Finite Group Databasebeta

← C5×D4×#41⋊C3 #14511335

Subgroups — C5×D4×#41⋊C3 #14511335

Order 1920.

796 conjugacy classes of subgroups; only the 140 normal subgroups are shown.

normal subgroups only

This group has 796 conjugacy classes of subgroups — too many to draw. Only its 140 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
1C22×C5×#41⋊C3C212yesmaximal, complemented
2C5×C4⋊(#41⋊C3)C211yesmaximal, characteristic, complemented
3C5×D4×SL(2,𝔽3)C211yesmaximal, characteristic, complemented
4C5×#548⋊C3C212yesmaximal, complemented
5C4×C5×#41⋊C3C211yesmaximal, characteristic, complemented
6C5×D4×#41C311yesmaximal, characteristic, complemented, Hall
7C2×C5×#41⋊C3—24no—
8C2×C5×#41⋊C3C2211yescharacteristic
9C2×C5×#41⋊C3C2212yescomplemented
10C22×C5×SL(2,𝔽3)C2212yescomplemented
11C3×C4×C5×D4—41nomaximal
12C4×C5×SL(2,𝔽3)C2211yescharacteristic, complemented
13C4×C5×SL(2,𝔽3)C2211yescharacteristic, complemented
14D4×#41⋊C3C511yesmaximal, characteristic, direct product factor, Hall
15C22×C5×#41C2×C312yescomplemented
16C5×#550C2×C311yescharacteristic, complemented
17C5×D4×Q8C2×C311yescharacteristic
18C5×#548C2×C312yescomplemented
19C5×#547—31no—
20C5×#546—32no—
21C5×D42—31no—
22C5×#532—31no—
23C5×#525—32no—
24C4×C5×#41C2×C311yescharacteristic, complemented
25C2×C4×C5×D4—31no—
26C2×C3×C5×D4—41no—
27C22×C3×C4×C5—42no—
28C5×#41⋊C3—22no—
29C5×#41⋊C3D412yesdirect product factor
30C2×C5×SL(2,𝔽3)—22no—
31C2×C5×SL(2,𝔽3)C2311yescharacteristic
32C3×C5×C4⋊C4—41no—
33C3×C5×C22⋊C4—42no—
34C3×C42×C5—41no—
35C22×#41⋊C3C2×C512yescomplemented
36C4⋊(#41⋊C3)C2×C511yescharacteristic, complemented
37D4×SL(2,𝔽3)C2×C511yescharacteristic, complemented
38#548⋊C3C2×C512yescomplemented
39C4×#41⋊C3C2×C511yescharacteristic, complemented
40C2×C5×#41—24no—
41C2×C5×#41—32no—
42C2×C5×#41—32no—
43C2×C5×#41—64no—
44C2×C5×#41C22×C312yes—
45C2×C5×#41C22×C311yescharacteristic
46C22×C5×Q8C22×C312yes—
47C22×C5×D4—32no—
48C22×C5×D4—31no—
49C23×C4×C5—32no—
50C5×C4⋊Q8—31no—
51C5×#127—31no—
52C5×#124—32no—
53C5×#123—34no—
54C5×C22⋊Q8—32no—
55C5×C22⋊Q8—32no—
56C5×#121—32no—
57C5×#121—32no—
58C5×#121—32no—
59C5×#121—32no—
60C5×#120—34no—
61C4×C5×Q8C22×C311yescharacteristic
62C4×C5×Q8C22×C311yescharacteristic
63C4×C5×D4—32no—
64C4×C5×D4—31no—
65C4×C5×D4—32no—
66C4×C5×D4—31no—
67C4×C5×D4—31no—
68C4×C5×D4—31no—
69C4×C5×D4—32no—
70C4×C5×D4—31no—
71C4×C5×D4A411yescharacteristic
72C5×#117—31no—
73C2×C5×C4⋊C4—31no—
74C2×C5×C22⋊C4—32no—
75C2×C42×C5—31no—
76D4×#41C3×C511yescharacteristic, complemented, Sylow
77C23×C3×C5—42no—
78C3×C5×D4—44no—
79C2×C3×C4×C5—41no—
80C2×C3×C4×C5—41no—
81C2×C3×C4×C5—41no—
82C2×C3×C4×C5—42no—
83C2×C3×C4×C5—84no—
84C5×SL(2,𝔽3)C2×D411yescharacteristic, complemented
85C2×#41⋊C3—24no—
86C2×#41⋊C3C22×C511yescharacteristic
87C2×#41⋊C3C22×C512yescomplemented
88C22×SL(2,𝔽3)C22×C512yescomplemented
89C3×C4×D4—41no—
90C4×SL(2,𝔽3)C22×C511yescharacteristic, complemented
91C4×SL(2,𝔽3)C22×C511yescharacteristic, complemented
92C24×C5—32no—
93C5×#41—22no—
94C5×#41—32no—
95C5×#41—64no—
96C5×#41—64no—
97C5×#41—64no—
98C5×#41—64no—
99C5×#41—62no—
100C5×#41C3×D412yescomplemented
101C2×C5×Q8—22no—
102C2×C5×Q8—32no—
103C2×C5×Q8—62no—
104C2×C5×Q8C23×C311yescharacteristic
105C2×C5×D4—31no—
106C2×C5×D4—32no—
107C2×C5×D4—34no—
108C2×C5×D4—32no—
109C2×C5×D4—32no—
110C2×C5×D4—31no—
111C2×C5×D4—64no—
112C2×C5×D4—64no—
113C2×C5×D4—64no—
114C2×C5×D4C2×A411yescharacteristic
115C22×C4×C5—31no—
116C22×C4×C5—32no—
117C22×C4×C5—31no—
118C22×C4×C5—32no—
119C22×C4×C5—32no—
120C22×C4×C5—32no—
121C22×C4×C5—31no—
122C22×C4×C5—64no—
123C22×C4×C5—64no—
124C22×C4×C5C2×A412yes—
125C5×C4⋊C4—31no—
126C5×C4⋊C4—31no—
127C5×C4⋊C4—32no—
128C5×C4⋊C4—31no—
129C5×C4⋊C4—32no—
130C5×C4⋊C4C2×A411yescharacteristic
131C5×C22⋊C4—32no—
132C5×C22⋊C4—34no—
133C5×C22⋊C4—32no—
134C5×C22⋊C4—32no—
135C5×C22⋊C4—32no—
136C5×C22⋊C4C2×A412yes—
137C42×C5—31no—
138C42×C5—31no—
139C42×C5—31no—
140C42×C5C2×A411yescharacteristic
141C22×#41C2×C3×C512yescomplemented
142#550C2×C3×C511yescharacteristic, complemented
143D4×Q8C2×C3×C511yescharacteristic
144#548C2×C3×C512yescomplemented
145#547—31no—
146#546—32no—
147D42—31no—
148#532—31no—
149#525—32no—
150C4×#41C2×C3×C511yescharacteristic, complemented
151C2×C4×D4—31no—
152C22×C3×C5—44no—
153C22×C3×C5—41no—
154C22×C3×C5—82no—
155C22×C3×C5—82no—
156C3×C4×C5—42no—
157C3×C4×C5—42no—
158C3×C4×C5—82no—
159C3×C4×C5—81no—
160C2×C3×D4—41no—
161C22×C3×C4—42no—
162#41⋊C3—22no—
163#41⋊C3C5×D412yesdirect product factor
164C2×SL(2,𝔽3)—22no—
165C2×SL(2,𝔽3)C23×C511yescharacteristic
166C3×C4⋊C4—41no—
167C3×C22⋊C4—42no—
168C3×C42—41no—
169C23×C5—31no—
170C23×C5—32no—
171C23×C5—64no—
172C23×C5—64no—
173C23×C5—122no—
174C23×C5C22×A412yes—
175C5×Q8—31no—
176C5×Q8—62no—
177C5×Q8—62no—
178C5×Q8C2×C3×D411yescharacteristic
179C5×D4—32no—
180C5×D4—32no—
181C5×D4—62no—
182C5×D4—62no—
183C5×D4—68no—
184C5×D4—64no—
185C5×D4—62no—
186C5×D4—122no—
187C5×D4#41⋊C314yesdirect product factor
188C2×C4×C5—24no—
189C2×C4×C5—31no—
190C2×C4×C5—32no—
191C2×C4×C5—32no—
192C2×C4×C5—31no—
193C2×C4×C5—31no—
194C2×C4×C5—32no—
195C2×C4×C5—62no—
196C2×C4×C5—62no—
197C2×C4×C5—64no—
198C2×C4×C5—62no—
199C2×C4×C5—62no—
200C2×C4×C5—64no—
201C2×C4×C5—62no—
202C2×C4×C5—121no—
203C2×C4×C5C22×A411yescharacteristic
204C2×C4×C5C22×A412yes—
205C2×C4×C5C22×A411yescharacteristic
206C2×C4×C5C22×A411yescharacteristic
207C2×#41—24no—
208C2×#41—32no—
209C2×#41—32no—
210C2×#41—64no—
211C2×#41C22×C3×C512yes—
212C2×#41C22×C3×C511yescharacteristic
213C22×Q8C22×C3×C512yes—
214C22×D4—32no—
215C22×D4—31no—
216C23×C4—32no—
217C4⋊Q8—31no—
218#127—31no—
219#124—32no—
220#123—34no—
221C22⋊Q8—32no—
222C22⋊Q8—32no—
223#121—32no—
224#121—32no—
225#121—32no—
226#121—32no—
227#120—34no—
228C4×Q8C22×C3×C511yescharacteristic
229C4×Q8C22×C3×C511yescharacteristic
230C4×D4—32no—
231C4×D4—31no—
232C4×D4—32no—
233C4×D4—31no—
234C4×D4—31no—
235C4×D4—31no—
236C4×D4—32no—
237C4×D4—31no—
238C4×D4C5×A411yescharacteristic
239#117—31no—
240C2×C4⋊C4—31no—
241C2×C22⋊C4—32no—
242C2×C42—31no—
243C2×C3×C5—41no—
244C2×C3×C5—41no—
245C2×C3×C5—41no—
246C2×C3×C5—84no—
247C23×C3—42no—
248C3×D4—44no—
249C2×C3×C4—41no—
250C2×C3×C4—41no—
251C2×C3×C4—41no—
252C2×C3×C4—42no—
253C2×C3×C4—84no—
254SL(2,𝔽3)C2×C5×D411yescharacteristic, complemented
255C22×C5—22no—
256C22×C5—22no—
257C22×C5—32no—
258C22×C5—61no—
259C22×C5—61no—
260C22×C5—62no—
261C22×C5—62no—
262C22×C5—62no—
263C22×C5—128no—
264C22×C5C2×#41⋊C314yescomplemented
265C22×C5C23×A411yescharacteristic
266C4×C5—22no—
267C4×C5—21no—
268C4×C5—31no—
269C4×C5—31no—
270C4×C5—62no—
271C4×C5—61no—
272C4×C5—61no—
273C4×C5D4×A412yes—
274C4×C5C2×#41⋊C312yescomplemented
275C24—32no—
276#41—22no—
277#41—32no—
278#41—64no—
279#41—64no—
280#41—64no—
281#41—64no—
282#41—62no—
283#41C3×C5×D412yescomplemented
284C2×Q8—22no—
285C2×Q8—32no—
286C2×Q8—62no—
287C2×Q8C23×C3×C511yescharacteristic
288C2×D4—31no—
289C2×D4—32no—
290C2×D4—34no—
291C2×D4—32no—
292C2×D4—32no—
293C2×D4—31no—
294C2×D4—64no—
295C2×D4—64no—
296C2×D4—64no—
297C2×D4C2×C5×A411yescharacteristic
298C22×C4—31no—
299C22×C4—32no—
300C22×C4—31no—
301C22×C4—32no—
302C22×C4—32no—
303C22×C4—32no—
304C22×C4—31no—
305C22×C4—64no—
306C22×C4—64no—
307C22×C4C2×C5×A412yes—
308C4⋊C4—31no—
309C4⋊C4—31no—
310C4⋊C4—32no—
311C4⋊C4—31no—
312C4⋊C4—32no—
313C4⋊C4C2×C5×A411yescharacteristic
314C22⋊C4—32no—
315C22⋊C4—34no—
316C22⋊C4—32no—
317C22⋊C4—32no—
318C22⋊C4—32no—
319C22⋊C4C2×C5×A412yes—
320C42—31no—
321C42—31no—
322C42—31no—
323C42C2×C5×A411yescharacteristic
324C3×C5—41noHall
325C22×C3—44no—
326C22×C3—41no—
327C22×C3—82no—
328C22×C3—82no—
329C3×C4—42no—
330C3×C4—42no—
331C3×C4—81no—
332C3×C4—82no—
333C2×C5—24no—
334C2×C5—62no—
335C2×C5—122no—
336C2×C5C2×D4×A411yescharacteristic
337C2×C5C22×#41⋊C311yescharacteristic
338C2×C5#594511yescharacteristic
339C23—31no—
340C23—32no—
341C23—64no—
342C23—64no—
343C23—122no—
344C23C22×C5×A412yes—
345Q8—31no—
346Q8—62no—
347Q8—62no—
348Q8C2×C3×C5×D411yescharacteristic
349D4—32no—
350D4—32no—
351D4—62no—
352D4—62no—
353D4—68no—
354D4—64no—
355D4—62no—
356D4—122no—
357D4C5×#41⋊C314yesdirect product factor
358C2×C4—24no—
359C2×C4—31no—
360C2×C4—32no—
361C2×C4—32no—
362C2×C4—31no—
363C2×C4—31no—
364C2×C4—32no—
365C2×C4—62no—
366C2×C4—62no—
367C2×C4—64no—
368C2×C4—62no—
369C2×C4—62no—
370C2×C4—64no—
371C2×C4—62no—
372C2×C4—121no—
373C2×C4C22×C5×A411yescharacteristic
374C2×C4C22×C5×A412yes—
375C2×C4C22×C5×A411yescharacteristic
376C2×C4C22×C5×A411yescharacteristic
377C2×C3—41no—
378C2×C3—41no—
379C2×C3—41no—
380C2×C3—84no—
381C5D4×#41⋊C311yescharacteristic, direct product factor, Sylow
382C22—22no—
383C22—22no—
384C22—32no—
385C22—61no—
386C22—61no—
387C22—62no—
388C22—62no—
389C22—62no—
390C22—128no—
391C22C2×C5×#41⋊C314yescomplemented
392C22C23×C5×A411yescharacteristic
393C4—22no—
394C4—21no—
395C4—31no—
396C4—31no—
397C4—62no—
398C4—61no—
399C4—61no—
400C4C5×D4×A412yes—
401C4C2×C5×#41⋊C312yescomplemented
402C3—41noSylow
403C2—24no—
404C2—62no—
405C2—122no—
406C2C2×C5×D4×A411yescharacteristic
407C2C22×C5×#41⋊C311yescharacteristic
408C2C5×#594511yescharacteristic
subgroupG/H
centerC2×C4×C5C22×A4
commutator, cosocleC2×Q8C23×C3×C5
FrattiniC22C23×C5×A4
FittingC5×D4×#41C3
socleC22×C5C23×A4
hypercenterC4×C5×D4A4
hypocenterQ8C2×C3×C5×D4
LCSG ▷ C2×Q8 ▷ Q8
UCSC1 ◁ C2×C4×C5 ◁ C4×C5×D4

Complements

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

NH ≅ G/Ntype
1. C22×C5×#41⋊C3C2semidirect
2. C5×C4⋊(#41⋊C3)C2semidirect
3. C5×D4×SL(2,𝔽3)C2semidirect
4. C5×#548⋊C3C2semidirect
5. C4×C5×#41⋊C3C2semidirect
6. C5×D4×#41C3semidirect
9. C2×C5×#41⋊C3C22semidirect
10. C22×C5×SL(2,𝔽3)C22semidirect
12. C4×C5×SL(2,𝔽3)C22semidirect
13. C4×C5×SL(2,𝔽3)C22semidirect
14. D4×#41⋊C3C5direct (N × H)
15. C22×C5×#41C2×C3semidirect
16. C5×#550C2×C3semidirect
18. C5×#548C2×C3semidirect
24. C4×C5×#41C2×C3semidirect
29. C5×#41⋊C3D4direct (N × H)
35. C22×#41⋊C3C2×C5semidirect
36. C4⋊(#41⋊C3)C2×C5semidirect
37. D4×SL(2,𝔽3)C2×C5semidirect
38. #548⋊C3C2×C5semidirect
39. C4×#41⋊C3C2×C5semidirect
76. D4×#41C3×C5semidirect
84. C5×SL(2,𝔽3)C2×D4semidirect
87. C2×#41⋊C3C22×C5semidirect
88. C22×SL(2,𝔽3)C22×C5semidirect
90. C4×SL(2,𝔽3)C22×C5semidirect
91. C4×SL(2,𝔽3)C22×C5semidirect
100. C5×#41C3×D4semidirect
141. C22×#41C2×C3×C5semidirect
142. #550C2×C3×C5semidirect
144. #548C2×C3×C5semidirect
150. C4×#41C2×C3×C5semidirect
163. #41⋊C3C5×D4direct (N × H)
187. C5×D4#41⋊C3direct (N × H)
254. SL(2,𝔽3)C2×C5×D4semidirect
264. C22×C5C2×#41⋊C3semidirect
274. C4×C5C2×#41⋊C3semidirect
283. #41C3×C5×D4semidirect
357. D4C5×#41⋊C3direct (N × H)
381. C5D4×#41⋊C3direct (N × H)
391. C22C2×C5×#41⋊C3semidirect
401. C4C2×C5×#41⋊C3semidirect

Maximal subgroups

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

subgroupindex
C22×C5×#41⋊C32
C5×C4⋊(#41⋊C3)2
C5×D4×SL(2,𝔽3)2
C5×#548⋊C32
C4×C5×#41⋊C32
C5×D4×#413
C3×C4×C5×D44
D4×#41⋊C35