Finite Group Databasebeta

← #14513502

Subgroups — #14513502

Order 1920.

570 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 570 conjugacy classes of subgroups — too many to draw. Only its 67 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
2#66161⋊C3C211yesmaximal, characteristic, complemented
3C5×#5424C211yesmaximal, characteristic, complemented
4#11751610C212yesmaximal, complemented
5#11751603C212yesmaximal, complemented
6#10610551—31nomaximal, Hall
7C2×C5×#41⋊C3C2211yescharacteristic
8#91956C414yescomplemented
9C2×C5⋊GL(2,𝔽3)C2212yes—
10#91428—41nomaximal
11Dic5×SL(2,𝔽3)C2212yescomplemented
12C5×#859C2211yescharacteristic, complemented
13C5×#859C2211yescharacteristic, complemented
14#85366—51nomaximal, Hall
15#66161D311yescharacteristic, complemented
16C2×#4095—31no—
17#65855—31no—
18C5×#416—31no—
19C2×#3953—31no—
20#65390—31no—
21#65284—31no—
22#65106—32no—
23#65077—32no—
24#65074—32no—
25#65045—32no—
26C2×D60—41no—
27C5×#41⋊C3C2×C412yescomplemented
28C2×C5×SL(2,𝔽3)C2311yescharacteristic
29C2×#1200—42no—
30C5⋊GL(2,𝔽3)C2×C414yescomplemented
31C4×C5×Dic3—41no—
32C3×C4⋊Dic5—41no—
33#6667—42no—
34C2×#986—51no—
35#520⋊C3—51no—
36#5424D511yescharacteristic, complemented
37#5394—52no—
38C4×GL(2,𝔽3)—52no—
39C2×C5×#41C2×D311yescharacteristic
40C22×D20—31no—
41C22×C5×C8—31no—
42C5×#117—31no—
43#4095—34no—
44#4095—34no—
45Q8×Dic5C2×D312yes—
46C2×#688—32no—
47D4×Dic5—32no—
48C2×#686—32no—
49#4072—31no—
50C2×C4⋊Dic5—31no—
51C2×#681—31no—
52#4039—32no—
53#4039—32no—
54D5×C22⋊C4—62no—
55C4×D20—61no—
56C4×D20—61no—
57C5×#103—31no—
58C5×#103—31no—
59C5×#102—31no—
60C5×#102—31no—
61#3953—32no—
62#3953—32no—
63#3947—32no—
64C8×Dic5—32no—
65#3940—32no—
66#3939—32no—
67#2946—151noSylow
68C22×D15—42no—
69C2×C3×C4×C5—41no—
70D60—44no—
71C2×C5×Dic3—41no—
72C2×C5×Dic3—41no—
73C2×C3×Dic5—42no—
74C5×SL(2,𝔽3)C22×C411yescharacteristic
75#1200—84no—
76C2×#41⋊C3C2×D511yescharacteristic
77#986—54no—
78C2×GL(2,𝔽3)—52no—
79#893—201no—
80C4×SL(2,𝔽3)—52no—
81#859C2×D511yescharacteristic, complemented
82#859C2×D511yescharacteristic, complemented
83C23×D5—61no—
84C5×#41—32no—
85C5×#41C4×D312yescomplemented
86C2×C5×Q8C22×D311yescharacteristic
87C2×C5×D4—31no—
88C22×C4×C5—31no—
89C22×Dic5—61no—
90C2×D20—32no—
91C2×D20—34no—
92C2×D20—62no—
93C2×D20—61no—
94C2×C4×D5—62no—
95C2×C4×D5—62no—
96C2×C5×C8—31no—
97C2×C5×C8—31no—
98C2×C5×C8—62no—
99C5×C4⋊C4—31no—
100C5×C4⋊C4—31no—
101C5×C22⋊C4—61no—
102C42×C5—61no—
103C22⋊Dic5—32no—
104#688—34no—
105#688—34no—
106#686—38no—
107#685—62no—
108#685—62no—
109C4⋊Dic5—31no—
110C4⋊Dic5—32no—
111C4⋊Dic5S411yescharacteristic
112C4×Dic5—32no—
113#681—34no—
114C2×#168—32no—
115C2×AGL(1,ℤ/8)—151no—
116#520—51no—
117#518—151no—
118#442—152no—
119#440—152no—
120C4×SD16—152no—
121C4×D8—152no—
122#428—151no—
123#416—31no—
124C2×#102—151no—
125#405—151no—
126C22×C3×C5—41no—
127C2×D15—44no—
128C2×D15—82no—
129C2×D15—82no—
130C3×C4×C5—42no—
131C3×Dic5—82no—
132C5×Dic3—42no—
133C5×Dic3—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—201no—
140(C2×D3)⋊C4—202no—
141C4×Dic3—41no—
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—61no—
155C2×C4×C5—61no—
156C2×C4×C5C2×S411yescharacteristic
157C2×Dic5—32no—
158C2×Dic5—241no—
159C2×Dic5C2×S412yes—
160D20—34no—
161D20—62no—
162D20—64no—
163C4×D5—242no—
164C4×D5—242no—
165C5×C8—61no—
166C5×C8—61no—
167#168—34no—
168C2×#41D3×D511yescharacteristic
169C22×D4—151no—
170AGL(1,ℤ/8)—154no—
171AGL(1,ℤ/8)—154no—
172C2×SD16—152no—
173C2×D8—152no—
174C2×M16—151no—
175C22×C8—31no—
176C4×Q8—52no—
177C4×D4—152no—
178C4×D4—152no—
179C4×D4—152no—
180C4×D4—301no—
181C4×D4—301no—
182#117—31no—
183#117—151no—
184C2×C4⋊C4—151no—
185C2×C22⋊C4—302no—
186#107—152no—
187#106—152no—
188#103—31no—
189#103—31no—
190#102—31no—
191#102—31no—
192#102—152no—
193#102—152no—
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—202no—
203C2×Dic3—41no—
204C2×Dic3—41no—
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—31no—
217C4×C5—31no—
218C4×C5—121no—
219C4×C5—121no—
220C4×C5C4×S412yes—
221Dic5—22no—
222Dic5—62no—
223C24—301no—
224#41—32no—
225#41#120012yescomplemented
226C2×Q8C2×D3×D511yescharacteristic
227C2×D4—31no—
228C2×D4—152no—
229C2×D4—154no—
230C2×D4—302no—
231C2×D4—301no—
232C22×C4—31no—
233C22×C4—302no—
234C22×C4—302no—
235C22×C4—301no—
236SD16—154no—
237SD16—154no—
238D8—158no—
239M16—154no—
240C2×C8—31no—
241C2×C8—31no—
242C2×C8—62no—
243C2×C8—152no—
244C4⋊C4—31no—
245C4⋊C4—31no—
246C4⋊C4—51no—
247C4⋊C4—152no—
248C4⋊C4—151no—
249C22⋊C4—61no—
250C22⋊C4—152no—
251C22⋊C4—302no—
252C22⋊C4—302no—
253C42—61no—
254C42—152no—
255C3×C5—41noHall
256C22×C3—41no—
257C2×D3—204no—
258C2×D3—402no—
259C2×D3—402no—
260C3×C4—42no—
261C3×C4—402no—
262Dic3—42no—
263Dic3—81no—
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×#120011yescharacteristic
276D4—32no—
277D4—61no—
278D4—154no—
279D4—302no—
280D4—304no—
281C2×C4—31no—
282C2×C4—32no—
283C2×C4—32no—
284C2×C4—52no—
285C2×C4—61no—
286C2×C4—61no—
287C2×C4—152no—
288C2×C4—1202no—
289C2×C4—1202no—
290C2×C4—1201no—
291C2×C4D5×S411yescharacteristic
292C8—61no—
293C8—61no—
294C8—154no—
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—
307C22C2×D5×S411yescharacteristic
308C4—31no—
309C4—31no—
310C4—102no—
311C4—121no—
312C4—121no—
313C4—302no—
314C4#9190112yes—
315C3—41noSylow
316C2—62no—
317C2—604no—
318C2#1175677511yescharacteristic
319C2#1175678511yescharacteristic
320C2C2×#9190111yescharacteristic
subgroupG/H
center, FrattiniC22C2×D5×S4
commutator, hypocenterC5×SL(2,𝔽3)C22×C4
FittingC2×C5×#41C2×D3
socleC22×C5C22×S4
prime radicalC2×#91956C2
cosocleC2×C5×SL(2,𝔽3)C23
hypercenterC2×C4D5×S4
LCSG ▷ C5×SL(2,𝔽3)
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
2. #66161⋊C3C2semidirect
3. C5×#5424C2semidirect
4. #11751610C2semidirect
5. #11751603C2semidirect
8. #91956C4semidirect
11. Dic5×SL(2,𝔽3)C22semidirect
12. C5×#859C22semidirect
13. C5×#859C22semidirect
15. #66161D3semidirect
27. C5×#41⋊C3C2×C4semidirect
30. C5⋊GL(2,𝔽3)C2×C4semidirect
36. #5424D5semidirect
81. #859C2×D5semidirect
82. #859C2×D5semidirect
85. C5×#41C4×D3semidirect
136. #41⋊C3C4×D5semidirect
225. #41#1200semidirect
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
#66161⋊C32
C5×#54242
#117516102
#117516032
#106105513
#914284
#853665