Finite Group Databasebeta

← D20×#41⋊C3 #14514034

Subgroups — D20×#41⋊C3 #14514034

Order 1920.

796 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 796 conjugacy classes of subgroups — too many to draw. Only its 99 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×D5×#41⋊C3C212yesmaximal, complemented
2C4×C5×#41⋊C3C211yesmaximal, characteristic, complemented
3#65910⋊C3C212yesmaximal, complemented
4SL(2,𝔽3)×D20C211yesmaximal, characteristic, complemented
5C4⋊(C5⋊(#41⋊C3))C211yesmaximal, characteristic, complemented
6#41×D20C311yesmaximal, characteristic, complemented, Hall
7C2×C5×#41⋊C3C2211yescharacteristic
8D5×#41⋊C3—24no—
9C2×D5×SL(2,𝔽3)C2212yescomplemented
10C2×C5⋊(#41⋊C3)C2212yescomplemented
11C3×C4×D20—41nomaximal
12C4×C5×SL(2,𝔽3)C2211yescharacteristic, complemented
13C4×C5×SL(2,𝔽3)C2211yescharacteristic, complemented
14D4×#41⋊C3—51nomaximal, Hall
15C2×D5×#41C2×C312yescomplemented
16C4×C5×#41C2×C311yescharacteristic, complemented
17#65911C2×C311yescharacteristic, complemented
18#65910C2×C312yescomplemented
19Q8×D20C2×C311yescharacteristic
20#65889—31no—
21#65888—32no—
22D4×D20—31no—
23#65858—32no—
24#65811—31no—
25C2×C4×D20—31no—
26C2×C3×D20—41no—
27C2×C3×C4×D5—42no—
28C5×#41⋊C3D412yescomplemented
29C2×C5×SL(2,𝔽3)C2311yescharacteristic
30D5×SL(2,𝔽3)—22no—
31C5⋊(#41⋊C3)—22no—
32C3×C42×C5—41no—
33C3×#685—42no—
34C3×C4⋊Dic5—41no—
35C22×#41⋊C3—52no—
36C4⋊(#41⋊C3)—51no—
37D4×SL(2,𝔽3)—51no—
38#548⋊C3—52no—
39C4×#41⋊C3D511yescharacteristic, complemented
40C2×C5×#41C22×C311yescharacteristic
41D5×#41—24no—
42D5×#41—64no—
43C2×#713C22×C312yes—
44C2×Q8×D5C22×C312yes—
45C2×#711—32no—
46C2×D4×D5—32no—
47C2×#709—32no—
48C22×D20—31no—
49C22×C4×D5—32no—
50C4×C5×Q8C22×C311yescharacteristic
51C4×C5×Q8C22×C311yescharacteristic
52C4×C5×D4—31no—
53C4×C5×D4—31no—
54C5×#117—31no—
55C2×C42×C5—31no—
56#4076—32no—
57#4076—32no—
58C2×#685—32no—
59C2×C4⋊Dic5—31no—
60#4043—32no—
61#4043—32no—
62#4041—32no—
63#4041—32no—
64#4032—34no—
65#4028—34no—
66#4021—32no—
67#4020—31no—
68C4×D20—32no—
69C4×D20—31no—
70C4×D20—32no—
71C4×D20—31no—
72C4×D20—32no—
73C4×D20—31no—
74C4×D20A411yescharacteristic
75#4015—31no—
76D4×#41—51noSylow
77C22×C3×D5—42no—
78C2×C3×C4×C5—41no—
79C2×C3×C4×C5—41no—
80C2×C3×C4×C5—41no—
81C2×C3×Dic5—42no—
82C3×D20—44no—
83C3×C4×D5—84no—
84C5×SL(2,𝔽3)C2×D411yescharacteristic, complemented
85C2×#41⋊C3—52no—
86C2×#41⋊C3—104no—
87C2×#41⋊C3C2×D511yescharacteristic
88C22×SL(2,𝔽3)—52no—
89C3×C4×D4—201no—
90C4×SL(2,𝔽3)C2×D511yescharacteristic, complemented
91C4×SL(2,𝔽3)C2×D511yescharacteristic, complemented
92C23×D5—32no—
93C5×#41—32no—
94C5×#41C3×D412yescomplemented
95C2×C5×Q8C23×C311yescharacteristic
96C2×C5×D4—31no—
97C22×C4×C5—31no—
98C22×C4×C5—31no—
99C22×C4×C5—31no—
100C2×C22⋊D5—34no—
101C22×Dic5—32no—
102#713—22no—
103#713—62no—
104Q8×D5—22no—
105Q8×D5—62no—
106#711—64no—
107#711—64no—
108D4×D5—64no—
109D4×D5—64no—
110#709—64no—
111#709—64no—
112C2×D20—32no—
113C2×D20—32no—
114C2×D20—31no—
115C2×D20—32no—
116C2×D20—64no—
117C2×D20C2×A411yescharacteristic
118C2×C4×D5—32no—
119C2×C4×D5—32no—
120C2×C4×D5—32no—
121C2×C4×D5—64no—
122C2×C4×D5—64no—
123C2×C4×D5C2×A412yes—
124C2×Dic10—32no—
125C5×C4⋊C4—31no—
126C5×C4⋊C4—31no—
127C5×C22⋊C4—32no—
128C42×C5—31no—
129C42×C5—31no—
130C42×C5—31no—
131C42×C5C2×A411yescharacteristic
132#685—34no—
133#685—32no—
134#685—32no—
135#685—32no—
136#685C2×A412yes—
137C4⋊Dic5—32no—
138C4⋊Dic5—31no—
139C4⋊Dic5—32no—
140C4⋊Dic5C2×A411yescharacteristic
141C22×#41—52no—
142#550—51no—
143D4×Q8—51no—
144#548—52no—
145#547—151no—
146#546—152no—
147D42—151no—
148#532—151no—
149#525—152no—
150C4×#41C3×D511yescharacteristic, complemented
151C2×C4×D4—151no—
152C22×C3×C5—41no—
153C2×C3×D5—44no—
154C2×C3×D5—82no—
155C2×C3×D5—82no—
156C3×C4×C5—42no—
157C3×C4×C5—42no—
158C3×C4×C5—81no—
159C3×Dic5—82no—
160C2×C3×D4—201no—
161C22×C3×C4—202no—
162#41⋊C3—102no—
163#41⋊C3D2012yesdirect product factor
164C2×SL(2,𝔽3)—102no—
165C2×SL(2,𝔽3)C22×D511yescharacteristic
166C3×C4⋊C4—201no—
167C3×C22⋊C4—202no—
168C3×C42—41no—
169C23×C5—31no—
170C22×D5—32no—
171C22×D5—64no—
172C22×D5—64no—
173C22×D5—122no—
174C22×D5C22×A412yes—
175C5×Q8—31no—
176C5×Q8C2×C3×D411yescharacteristic
177C5×D4—32no—
178C5×D4—32no—
179C2×C4×C5—31no—
180C2×C4×C5—32no—
181C2×C4×C5—32no—
182C2×C4×C5—31no—
183C2×C4×C5—31no—
184C2×C4×C5—62no—
185C2×C4×C5—121no—
186C2×C4×C5C22×A411yescharacteristic
187C2×C4×C5C22×A411yescharacteristic
188C2×C4×C5C22×A411yescharacteristic
189C22⋊D5—68no—
190C2×Dic5—32no—
191C2×Dic5—64no—
192C2×Dic5C22×A412yes—
193D20—62no—
194D20—62no—
195D20—64no—
196D20—62no—
197D20—122no—
198D20#41⋊C314yesdirect product factor
199C4×D5—24no—
200C4×D5—62no—
201C4×D5—62no—
202C4×D5—62no—
203C4×D5—62no—
204C4×D5—64no—
205Dic10—62no—
206Dic10—62no—
207C2×#41—52no—
208C2×#41—104no—
209C2×#41—152no—
210C2×#41—152no—
211C2×#41—304no—
212C2×#41C2×C3×D511yescharacteristic
213C22×Q8—52no—
214C22×D4—151no—
215C22×D4—152no—
216C23×C4—152no—
217C4⋊Q8—151no—
218#127—151no—
219#124—152no—
220#123—154no—
221C22⋊Q8—152no—
222C22⋊Q8—152no—
223#121—152no—
224#121—152no—
225#121—152no—
226#121—152no—
227#120—154no—
228C4×Q8C2×C3×D511yescharacteristic
229C4×Q8C2×C3×D511yescharacteristic
230C4×D4—31no—
231C4×D4—31no—
232C4×D4—51no—
233C4×D4—152no—
234C4×D4—151no—
235C4×D4—152no—
236C4×D4—151no—
237C4×D4—152no—
238C4×D4—151no—
239#117—31no—
240C2×C4⋊C4—151no—
241C2×C22⋊C4—152no—
242C2×C42—31no—
243C2×C3×C5—41no—
244C2×C3×C5—41no—
245C2×C3×C5—41no—
246C3×D5—84no—
247C23×C3—202no—
248C3×D4—204no—
249C2×C3×C4—41no—
250C2×C3×C4—41no—
251C2×C3×C4—41no—
252C2×C3×C4—202no—
253C2×C3×C4—404no—
254SL(2,𝔽3)C2×D2011yescharacteristic, complemented
255C22×C5—32no—
256C22×C5—61no—
257C22×C5—61no—
258C22×C5C23×A411yescharacteristic
259C2×D5—22no—
260C2×D5—22no—
261C2×D5—62no—
262C2×D5—62no—
263C2×D5—62no—
264C2×D5—128no—
265C2×D5C2×#41⋊C314yescomplemented
266C4×C5—21no—
267C4×C5—31no—
268C4×C5—31no—
269C4×C5—61no—
270C4×C5—61no—
271C4×C5D4×A412yes—
272C4×C5C2×#41⋊C312yescomplemented
273Dic5—22no—
274Dic5—62no—
275C24—152no—
276#41—32no—
277#41—102no—
278#41—304no—
279#41—304no—
280#41—304no—
281#41—304no—
282#41—302no—
283#41C3×D2012yescomplemented
284C2×Q8—102no—
285C2×Q8—152no—
286C2×Q8—302no—
287C2×Q8C22×C3×D511yescharacteristic
288C2×D4—31no—
289C2×D4—51no—
290C2×D4—152no—
291C2×D4—152no—
292C2×D4—152no—
293C2×D4—154no—
294C2×D4—151no—
295C2×D4—304no—
296C2×D4—304no—
297C2×D4—304no—
298C22×C4—31no—
299C22×C4—31no—
300C22×C4—31no—
301C22×C4—52no—
302C22×C4—152no—
303C22×C4—152no—
304C22×C4—152no—
305C22×C4—152no—
306C22×C4—304no—
307C22×C4—304no—
308C4⋊C4—31no—
309C4⋊C4—31no—
310C4⋊C4—51no—
311C4⋊C4—152no—
312C4⋊C4—152no—
313C4⋊C4—151no—
314C22⋊C4—32no—
315C22⋊C4—52no—
316C22⋊C4—152no—
317C22⋊C4—152no—
318C22⋊C4—154no—
319C22⋊C4—152no—
320C42—31no—
321C42—31no—
322C42—31no—
323C42D5×A411yescharacteristic
324C3×C5—41noHall
325C22×C3—41no—
326C22×C3—204no—
327C22×C3—402no—
328C22×C3—402no—
329C3×C4—42no—
330C3×C4—42no—
331C3×C4—81no—
332C3×C4—402no—
333C2×C5—62no—
334C2×C5C2×D4×A411yescharacteristic
335C2×C5C22×#41⋊C311yescharacteristic
336C2×C5#594511yescharacteristic
337D5—24no—
338D5—122no—
339C23—31no—
340C23—52no—
341C23—152no—
342C23—304no—
343C23—304no—
344C23—602no—
345Q8—31no—
346Q8—302no—
347Q8—302no—
348Q8C2×C3×D2011yescharacteristic
349D4—32no—
350D4—32no—
351D4—54no—
352D4—302no—
353D4—302no—
354D4—304no—
355D4—308no—
356D4—302no—
357D4—602no—
358C2×C4—31no—
359C2×C4—32no—
360C2×C4—32no—
361C2×C4—31no—
362C2×C4—31no—
363C2×C4—52no—
364C2×C4—62no—
365C2×C4—104no—
366C2×C4—121no—
367C2×C4—152no—
368C2×C4—302no—
369C2×C4—302no—
370C2×C4—302no—
371C2×C4—302no—
372C2×C4—304no—
373C2×C4—304no—
374C2×C4C2×D5×A411yescharacteristic
375C2×C4C2×D5×A411yescharacteristic
376C2×C4C2×D5×A411yescharacteristic
377C2×C3—41no—
378C2×C3—41no—
379C2×C3—41no—
380C2×C3—404no—
381C5D4×#41⋊C311yescharacteristic, complemented, Sylow
382C22—32no—
383C22—54no—
384C22—61no—
385C22—61no—
386C22—102no—
387C22—102no—
388C22—302no—
389C22—302no—
390C22—302no—
391C22—608no—
392C22C22×D5×A411yescharacteristic
393C4—21no—
394C4—31no—
395C4—31no—
396C4—61no—
397C4—61no—
398C4—102no—
399C4—302no—
400C4A4×D2012yes—
401C4D5×#41⋊C312yescomplemented
402C3—41noSylow
403C2—62no—
404C2—104no—
405C2—602no—
406C2C2×A4×D2011yescharacteristic
407C2C2×D5×#41⋊C311yescharacteristic
408C2#66283⋊C311yescharacteristic
subgroupG/H
centerC2×C4C2×D5×A4
commutator, cosocleC2×C5×Q8C23×C3
FrattiniC22C22×D5×A4
FittingC4×C5×#41C2×C3
socleC22×C5C23×A4
hypercenterC42D5×A4
hypocenterC5×Q8C2×C3×D4
LCSG ▷ C2×C5×Q8 ▷ C5×Q8
UCSC1 ◁ C2×C4 ◁ C42

Complements

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

NH ≅ G/Ntype
1. C2×D5×#41⋊C3C2semidirect
2. C4×C5×#41⋊C3C2semidirect
3. #65910⋊C3C2semidirect
4. SL(2,𝔽3)×D20C2semidirect
5. C4⋊(C5⋊(#41⋊C3))C2semidirect
6. #41×D20C3semidirect
9. C2×D5×SL(2,𝔽3)C22semidirect
10. C2×C5⋊(#41⋊C3)C22semidirect
12. C4×C5×SL(2,𝔽3)C22semidirect
13. C4×C5×SL(2,𝔽3)C22semidirect
15. C2×D5×#41C2×C3semidirect
16. C4×C5×#41C2×C3semidirect
17. #65911C2×C3semidirect
18. #65910C2×C3semidirect
28. C5×#41⋊C3D4semidirect
39. C4×#41⋊C3D5semidirect
84. C5×SL(2,𝔽3)C2×D4semidirect
90. C4×SL(2,𝔽3)C2×D5semidirect
91. C4×SL(2,𝔽3)C2×D5semidirect
94. C5×#41C3×D4semidirect
150. C4×#41C3×D5semidirect
163. #41⋊C3D20direct (N × H)
198. D20#41⋊C3direct (N × H)
254. SL(2,𝔽3)C2×D20semidirect
265. C2×D5C2×#41⋊C3semidirect
272. C4×C5C2×#41⋊C3semidirect
283. #41C3×D20semidirect
381. C5D4×#41⋊C3semidirect
401. C4D5×#41⋊C3semidirect

Maximal subgroups

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

subgroupindex
C2×D5×#41⋊C32
C4×C5×#41⋊C32
#65910⋊C32
SL(2,𝔽3)×D202
C4⋊(C5⋊(#41⋊C3))2
#41×D203
C3×C4×D204
D4×#41⋊C35