Finite Group Databasebeta

← #14513769

Subgroups — #14513769

Order 1920.

570 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 570 conjugacy classes of subgroups — too many to draw. Only its 73 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×#91956C211yesmaximal, characteristic
2C5×#520⋊C3C211yesmaximal, characteristic, complemented
3#11752143C211yesmaximal, characteristic, complemented
4#11752113C212yesmaximal, complemented
5C4×C5⋊GL(2,𝔽3)C212yesmaximal, complemented
6#10614295—31nomaximal, Hall
7C2×C5×#41⋊C3C2211yescharacteristic
8#91956C414yescomplemented
9C2×C5⋊GL(2,𝔽3)C2212yes—
10#91782—41nomaximal
11C4×C5×SL(2,𝔽3)C2212yescomplemented
12#91184C2211yescharacteristic, complemented
13#91184C2211yescharacteristic, complemented
14#85366—51nomaximal, Hall
15C5×#520D311yescharacteristic, complemented
16C2×#4095—31no—
17#65855—31no—
18#65522—31no—
19#65315—32no—
20C4×#688—32no—
21#65303—32no—
22C4×#686—32no—
23#65286—31no—
24C2×#3941—31no—
25#65253—31no—
26C2×D60—41no—
27C2×C4×D15—42no—
28C5×#41⋊C3C2×C412yescomplemented
29C2×C5×SL(2,𝔽3)C2311yescharacteristic
30C5⋊GL(2,𝔽3)C2×C414yescomplemented
31C3×C5×C4⋊C4—41no—
32#6714—42no—
33C4×Dic15—41no—
34C2×#986—51no—
35#520⋊C3D511yescharacteristic, complemented
36#5424—51no—
37#5394—52no—
38C4×GL(2,𝔽3)—52no—
39C2×C5×#41C2×D311yescharacteristic
40C22×D20—31no—
41C4×C5×Q8C2×D312yes—
42C4×C5×D4—32no—
43C5×#117—31no—
44C2×C5×C4⋊C4—31no—
45#4095—34no—
46#4095—34no—
47C2×#688—32no—
48C2×#686—32no—
49#4072—31no—
50C2×#681—31no—
51C22×#168—31no—
52#4039—61no—
53#4039—61no—
54D5×C22⋊C4—62no—
55C4×D20—32no—
56C4×D20—32no—
57#3967—31no—
58#3967—31no—
59#3964—31no—
60#3964—31no—
61#3941—32no—
62#3941—32no—
63#3940—32no—
64#3939—32no—
65#3935—32no—
66C4×#168—32no—
67#2946—151noSylow
68C22×D15—42no—
69C2×C3×C4×C5—41no—
70C2×C3×C4×C5—42no—
71C2×Dic15—41no—
72C2×Dic15—41no—
73D60—44no—
74C4×D15—84no—
75C5×SL(2,𝔽3)C22×C411yescharacteristic
76C2×#41⋊C3C2×D511yescharacteristic
77#986—54no—
78C2×GL(2,𝔽3)—52no—
79#893—201no—
80C4×SL(2,𝔽3)C2×D512yescomplemented
81#859—51no—
82#859—51no—
83C23×D5—61no—
84C5×#41—32no—
85C5×#41C4×D312yescomplemented
86C2×C5×Q8C22×D311yescharacteristic
87C2×C5×D4—31no—
88C22×C4×C5—31no—
89C22×C4×C5—61no—
90C2×D20—32no—
91C2×D20—34no—
92C2×D20—62no—
93C2×D20—61no—
94C2×C4×D5—62no—
95C2×C4×D5—62no—
96C5×C4⋊C4—32no—
97C5×C4⋊C4—31no—
98C5×C4⋊C4S411yescharacteristic
99C5×C22⋊C4—32no—
100C42×C5—32no—
101C22⋊Dic5—61no—
102#688—34no—
103#688—34no—
104#686—38no—
105#685—62no—
106#685—62no—
107C4⋊Dic5—31no—
108C4⋊Dic5—31no—
109C4×Dic5—61no—
110#681—34no—
111C2×#168—32no—
112C2×#168—31no—
113C2×#168—31no—
114C2×#168—62no—
115C2×AGL(1,ℤ/8)—151no—
116#520D1511yescharacteristic, complemented
117#518—151no—
118#442—152no—
119#440—152no—
120C4×SD16—152no—
121C4×D8—152no—
122#428—151no—
123#416—151no—
124C2×#102—151no—
125#405—151no—
126C22×C3×C5—41no—
127C2×D15—44no—
128C2×D15—82no—
129C2×D15—82no—
130C3×C4×C5—42no—
131C3×C4×C5—82no—
132Dic15—42no—
133Dic15—81no—
134C2×D12—201no—
135C2×C4×D3—202no—
136#41⋊C3C4×D512yescomplemented
137C2×SL(2,𝔽3)C22×D511yescharacteristic
138GL(2,𝔽3)—54no—
139C3×C4⋊C4—41no—
140(C2×D3)⋊C4—202no—
141C4×Dic3—201no—
142C23×C5—31no—
143C22×D5—62no—
144C22×D5—64no—
145C22×D5—241no—
146C22×D5—241no—
147C5×Q8—31no—
148C5×Q8C2×C4×D311yescharacteristic
149C5×D4—32no—
150C5×D4—61no—
151C2×C4×C5—31no—
152C2×C4×C5—32no—
153C2×C4×C5—32no—
154C2×C4×C5—32no—
155C2×C4×C5—241no—
156C2×C4×C5C2×S412yes—
157C2×C4×C5C2×S411yescharacteristic
158C2×Dic5—61no—
159C2×Dic5—61no—
160D20—34no—
161D20—62no—
162D20—64no—
163C4×D5—242no—
164C4×D5—242no—
165#168—34no—
166#168—61no—
167#168—61no—
168C2×#41C2×D1511yescharacteristic
169C22×D4—151no—
170AGL(1,ℤ/8)—154no—
171AGL(1,ℤ/8)—154no—
172C2×SD16—152no—
173C2×D8—152no—
174C2×M16—151no—
175C22×C8—151no—
176C4×Q8C2×D1512yes—
177C4×D4—32no—
178C4×D4—152no—
179C4×D4—152no—
180C4×D4—301no—
181C4×D4—301no—
182#117—31no—
183#117—151no—
184C2×C4⋊C4—31no—
185C2×C22⋊C4—302no—
186#107—152no—
187#106—152no—
188#103—151no—
189#103—151no—
190#102—152no—
191#102—152no—
192#102—151no—
193#102—151no—
194#97—152no—
195C4×C8—152no—
196C2×C3×C5—41no—
197C2×C3×C5—41no—
198C2×C3×C5—41no—
199D15—84no—
200C22×D3—202no—
201C2×C3×C4—41no—
202C2×C3×C4—42no—
203C2×Dic3—201no—
204C2×Dic3—201no—
205D12—204no—
206C4×D3—404no—
207SL(2,𝔽3)C2×C4×D511yescharacteristic
208C22×C5—32no—
209C22×C5—61no—
210C22×C5—61no—
211C22×C5C22×S411yescharacteristic
212C2×D5—64no—
213C2×D5—122no—
214C2×D5—122no—
215C2×D5—244no—
216C4×C5—22no—
217C4×C5—31no—
218C4×C5—31no—
219C4×C5—62no—
220C4×C5C4×S412yes—
221Dic5—121no—
222Dic5—121no—
223C24—301no—
224#41—32no—
225#41C4×D1512yescomplemented
226C2×Q8C22×D1511yescharacteristic
227C2×D4—31no—
228C2×D4—152no—
229C2×D4—154no—
230C2×D4—302no—
231C2×D4—301no—
232C22×C4—31no—
233C22×C4—61no—
234C22×C4—302no—
235C22×C4—302no—
236SD16—154no—
237SD16—154no—
238D8—158no—
239M16—154no—
240C2×C8—152no—
241C2×C8—151no—
242C2×C8—151no—
243C2×C8—302no—
244C4⋊C4—32no—
245C4⋊C4—31no—
246C4⋊C4—151no—
247C4⋊C4—151no—
248C4⋊C4C5⋊S411yescharacteristic
249C22⋊C4—32no—
250C22⋊C4—302no—
251C22⋊C4—301no—
252C22⋊C4—302no—
253C42—32no—
254C42—301no—
255C3×C5—41noHall
256C22×C3—41no—
257C2×D3—204no—
258C2×D3—402no—
259C2×D3—402no—
260C3×C4—42no—
261C3×C4—82no—
262Dic3—202no—
263Dic3—401no—
264C2×C5—62no—
265C2×C5C2×C4×S411yescharacteristic
266C2×C5#592511yescharacteristic
267C2×C5#592611yescharacteristic
268D5—124no—
269C23—31no—
270C23—304no—
271C23—302no—
272C23—1201no—
273C23—1201no—
274Q8—31no—
275Q8C2×C4×D1511yescharacteristic
276D4—32no—
277D4—61no—
278D4—154no—
279D4—302no—
280D4—304no—
281C2×C4—31no—
282C2×C4—32no—
283C2×C4—32no—
284C2×C4—32no—
285C2×C4—241no—
286C2×C4—301no—
287C2×C4—301no—
288C2×C4—1202no—
289C2×C4—1202no—
290C2×C4C2×C5⋊S412yes—
291C2×C4C2×C5⋊S411yescharacteristic
292C8—154no—
293C8—301no—
294C8—301no—
295C2×C3—41no—
296C2×C3—41no—
297C2×C3—41no—
298D3—404no—
299C5#8536611yescharacteristic, complemented, Sylow
300C22—32no—
301C22—61no—
302C22—61no—
303C22—304no—
304C22—602no—
305C22—602no—
306C22—1204no—
307C22C22×C5⋊S411yescharacteristic
308C4—22no—
309C4—31no—
310C4—31no—
311C4—62no—
312C4—601no—
313C4—601no—
314C4C4×C5⋊S412yes—
315C3—41noSylow
316C2—62no—
317C2—604no—
318C2C2×C4×C5⋊S411yescharacteristic
319C2#1175690911yescharacteristic
320C2#1175691011yescharacteristic
subgroupG/H
center, FrattiniC22C22×C5⋊S4
commutator, hypocenterC5×SL(2,𝔽3)C22×C4
FittingC5×#520D3
socleC22×C5C22×S4
prime radicalC2×#91956C2
cosocleC2×C5×SL(2,𝔽3)C23
hypercenterC4⋊C4C5⋊S4
LCSG ▷ C5×SL(2,𝔽3)
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C5×#520⋊C3C2semidirect
3. #11752143C2semidirect
4. #11752113C2semidirect
5. C4×C5⋊GL(2,𝔽3)C2semidirect
8. #91956C4semidirect
11. C4×C5×SL(2,𝔽3)C22semidirect
12. #91184C22semidirect
13. #91184C22semidirect
15. C5×#520D3semidirect
28. C5×#41⋊C3C2×C4semidirect
30. C5⋊GL(2,𝔽3)C2×C4semidirect
35. #520⋊C3D5semidirect
80. C4×SL(2,𝔽3)C2×D5semidirect
85. C5×#41C4×D3semidirect
116. #520D15semidirect
136. #41⋊C3C4×D5semidirect
225. #41C4×D15semidirect
299. C5#85366semidirect

Maximal subgroups

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

subgroupindex
C2×#919562
C5×#520⋊C32
#117521432
#117521132
C4×C5⋊GL(2,𝔽3)2
#106142953
#917824
#853665