)2
#117521102
C5×C4⋊#2262
#117515942
#117515902
#106121903
#913884
#853385