Finite Group Databasebeta

← C22⋊D5×#41⋊C3 #14514217

Subgroups — C22⋊D5×#41⋊C3 #14514217

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
1C22×C5×#41⋊C3C211yesmaximal, characteristic, complemented
2C2×D5×#41⋊C3C211yesmaximal, characteristic, complemented
3#66165⋊C3C211yesmaximal, characteristic, complemented
4#66168⋊C3C211yesmaximal, characteristic, complemented
5Dic5×#41⋊C3C211yesmaximal, characteristic, complemented
6SL(2,𝔽3)×C22⋊D5C211yesmaximal, characteristic, complemented
7#66151⋊C3C211yesmaximal, characteristic, complemented
8#41×C22⋊D5C311yesmaximal, characteristic, complemented, Hall
9C2×C5×#41⋊C3—22no—
10C2×C5×#41⋊C3C2211yescharacteristic
11C2×C5×#41⋊C3C2211yescharacteristic, complemented
12C22×C5×SL(2,𝔽3)C2211yescharacteristic, complemented
13D5×#41⋊C3—22no—
14C2×D5×SL(2,𝔽3)C2211yescharacteristic, complemented
15C2×C5⋊(#41⋊C3)C2211yescharacteristic, complemented
16C3×C4×C22⋊D5—41nomaximal
17Dic5×SL(2,𝔽3)C2211yescharacteristic, complemented
18Dic5×SL(2,𝔽3)C2211yescharacteristic, complemented
19D4×#41⋊C3—51nomaximal, Hall
20C22×C5×#41C2×C311yescharacteristic, complemented
21C2×D5×#41C2×C311yescharacteristic, complemented
22#66168C2×C311yescharacteristic, complemented
23#66166—31no—
24#66165C2×C311yescharacteristic, complemented
25#66163—31no—
26#66162—31no—
27#41×Dic5C2×C311yescharacteristic, complemented
28#66158—31no—
29#66151C2×C311yescharacteristic, complemented
30Q8×C22⋊D5C2×C311yescharacteristic
31#66140—31no—
32D4×C22⋊D5—31no—
33#66125—31no—
34C2×C4×C22⋊D5—31no—
35C22×C3×C4×C5—41no—
36C2×C3×C22⋊D5—41no—
37C2×C3×C4×D5—41no—
38C5×#41⋊C3—21no—
39C5×#41⋊C3D412yescomplemented
40C2×C5×SL(2,𝔽3)—21no—
41C2×C5×SL(2,𝔽3)C2311yescharacteristic
42D5×SL(2,𝔽3)—21no—
43C5⋊(#41⋊C3)—21no—
44C3×C22⋊Dic5—41no—
45C3×#685—41no—
46C3×#683—41no—
47C3×C4×Dic5—41no—
48C22×#41⋊C3—51no—
49C22×#41⋊C3D511yescharacteristic, complemented
50C4⋊(#41⋊C3)—51no—
51D4×SL(2,𝔽3)—51no—
52#548⋊C3—51no—
53#548⋊C3—51no—
54C4×#41⋊C3—51no—
55C2×C5×#41—22no—
56C2×C5×#41—31no—
57C2×C5×#41—31no—
58C2×C5×#41—62no—
59C2×C5×#41C22×C311yescharacteristic
60C2×C5×#41C22×C311yescharacteristic
61C22×C5×Q8C22×C311yescharacteristic
62C22×C5×D4—31no—
63C23×C4×C5—31no—
64C22×C22⋊D5—31no—
65D5×#41—22no—
66D5×#41—62no—
67C2×#713C22×C311yescharacteristic
68C2×Q8×D5C22×C311yescharacteristic
69C2×#711—31no—
70C2×D4×D5—31no—
71C2×#709—31no—
72C22×C4×D5—31no—
73#4099—32no—
74C2×C22⋊Dic5—31no—
75#4093—31no—
76#4092—31no—
77#4092—31no—
78Q8×Dic5C22×C311yescharacteristic
79Q8×Dic5C22×C311yescharacteristic
80#4090—31no—
81#4086—31no—
82#4085—32no—
83#4085—32no—
84#4084—31no—
85#4084—31no—
86#4083—32no—
87#4082—31no—
88#4081—32no—
89D4×Dic5—31no—
90D4×Dic5—31no—
91#4076—31no—
92#4076—31no—
93#4075—32no—
94C4×C22⋊D5—32no—
95C4×C22⋊D5—31no—
96C4×C22⋊D5—31no—
97C4×C22⋊D5—31no—
98C4×C22⋊D5—31no—
99C4×C22⋊D5—31no—
100C4×C22⋊D5—31no—
101C4×C22⋊D5—31no—
102C4×C22⋊D5A411yescharacteristic
103C2×#685—31no—
104#4072—31no—
105#4070—31no—
106#4070—31no—
107C2×#683—31no—
108C2×C4×Dic5—31no—
109D4×#41—51noSylow
110C23×C3×C5—41no—
111C22×C3×D5—41no—
112C2×C3×C4×C5—41no—
113C2×C3×C4×C5—41no—
114C2×C3×C4×C5—82no—
115C3×C22⋊D5—44no—
116C2×C3×Dic5—41no—
117C2×C3×Dic5—41no—
118C2×C3×Dic5—41no—
119C3×C4×D5—82no—
120C5×SL(2,𝔽3)C2×D411yescharacteristic, complemented
121C2×#41⋊C3—22no—
122C2×#41⋊C3—51no—
123C2×#41⋊C3—102no—
124C2×#41⋊C3C2×D511yescharacteristic
125C2×#41⋊C3C2×D511yescharacteristic, complemented
126C22×SL(2,𝔽3)—51no—
127C22×SL(2,𝔽3)C2×D511yescharacteristic, complemented
128C3×C4×D4—201no—
129C4×SL(2,𝔽3)—51no—
130C4×SL(2,𝔽3)—51no—
131C24×C5—31no—
132C23×D5—31no—
133C5×#41—21no—
134C5×#41—32no—
135C5×#41—62no—
136C5×#41—62no—
137C5×#41—62no—
138C5×#41—62no—
139C5×#41—61no—
140C5×#41C3×D412yescomplemented
141C2×C5×Q8—21no—
142C2×C5×Q8—31no—
143C2×C5×Q8—61no—
144C2×C5×Q8C23×C311yescharacteristic
145C2×C5×D4—31no—
146C2×C5×D4—31no—
147C2×C5×D4—32no—
148C2×C5×D4—62no—
149C2×C5×D4—62no—
150C22×C4×C5—31no—
151C22×C4×C5—31no—
152C22×C4×C5—31no—
153C22×C4×C5—31no—
154C22×C4×C5—31no—
155C22×C4×C5—62no—
156C22×C4×C5—62no—
157C22×C4×C5C2×A411yescharacteristic
158C2×C22⋊D5—32no—
159C2×C22⋊D5—31no—
160C2×C22⋊D5—31no—
161C2×C22⋊D5—32no—
162C2×C22⋊D5—31no—
163C2×C22⋊D5—64no—
164C2×C22⋊D5C2×A411yescharacteristic
165C22×Dic5—31no—
166C22×Dic5—31no—
167C22×Dic5—31no—
168#713—21no—
169#713—61no—
170Q8×D5—21no—
171Q8×D5—61no—
172#711—62no—
173#711—62no—
174D4×D5—62no—
175D4×D5—62no—
176#709—62no—
177#709—62no—
178C2×D20—31no—
179C2×C4×D5—31no—
180C2×C4×D5—31no—
181C2×C4×D5—31no—
182C2×C4×D5—62no—
183C2×C4×D5—62no—
184C2×C4×D5C2×A411yescharacteristic
185C2×Dic10—31no—
186C22⋊Dic5—32no—
187C22⋊Dic5—32no—
188C22⋊Dic5—31no—
189C22⋊Dic5—31no—
190C22⋊Dic5—31no—
191C22⋊Dic5C2×A411yescharacteristic
192#685—32no—
193#685—31no—
194#685—31no—
195#685—31no—
196#685C2×A411yescharacteristic
197C4⋊Dic5—31no—
198C4⋊Dic5—31no—
199#683—32no—
200#683—31no—
201#683—31no—
202#683—31no—
203#683C2×A411yescharacteristic
204C4×Dic5—31no—
205C4×Dic5—31no—
206C4×Dic5—31no—
207C4×Dic5C2×A411yescharacteristic
208C22×#41—51no—
209C22×#41C3×D511yescharacteristic, complemented
210#550—51no—
211D4×Q8—51no—
212#548—51no—
213#548—51no—
214#547—151no—
215#546—151no—
216#546—151no—
217D42—151no—
218#532—151no—
219#525—151no—
220#525—151no—
221C4×#41—51no—
222C2×C4×D4—151no—
223C22×C3×C5—42no—
224C22×C3×C5—41no—
225C22×C3×C5—81no—
226C22×C3×C5—81no—
227C2×C3×D5—42no—
228C2×C3×D5—81no—
229C2×C3×D5—81no—
230C3×C4×C5—42no—
231C3×C4×C5—81no—
232C3×Dic5—42no—
233C3×Dic5—81no—
234C3×Dic5—81no—
235C2×C3×D4—201no—
236C22×C3×C4—41no—
237C22×C3×C4—201no—
238#41⋊C3—21no—
239#41⋊C3—101no—
240#41⋊C3C22⋊D512yesdirect product factor
241C2×SL(2,𝔽3)—21no—
242C2×SL(2,𝔽3)—101no—
243C2×SL(2,𝔽3)C22×D511yescharacteristic
244C3×C4⋊C4—201no—
245C3×C22⋊C4—201no—
246C3×C22⋊C4—201no—
247C3×C42—201no—
248C23×C5—31no—
249C23×C5—31no—
250C23×C5—62no—
251C23×C5—62no—
252C23×C5—121no—
253C23×C5C22×A411yescharacteristic
254C22×D5—31no—
255C22×D5—62no—
256C22×D5—62no—
257C22×D5—121no—
258C22×D5C22×A411yescharacteristic
259C5×Q8—31no—
260C5×Q8—61no—
261C5×Q8—61no—
262C5×Q8C2×C3×D411yescharacteristic
263C5×D4—32no—
264C5×D4—32no—
265C5×D4—61no—
266C5×D4—61no—
267C5×D4—64no—
268C2×C4×C5—22no—
269C2×C4×C5—31no—
270C2×C4×C5—32no—
271C2×C4×C5—32no—
272C2×C4×C5—31no—
273C2×C4×C5—61no—
274C2×C4×C5—61no—
275C2×C4×C5—62no—
276C2×C4×C5—61no—
277C2×C4×C5—61no—
278C2×C4×C5—62no—
279C2×C4×C5C22×A411yescharacteristic
280C2×C4×C5C22×A411yescharacteristic
281C22⋊D5—64no—
282C22⋊D5—62no—
283C22⋊D5—62no—
284C22⋊D5—62no—
285C22⋊D5—122no—
286C22⋊D5#41⋊C314yesdirect product factor
287C2×Dic5—31no—
288C2×Dic5—31no—
289C2×Dic5—31no—
290C2×Dic5—62no—
291C2×Dic5—62no—
292C2×Dic5—121no—
293C2×Dic5C22×A411yescharacteristic
294C2×Dic5C22×A411yescharacteristic
295C2×Dic5C22×A411yescharacteristic
296D20—61no—
297D20—61no—
298C4×D5—22no—
299C4×D5—61no—
300C4×D5—61no—
301C4×D5—61no—
302C4×D5—61no—
303C4×D5—62no—
304Dic10—61no—
305Dic10—61no—
306C2×#41—22no—
307C2×#41—31no—
308C2×#41—31no—
309C2×#41—51no—
310C2×#41—62no—
311C2×#41—102no—
312C2×#41—151no—
313C2×#41—151no—
314C2×#41—302no—
315C2×#41C2×C3×D511yescharacteristic
316C2×#41C2×C3×D511yescharacteristic
317C22×Q8—51no—
318C22×Q8C2×C3×D511yescharacteristic
319C22×D4—31no—
320C22×D4—151no—
321C22×D4—151no—
322C23×C4—31no—
323C23×C4—151no—
324C4⋊Q8—151no—
325#127—151no—
326#124—151no—
327#124—151no—
328#123—152no—
329#123—152no—
330C22⋊Q8—151no—
331C22⋊Q8—151no—
332C22⋊Q8—151no—
333C22⋊Q8—151no—
334#121—151no—
335#121—151no—
336#121—152no—
337#121—152no—
338#121—151no—
339#121—151no—
340#120—152no—
341#120—152no—
342C4×Q8—51no—
343C4×Q8—51no—
344C4×D4—51no—
345C4×D4—151no—
346C4×D4—151no—
347C4×D4—151no—
348C4×D4—151no—
349C4×D4—151no—
350C4×D4—151no—
351C4×D4—152no—
352C4×D4—151no—
353C4×D4—151no—
354C4×D4—151no—
355#117—151no—
356C2×C4⋊C4—151no—
357C2×C22⋊C4—151no—
358C2×C22⋊C4—151no—
359C2×C42—151no—
360C2×C3×C5—41no—
361C2×C3×C5—41no—
362C2×C3×C5—41no—
363C2×C3×C5—82no—
364C3×D5—82no—
365C23×C3—41no—
366C23×C3—201no—
367C3×D4—204no—
368C2×C3×C4—41no—
369C2×C3×C4—41no—
370C2×C3×C4—82no—
371C2×C3×C4—201no—
372C2×C3×C4—201no—
373C2×C3×C4—201no—
374C2×C3×C4—402no—
375SL(2,𝔽3)C2×C22⋊D511yescharacteristic, complemented
376C22×C5—21no—
377C22×C5—21no—
378C22×C5—32no—
379C22×C5—61no—
380C22×C5—61no—
381C22×C5—61no—
382C22×C5—61no—
383C22×C5—61no—
384C22×C5—124no—
385C22×C5C2×#41⋊C312yescomplemented
386C22×C5C23×A411yescharacteristic
387C2×D5—21no—
388C2×D5—21no—
389C2×D5—61no—
390C2×D5—61no—
391C2×D5—61no—
392C2×D5—124no—
393C2×D5C2×#41⋊C312yescomplemented
394C4×C5—21no—
395C4×C5—31no—
396C4×C5—31no—
397C4×C5—61no—
398C4×C5D4×A412yes—
399Dic5—21no—
400Dic5—21no—
401Dic5—61no—
402Dic5—61no—
403Dic5—61no—
404Dic5C2×#41⋊C312yescomplemented
405C24—31no—
406C24—151no—
407#41—21no—
408#41—32no—
409#41—62no—
410#41—62no—
411#41—62no—
412#41—62no—
413#41—61no—
414#41—101no—
415#41—302no—
416#41—302no—
417#41—302no—
418#41—302no—
419#41—301no—
420#41C3×C22⋊D512yescomplemented
421C2×Q8—21no—
422C2×Q8—31no—
423C2×Q8—61no—
424C2×Q8—101no—
425C2×Q8—151no—
426C2×Q8—301no—
427C2×Q8C22×C3×D511yescharacteristic
428C2×D4—31no—
429C2×D4—31no—
430C2×D4—32no—
431C2×D4—51no—
432C2×D4—62no—
433C2×D4—62no—
434C2×D4—151no—
435C2×D4—151no—
436C2×D4—151no—
437C2×D4—152no—
438C2×D4—151no—
439C2×D4—152no—
440C2×D4—302no—
441C2×D4—302no—
442C2×D4—304no—
443C22×C4—31no—
444C22×C4—31no—
445C22×C4—31no—
446C22×C4—31no—
447C22×C4—31no—
448C22×C4—51no—
449C22×C4—62no—
450C22×C4—62no—
451C22×C4—151no—
452C22×C4—151no—
453C22×C4—151no—
454C22×C4—151no—
455C22×C4—151no—
456C22×C4—151no—
457C22×C4—302no—
458C22×C4—302no—
459C22×C4D5×A411yescharacteristic
460C4⋊C4—51no—
461C4⋊C4—151no—
462C4⋊C4—151no—
463C4⋊C4—151no—
464C4⋊C4—151no—
465C4⋊C4—152no—
466C4⋊C4—151no—
467C22⋊C4—51no—
468C22⋊C4—51no—
469C22⋊C4—151no—
470C22⋊C4—151no—
471C22⋊C4—152no—
472C22⋊C4—151no—
473C22⋊C4—151no—
474C22⋊C4—152no—
475C22⋊C4—152no—
476C22⋊C4—151no—
477C22⋊C4—151no—
478C42—51no—
479C42—151no—
480C42—151no—
481C42—151no—
482C3×C5—41noHall
483C22×C3—42no—
484C22×C3—41no—
485C22×C3—81no—
486C22×C3—81no—
487C22×C3—202no—
488C22×C3—401no—
489C22×C3—401no—
490C3×C4—42no—
491C3×C4—81no—
492C3×C4—202no—
493C3×C4—401no—
494C3×C4—401no—
495C2×C5—22no—
496C2×C5—62no—
497C2×C5—121no—
498C2×C5C2×D4×A411yescharacteristic
499C2×C5C22×#41⋊C311yescharacteristic
500C2×C5#594511yescharacteristic
501D5—22no—
502D5—121no—
503C23—31no—
504C23—31no—
505C23—51no—
506C23—62no—
507C23—62no—
508C23—121no—
509C23—151no—
510C23—302no—
511C23—302no—
512C23—601no—
513C23C2×D5×A411yescharacteristic
514Q8—31no—
515Q8—61no—
516Q8—61no—
517Q8—301no—
518Q8—301no—
519Q8C2×C3×C22⋊D511yescharacteristic
520D4—32no—
521D4—32no—
522D4—54no—
523D4—61no—
524D4—61no—
525D4—64no—
526D4—301no—
527D4—301no—
528D4—302no—
529D4—304no—
530D4—302no—
531D4—302no—
532D4—602no—
533C2×C4—22no—
534C2×C4—31no—
535C2×C4—32no—
536C2×C4—32no—
537C2×C4—31no—
538C2×C4—51no—
539C2×C4—51no—
540C2×C4—51no—
541C2×C4—61no—
542C2×C4—61no—
543C2×C4—62no—
544C2×C4—61no—
545C2×C4—61no—
546C2×C4—62no—
547C2×C4—102no—
548C2×C4—151no—
549C2×C4—151no—
550C2×C4—151no—
551C2×C4—301no—
552C2×C4—301no—
553C2×C4—301no—
554C2×C4—301no—
555C2×C4—302no—
556C2×C4—302no—
557C2×C4—302no—
558C2×C4—601no—
559C2×C4C2×D5×A411yescharacteristic
560C2×C4C2×D5×A411yescharacteristic
561C2×C3—41no—
562C2×C3—41no—
563C2×C3—41no—
564C2×C3—82no—
565C2×C3—402no—
566C5D4×#41⋊C311yescharacteristic, complemented, Sylow
567C22—21no—
568C22—21no—
569C22—32no—
570C22—52no—
571C22—61no—
572C22—61no—
573C22—61no—
574C22—61no—
575C22—61no—
576C22—101no—
577C22—101no—
578C22—124no—
579C22—301no—
580C22—301no—
581C22—301no—
582C22—604no—
583C22D5×#41⋊C312yescomplemented
584C22C22×D5×A411yescharacteristic
585C4—21no—
586C4—31no—
587C4—31no—
588C4—52no—
589C4—61no—
590C4—101no—
591C4—101no—
592C4—301no—
593C4—301no—
594C4—301no—
595C4A4×C22⋊D512yes—
596C3—41noSylow
597C2—22no—
598C2—62no—
599C2—102no—
600C2—121no—
601C2—601no—
602C2C2×D5×#41⋊C311yescharacteristic
603C2#66283⋊C311yescharacteristic
604C2C2×A4×C22⋊D511yescharacteristic
subgroupG/H
centerC2×C4C2×D5×A4
commutator, cosocleC2×C5×Q8C23×C3
FrattiniC22C22×D5×A4
FittingC22×C5×#41C2×C3
socleC22×C5C23×A4
hypercenterC22×C4D5×A4
hypocenterC5×Q8C2×C3×D4
LCSG ▷ C2×C5×Q8 ▷ C5×Q8
UCSC1 ◁ C2×C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. C22×C5×#41⋊C3C2semidirect
2. C2×D5×#41⋊C3C2semidirect
3. #66165⋊C3C2semidirect
4. #66168⋊C3C2semidirect
5. Dic5×#41⋊C3C2semidirect
6. SL(2,𝔽3)×C22⋊D5C2semidirect
7. #66151⋊C3C2semidirect
8. #41×C22⋊D5C3semidirect
11. C2×C5×#41⋊C3C22semidirect
12. C22×C5×SL(2,𝔽3)C22semidirect
14. C2×D5×SL(2,𝔽3)C22semidirect
15. C2×C5⋊(#41⋊C3)C22semidirect
17. Dic5×SL(2,𝔽3)C22semidirect
18. Dic5×SL(2,𝔽3)C22semidirect
20. C22×C5×#41C2×C3semidirect
21. C2×D5×#41C2×C3semidirect
22. #66168C2×C3semidirect
24. #66165C2×C3semidirect
27. #41×Dic5C2×C3semidirect
29. #66151C2×C3semidirect
39. C5×#41⋊C3D4semidirect
49. C22×#41⋊C3D5semidirect
120. C5×SL(2,𝔽3)C2×D4semidirect
125. C2×#41⋊C3C2×D5semidirect
127. C22×SL(2,𝔽3)C2×D5semidirect
140. C5×#41C3×D4semidirect
209. C22×#41C3×D5semidirect
240. #41⋊C3C22⋊D5direct (N × H)
286. C22⋊D5#41⋊C3direct (N × H)
375. SL(2,𝔽3)C2×C22⋊D5semidirect
385. C22×C5C2×#41⋊C3semidirect
393. C2×D5C2×#41⋊C3semidirect
404. Dic5C2×#41⋊C3semidirect
420. #41C3×C22⋊D5semidirect
566. C5D4×#41⋊C3semidirect
583. C22D5×#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
C2×D5×#41⋊C32
#66165⋊C32
#66168⋊C32
Dic5×#41⋊C32
SL(2,𝔽3)×C22⋊D52
#66151⋊C32
#41×C22⋊D53
C3×C4×C22⋊D54
D4×#41⋊C35