Finite Group Databasebeta

← C4×#91956 #14513744

Subgroups — C4×#91956 #14513744

Order 1920.

608 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 608 conjugacy classes of subgroups — too many to draw. Only its 77 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
2C4×C5×#41⋊C3C211yesmaximal, characteristic, complemented
3#11752145C211yesmaximal, characteristic, complemented
4#11752113C212yesmaximal, complemented
5C4×C5⋊GL(2,𝔽3)C212yesmaximal, complemented
6C4×#4095—31nomaximal, Hall
7C2×C5×#41⋊C3C2211yescharacteristic
8#91956C414yesdirect product factor
9C2×C5⋊GL(2,𝔽3)C2212yes—
10C4×D60—41nomaximal
11C4×C5×SL(2,𝔽3)C2211yescharacteristic, complemented
12C4×C5×SL(2,𝔽3)C2211yescharacteristic, complemented
13#91184C2212yescomplemented
14C4×#986—51nomaximal, Hall
15C4×C5×#41D311yescharacteristic, complemented
16C2×#4095—31no—
17C2×C4×D20—31no—
18#65521—31no—
19#65315—32no—
20C4×#688—32no—
21#65303—32no—
22C4×#686—32no—
23#65290—31no—
24#65284—31no—
25C4×#681—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×C42×C5—41no—
32#6714—42no—
33C4⋊Dic15—41no—
34C2×#986—51no—
35C4×#41⋊C3D511yescharacteristic, complemented
36#5426—51no—
37#5394—52no—
38C4×GL(2,𝔽3)—52no—
39C2×C5×#41C2×D311yescharacteristic
40C22×D20—31no—
41C22×C4×D5—61no—
42C4×C5×Q8C2×D311yescharacteristic
43C4×C5×Q8C2×D311yescharacteristic
44C4×C5×D4—31no—
45C4×C5×D4—31no—
46C5×#117—31no—
47C2×C42×C5—31no—
48#4095—34no—
49#4095—34no—
50C2×#688—32no—
51C2×#686—32no—
52C2×#685—61no—
53C2×C4⋊Dic5—31no—
54C2×#681—31no—
55C2×#681—31no—
56C4×D20—32no—
57C4×D20—32no—
58C4×D20—61no—
59C4×D20—61no—
60#3967—32no—
61#3964—32no—
62#3941—32no—
63#3941—32no—
64#3940—32no—
65#3939—32no—
66#3935—32no—
67C4×#168—32no—
68C4×AGL(1,ℤ/8)—151noSylow
69C22×D15—42no—
70C2×C3×C4×C5—41no—
71C2×C3×C4×C5—41no—
72C2×C3×C4×C5—41no—
73C2×Dic15—42no—
74D60—44no—
75C4×D15—84no—
76C5×SL(2,𝔽3)C22×C411yescharacteristic, complemented
77C2×#41⋊C3C2×D511yescharacteristic
78#986—54no—
79C2×GL(2,𝔽3)—52no—
80C4×D12—201no—
81C4×SL(2,𝔽3)C2×D511yescharacteristic, complemented
82C4×SL(2,𝔽3)C2×D511yescharacteristic, complemented
83#859—52no—
84C23×D5—61no—
85C5×#41—32no—
86C5×#41C4×D312yescomplemented
87C2×C5×Q8C22×D311yescharacteristic
88C2×C5×D4—31no—
89C22×C4×C5—31no—
90C22×C4×C5—31no—
91C22×C4×C5—31no—
92C22×Dic5—61no—
93C2×D20—32no—
94C2×D20—34no—
95C2×D20—62no—
96C2×D20—61no—
97C2×C4×D5—62no—
98C2×C4×D5—62no—
99C2×C4×D5—124no—
100C5×C4⋊C4—31no—
101C5×C4⋊C4—31no—
102C5×C22⋊C4—61no—
103C42×C5—31no—
104C42×C5—31no—
105C42×C5—31no—
106C42×C5S411yescharacteristic
107#688—34no—
108#688—34no—
109#686—38no—
110#685—62no—
111#685—62no—
112C4⋊Dic5—32no—
113C4⋊Dic5—61no—
114#681—34no—
115#681—62no—
116C2×#168—32no—
117C2×#168—32no—
118C2×AGL(1,ℤ/8)—151no—
119C4×#41D1511yescharacteristic, complemented
120C2×C4×D4—151no—
121#442—152no—
122#440—152no—
123C4×SD16—152no—
124C4×D8—152no—
125#428—151no—
126#418—151no—
127#417—151no—
128C4×M16—151no—
129C22×C3×C5—41no—
130C2×D15—44no—
131C2×D15—82no—
132C2×D15—82no—
133C3×C4×C5—42no—
134C3×C4×C5—42no—
135C3×C4×C5—81no—
136Dic15—82no—
137C2×D12—201no—
138C2×C4×D3—202no—
139#41⋊C3C4×D512yescomplemented
140C2×SL(2,𝔽3)C22×D511yescharacteristic
141GL(2,𝔽3)—54no—
142C3×C42—41no—
143(C2×D3)⋊C4—202no—
144C4⋊Dic3—201no—
145C23×C5—31no—
146C22×D5—64no—
147C22×D5—62no—
148C22×D5—122no—
149C22×D5—122no—
150C5×Q8—31no—
151C5×Q8C2×C4×D311yescharacteristic
152C5×D4—32no—
153C5×D4—61no—
154C2×C4×C5—31no—
155C2×C4×C5—32no—
156C2×C4×C5—32no—
157C2×C4×C5—31no—
158C2×C4×C5—31no—
159C2×C4×C5—62no—
160C2×C4×C5—121no—
161C2×C4×C5C2×S411yescharacteristic
162C2×C4×C5C2×S411yescharacteristic
163C2×C4×C5C2×S411yescharacteristic
164C2×Dic5—62no—
165C2×Dic5—122no—
166D20—34no—
167D20—62no—
168D20—64no—
169C4×D5—124no—
170C4×D5—124no—
171#168—34no—
172#168—62no—
173C2×#41C2×D1511yescharacteristic
174C22×D4—151no—
175C23×C4—301no—
176AGL(1,ℤ/8)—154no—
177AGL(1,ℤ/8)—154no—
178C2×SD16—152no—
179C2×D8—152no—
180C2×M16—151no—
181C2×M16—151no—
182C4×Q8C2×D1511yescharacteristic
183C4×Q8C2×D1511yescharacteristic
184C4×D4—31no—
185C4×D4—31no—
186C4×D4—152no—
187C4×D4—152no—
188C4×D4—301no—
189C4×D4—301no—
190#117—31no—
191C2×C4⋊C4—151no—
192C2×C22⋊C4—301no—
193C2×C42—31no—
194#107—152no—
195#106—152no—
196#103—152no—
197#102—152no—
198#102—152no—
199#102—152no—
200#97—152no—
201C4×C8—152no—
202C2×C3×C5—41no—
203C2×C3×C5—41no—
204C2×C3×C5—41no—
205D15—84no—
206C22×D3—202no—
207C2×C3×C4—41no—
208C2×C3×C4—41no—
209C2×C3×C4—41no—
210C2×Dic3—202no—
211D12—204no—
212C4×D3—404no—
213SL(2,𝔽3)C2×C4×D511yescharacteristic, complemented
214C22×C5—32no—
215C22×C5—61no—
216C22×C5—61no—
217C22×C5C22×S411yescharacteristic
218C2×D5—64no—
219C2×D5—128no—
220C2×D5—122no—
221C2×D5—122no—
222C4×C5—21no—
223C4×C5—31no—
224C4×C5—31no—
225C4×C5—61no—
226C4×C5—61no—
227C4×C5C4×S412yes—
228C4×C5#98612yescomplemented
229Dic5—122no—
230C24—301no—
231#41—32no—
232#41C4×D1512yescomplemented
233C2×Q8C22×D1511yescharacteristic
234C2×D4—31no—
235C2×D4—152no—
236C2×D4—154no—
237C2×D4—302no—
238C2×D4—301no—
239C22×C4—31no—
240C22×C4—31no—
241C22×C4—31no—
242C22×C4—302no—
243C22×C4—301no—
244C22×C4—302no—
245C22×C4—604no—
246SD16—154no—
247SD16—154no—
248D8—158no—
249M16—154no—
250M16—302no—
251C2×C8—152no—
252C2×C8—152no—
253C4⋊C4—31no—
254C4⋊C4—31no—
255C4⋊C4—152no—
256C4⋊C4—301no—
257C22⋊C4—61no—
258C22⋊C4—302no—
259C22⋊C4—302no—
260C42—31no—
261C42—31no—
262C42—31no—
263C42C5⋊S411yescharacteristic
264C3×C5—41noHall
265C22×C3—41no—
266C2×D3—204no—
267C2×D3—402no—
268C2×D3—402no—
269C3×C4—42no—
270C3×C4—42no—
271C3×C4—81no—
272Dic3—402no—
273C2×C5—62no—
274C2×C5C2×C4×S411yescharacteristic
275C2×C5C2×#98611yescharacteristic
276C2×C5#592311yescharacteristic
277D5—124no—
278C23—31no—
279C23—304no—
280C23—302no—
281C23—602no—
282C23—602no—
283Q8—31no—
284Q8C2×C4×D1511yescharacteristic
285D4—32no—
286D4—61no—
287D4—154no—
288D4—302no—
289D4—304no—
290C2×C4—31no—
291C2×C4—32no—
292C2×C4—32no—
293C2×C4—31no—
294C2×C4—31no—
295C2×C4—62no—
296C2×C4—121no—
297C2×C4—302no—
298C2×C4—604no—
299C2×C4—602no—
300C2×C4—604no—
301C2×C4C2×C5⋊S411yescharacteristic
302C2×C4C2×C5⋊S411yescharacteristic
303C2×C4C2×C5⋊S411yescharacteristic
304C8—154no—
305C8—302no—
306C2×C3—41no—
307C2×C3—41no—
308C2×C3—41no—
309D3—404no—
310C5C4×#98611yescharacteristic, complemented, Sylow
311C22—32no—
312C22—61no—
313C22—61no—
314C22—304no—
315C22—608no—
316C22—602no—
317C22—602no—
318C22C22×C5⋊S411yescharacteristic
319C4—21no—
320C4—31no—
321C4—31no—
322C4—61no—
323C4—61no—
324C4—602no—
325C4C4×C5⋊S412yes—
326C4#9195612yesdirect product factor
327C3—41noSylow
328C2—62no—
329C2—604no—
330C2C2×C4×C5⋊S411yescharacteristic
331C2C2×#9195611yescharacteristic
332C2#1175690711yescharacteristic
subgroupG/H
centerC2×C4C2×C5⋊S4
commutator, hypocenterC5×SL(2,𝔽3)C22×C4
FrattiniC22C22×C5⋊S4
FittingC4×C5×#41D3
socleC22×C5C22×S4
prime radicalC2×#91956C2
cosocleC2×C5×SL(2,𝔽3)C23
hypercenterC42C5⋊S4
LCSG ▷ C5×SL(2,𝔽3)
UCSC1 ◁ C2×C4 ◁ C42

Complements

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

NH ≅ G/Ntype
2. C4×C5×#41⋊C3C2semidirect
3. #11752145C2semidirect
4. #11752113C2semidirect
5. C4×C5⋊GL(2,𝔽3)C2semidirect
8. #91956C4direct (N × H)
11. C4×C5×SL(2,𝔽3)C22semidirect
12. C4×C5×SL(2,𝔽3)C22semidirect
13. #91184C22semidirect
15. C4×C5×#41D3semidirect
28. C5×#41⋊C3C2×C4semidirect
30. C5⋊GL(2,𝔽3)C2×C4semidirect
35. C4×#41⋊C3D5semidirect
76. C5×SL(2,𝔽3)C22×C4semidirect
81. C4×SL(2,𝔽3)C2×D5semidirect
82. C4×SL(2,𝔽3)C2×D5semidirect
86. C5×#41C4×D3semidirect
119. C4×#41D15semidirect
139. #41⋊C3C4×D5semidirect
213. SL(2,𝔽3)C2×C4×D5semidirect
228. C4×C5#986semidirect
232. #41C4×D15semidirect
310. C5C4×#986semidirect
326. C4#91956direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#919562
C4×C5×#41⋊C32
#117521452
#117521132
C4×C5⋊GL(2,𝔽3)2
C4×#40953
C4×D604
C4×#9865