Finite Group Databasebeta

← #41×D60 #14483059

Subgroups — #41×D60 #14483059

Order 1920.

3296 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#41×D15C212yesmaximal, complemented
2C3×C4×C5×#41C211yesmaximal, characteristic, complemented
3#11756336C211yesmaximal, characteristic, complemented
4#11756335C212yesmaximal, complemented
5Q8×D60C211yesmaximal, characteristic, complemented
6#11756314C213yesmaximal, complemented
7#11756313C216yesmaximal, complemented
8D4×D60C213yesmaximal, complemented
9#11756283C216yesmaximal, complemented
10#11756236C213yesmaximal, complemented
11C2×C4×D60C213yesmaximal, complemented
12#41×D20—31nomaximal, Hall
13C2×C3×C5×#41C2211yescharacteristic
14#41×D15—216no—
15C2×#6821C2212yescomplemented
16C2×Q8×D15C2212yescomplemented
17C2×#6819C2216yescomplemented
18C2×D4×D15C2216yescomplemented
19C2×#6817C2216yescomplemented
20C22×D60C2213yes—
21C22×C4×D15C2216yescomplemented
22C3×C4×C5×Q8C2211yescharacteristic, complemented
23C3×C4×C5×Q8C2211yescharacteristic, complemented
24C3×C4×C5×D4C2213yescomplemented
25C3×C4×C5×D4C2213yescomplemented
26C3×C5×#117C2213yescomplemented
27C2×C3×C42×C5C2213yescomplemented
28#91819C2216yescomplemented
29#91819C2216yescomplemented
30C2×#6714C2216yescomplemented
31C2×C4⋊Dic15C2213yescomplemented
32#91786C2216yescomplemented
33#91786C2216yescomplemented
34#91784C2216yescomplemented
35#91784C2216yescomplemented
36#91775C22112yescomplemented
37#91771C22112yescomplemented
38#91764C2216yescomplemented
39#91763C2213yescomplemented
40C4×D60C2213yes—
41C4×D60C2211yescharacteristic
42C4×D60C2216yescomplemented
43C4×D60C2213yescomplemented
44C4×D60C2213yescomplemented
45C4×D60C2216yescomplemented
46C4×D60C2216yescomplemented
47#91758C2213yescomplemented
48#41×D12—51nomaximal, Hall
49C2×D5×#41—32no—
50C4×C5×#41D311yescharacteristic, complemented
51#65911—31no—
52#65910—32no—
53Q8×D20—31no—
54#65889—33no—
55#65888—36no—
56D4×D20—33no—
57#65858—36no—
58#65811—33no—
59C2×C4×D20—33no—
60C23×D15C2316yes—
61C3×C5×#41D418yescomplemented
62C2×C3×C5×Q8C2311yescharacteristic
63C2×C3×C5×D4C2313yes—
64C22×C3×C4×C5C2313yes—
65C22×C3×C4×C5C2313yes—
66C22×C3×C4×C5C2313yes—
67C2×#1220C23112yes—
68C22×Dic15C2316yes—
69#6821—28no—
70Q8×D15—28no—
71#6819—224no—
72D4×D15—224no—
73#6817—224no—
74C2×D60—212no—
75C2×D60C2313yes—
76C2×D60C2316yes—
77C2×D60C2316yes—
78C2×D60C2316yes—
79C2×D60C2311yescharacteristic
80C2×C4×D15—224no—
81C2×C4×D15C2312yes—
82C2×C4×D15C2316yes—
83C2×C4×D15C2316yes—
84C2×C4×D15C2316yes—
85C2×Dic30C2316yes—
86C3×C5×C4⋊C4C2313yes—
87C3×C5×C4⋊C4C2313yes—
88C3×C5×C22⋊C4C2316yes—
89C3×C42×C5C2313yes—
90C3×C42×C5C2311yescharacteristic
91C3×C42×C5C2313yes—
92C3×C42×C5C2313yes—
93#6714C2312yes—
94#6714C2316yes—
95#6714C2316yes—
96#6714C2316yes—
97#6714C23112yes—
98C4⋊Dic15C2313yes—
99C4⋊Dic15C2316yes—
100C4⋊Dic15C2311yescharacteristic
101C4⋊Dic15C2316yes—
102C2×D3×#41—52no—
103C3×C4×#41D511yescharacteristic, complemented
104#5577—51no—
105#5576—52no—
106Q8×D12—51no—
107#5555—53no—
108#5554—56no—
109D4×D12—53no—
110#5524—56no—
111#5477—53no—
112C2×C4×D12—53no—
113C2×C5×#41C2×D311yescharacteristic
114D5×#41—616no—
115C2×#713—32no—
116C2×Q8×D5—32no—
117C2×#711—36no—
118C2×D4×D5—36no—
119C2×#709—36no—
120C22×D20—33no—
121C22×C4×D5—36no—
122C4×C5×Q8C2×D311yescharacteristic, complemented
123C4×C5×Q8C2×D311yescharacteristic, complemented
124C4×C5×D4C2×D313yescomplemented
125C4×C5×D4C2×D313yescomplemented
126C5×#117C2×D313yescomplemented
127C2×C42×C5C2×D313yescomplemented
128#4076—36no—
129#4076—36no—
130C2×#685—36no—
131C2×C4⋊Dic5—33no—
132#4043—36no—
133#4043—36no—
134#4041—36no—
135#4041—36no—
136#4032—312no—
137#4028—312no—
138#4021—36no—
139#4020—33no—
140C4×D20—31no—
141C4×D20—33no—
142C4×D20—36no—
143C4×D20—33no—
144C4×D20—36no—
145C4×D20—33no—
146C4×D20—36no—
147#4015—33no—
148D4×#41—151noSylow
149C23×C3×C5C2413yes—
150C22×D15—212no—
151C22×D15—212no—
152C22×D15—46no—
153C22×D15C2416yes—
154C22×D15C2412yes—
155C3×C5×Q8C2×D414yescomplemented
156C3×C5×D4C2×D4112yescomplemented
157C2×C3×C4×C5—26no—
158C2×C3×C4×C5—43no—
159C2×C3×C4×C5C2×D4112yescomplemented
160C2×C3×C4×C5C2413yes—
161C2×C3×C4×C5C2413yes—
162C2×C3×C4×C5C2411yescharacteristic
163C2×C3×C4×C5C2411yescharacteristic
164C2×C3×C4×C5C2413yes—
165C2×C3×C4×C5C2411yescharacteristic
166#1220—224no—
167C2×Dic15—212no—
168C2×Dic15C2416yes—
169C2×Dic15C2412yes—
170D60—212no—
171D60—212no—
172D60—26no—
173D60—46no—
174D60#4114yesdirect product factor
175C4×D15—24no—
176C4×D15—212no—
177C4×D15—212no—
178C4×D15—212no—
179Dic30—212no—
180C2×C3×#41C2×D511yescharacteristic
181D3×#41—1016no—
182C2×#239—52no—
183C2×D3×Q8—52no—
184C2×#237—56no—
185C2×D3×D4—56no—
186C2×#235—56no—
187C22×D12—53no—
188C22×C4×D3—56no—
189C3×C4×Q8C2×D511yescharacteristic, complemented
190C3×C4×Q8C2×D511yescharacteristic, complemented
191C3×C4×D4C2×D513yescomplemented
192C3×C4×D4C2×D513yescomplemented
193C3×#117C2×D513yescomplemented
194C2×C3×C42C2×D513yescomplemented
195#930—56no—
196#930—56no—
197C2×(C2×D3)⋊C4—56no—
198C2×C4⋊Dic3—53no—
199#897—56no—
200#897—56no—
201#895—56no—
202#895—56no—
203#886—512no—
204#882—512no—
205#875—56no—
206#874—53no—
207C4×D12—51no—
208C4×D12—53no—
209C4×D12—53no—
210C4×D12—56no—
211C4×D12—56no—
212C4×D12—53no—
213C4×D12—56no—
214#869—53no—
215C23×D5—36no—
216C5×#41D1218yescomplemented
217C2×C5×Q8C22×D311yescharacteristic
218C2×C5×D4C22×D313yes—
219C22×C4×C5C22×D313yes—
220C22×C4×C5C22×D313yes—
221C22×C4×C5C22×D313yes—
222C2×C22⋊D5—312no—
223C22×Dic5—36no—
224#713—68no—
225Q8×D5—68no—
226#711—624no—
227D4×D5—624no—
228#709—624no—
229C2×D20—31no—
230C2×D20—33no—
231C2×D20—36no—
232C2×D20—36no—
233C2×D20—36no—
234C2×D20—612no—
235C2×C4×D5—32no—
236C2×C4×D5—36no—
237C2×C4×D5—36no—
238C2×C4×D5—36no—
239C2×C4×D5—624no—
240C2×Dic10—36no—
241C5×C4⋊C4C22×D313yes—
242C5×C4⋊C4C22×D313yes—
243C5×C22⋊C4C22×D316yes—
244C42×C5C22×D311yescharacteristic
245C42×C5C22×D313yes—
246C42×C5C22×D313yes—
247C42×C5C22×D313yes—
248#685—32no—
249#685—36no—
250#685—36no—
251#685—36no—
252#685—312no—
253C4⋊Dic5—33no—
254C4⋊Dic5—36no—
255C4⋊Dic5—31no—
256C4⋊Dic5—36no—
257C22×#41—152no—
258#550—151no—
259D4×Q8—151no—
260#548—152no—
261#547—153no—
262#546—156no—
263D42—153no—
264#532—153no—
265#525—156no—
266C4×#41D1511yescharacteristic, complemented
267C2×C4×D4—153no—
268C22×C3×C5—23no—
269C22×C3×C5—23no—
270C22×C3×C5C22×D416yes—
271C22×C3×C5C2511yescharacteristic
272C2×D15—22no—
273C2×D15—22no—
274C2×D15—26no—
275C2×D15—26no—
276C2×D15—26no—
277C2×D15—424no—
278C2×D15C2×#4114yescomplemented
279C3×C4×C5—23no—
280C3×C4×C5—23no—
281C3×C4×C5—21no—
282C3×C4×C5C22×D416yes—
283C3×C4×C5C22×D412yes—
284C3×C4×C5C2×#4112yescomplemented
285Dic15—26no—
286Dic15—22no—
287C23×D3—56no—
288C3×#41D2018yescomplemented
289C2×C3×Q8C22×D511yescharacteristic
290C2×C3×D4C22×D513yes—
291C22×C3×C4C22×D513yes—
292C22×C3×C4C22×D513yes—
293C22×C3×C4C22×D513yes—
294C2×#67—512no—
295C22×Dic3—56no—
296#239—108no—
297D3×Q8—108no—
298#237—1024no—
299D3×D4—1024no—
300#235—1024no—
301C2×D12—51no—
302C2×D12—53no—
303C2×D12—56no—
304C2×D12—56no—
305C2×D12—56no—
306C2×D12—1012no—
307C2×C4×D3—52no—
308C2×C4×D3—56no—
309C2×C4×D3—56no—
310C2×C4×D3—56no—
311C2×C4×D3—1024no—
312C2×Dic6—56no—
313C3×C4⋊C4C22×D513yes—
314C3×C4⋊C4C22×D513yes—
315C3×C22⋊C4C22×D516yes—
316C3×C42C22×D513yes—
317C3×C42C22×D511yescharacteristic
318C3×C42C22×D513yes—
319C3×C42C22×D513yes—
320(C2×D3)⋊C4—52no—
321(C2×D3)⋊C4—56no—
322(C2×D3)⋊C4—56no—
323(C2×D3)⋊C4—56no—
324(C2×D3)⋊C4—512no—
325C4⋊Dic3—53no—
326C4⋊Dic3—56no—
327C4⋊Dic3—51no—
328C4⋊Dic3—56no—
329C23×C5C23×D313yes—
330C22×D5—32no—
331C22×D5—36no—
332C22×D5—612no—
333C22×D5—612no—
334C22×D5—126no—
335C5×Q8C2×D1214yescomplemented
336C5×D4C2×D12112yescomplemented
337C2×C4×C5—26no—
338C2×C4×C5—43no—
339C2×C4×C5C2×D12112yescomplemented
340C2×C4×C5C23×D313yes—
341C2×C4×C5C23×D313yes—
342C2×C4×C5C23×D311yescharacteristic
343C2×C4×C5C23×D313yes—
344C2×C4×C5C23×D311yescharacteristic
345C2×C4×C5C23×D311yescharacteristic
346C22⋊D5—624no—
347C2×Dic5—36no—
348C2×Dic5—32no—
349C2×Dic5—612no—
350D20—34no—
351D20—612no—
352D20—612no—
353D20—66no—
354D20—126no—
355C4×D5—64no—
356C4×D5—612no—
357C4×D5—612no—
358C4×D5—612no—
359Dic10—612no—
360C2×#41—152no—
361C2×#41—156no—
362C2×#41—156no—
363C2×#41—3016no—
364C2×#41C2×D1511yescharacteristic
365C22×Q8—152no—
366C22×D4—156no—
367C22×D4—153no—
368C23×C4—156no—
369C4⋊Q8—153no—
370#127—153no—
371#124—156no—
372#123—1512no—
373C22⋊Q8—156no—
374C22⋊Q8—156no—
375#121—156no—
376#121—156no—
377#121—156no—
378#121—156no—
379#120—1512no—
380C4×Q8C2×D1511yescharacteristic, complemented
381C4×Q8C2×D1511yescharacteristic, complemented
382C4×D4—151no—
383C4×D4—156no—
384C4×D4—153no—
385C4×D4—153no—
386C4×D4—156no—
387C4×D4—153no—
388C4×D4—156no—
389C4×D4C2×D1513yescomplemented
390C4×D4C2×D1513yescomplemented
391#117C2×D1513yescomplemented
392C2×C4⋊C4—153no—
393C2×C22⋊C4—156no—
394C2×C42C2×D1513yescomplemented
395C2×C3×C5—26no—
396C2×C3×C5C23×D411yescharacteristic
397C2×C3×C5C22×#4111yescharacteristic
398C2×C3×C5#58511yescharacteristic
399D15—24no—
400D15—46no—
401C23×C3C23×D513yes—
402C22×D3—52no—
403C22×D3—56no—
404C22×D3—1012no—
405C22×D3—1012no—
406C22×D3—206no—
407C3×Q8C2×D2014yescomplemented
408C3×D4C2×D20112yescomplemented
409C2×C3×C4—26no—
410C2×C3×C4—43no—
411C2×C3×C4C2×D20112yescomplemented
412C2×C3×C4C23×D513yes—
413C2×C3×C4C23×D513yes—
414C2×C3×C4C23×D511yescharacteristic
415C2×C3×C4C23×D513yes—
416C2×C3×C4C23×D511yescharacteristic
417C2×C3×C4C23×D511yescharacteristic
418#67—1024no—
419C2×Dic3—56no—
420C2×Dic3—52no—
421C2×Dic3—1012no—
422D12—54no—
423D12—1012no—
424D12—1012no—
425D12—106no—
426D12—206no—
427C4×D3—104no—
428C4×D3—1012no—
429C4×D3—1012no—
430C4×D3—1012no—
431Dic6—1012no—
432C22×C5—23no—
433C22×C5—23no—
434C22×C5C22×D1216yes—
435C22×C5C24×D311yescharacteristic
436C2×D5—34no—
437C2×D5—62no—
438C2×D5—62no—
439C2×D5—66no—
440C2×D5—66no—
441C2×D5—66no—
442C2×D5—1224no—
443C4×C5—23no—
444C4×C5—23no—
445C4×C5—21no—
446C4×C5C22×D1216yes—
447C4×C5C22×D1212yes—
448C4×C5D3×#4112yescomplemented
449Dic5—66no—
450Dic5—62no—
451C24—156no—
452#41—308no—
453#41—3024no—
454#41—3024no—
455#41D6018yesdirect product factor
456C2×Q8—156no—
457C2×Q8—308no—
458C2×Q8C22×D1511yescharacteristic
459C2×D4—1512no—
460C2×D4—151no—
461C2×D4—156no—
462C2×D4—153no—
463C2×D4—156no—
464C2×D4—156no—
465C2×D4—3012no—
466C2×D4—3024no—
467C2×D4C22×D1513yes—
468C22×C4—156no—
469C22×C4—156no—
470C22×C4—156no—
471C22×C4—152no—
472C22×C4—156no—
473C22×C4—3024no—
474C22×C4C22×D1513yes—
475C22×C4C22×D1513yes—
476C22×C4C22×D1513yes—
477C4⋊C4—151no—
478C4⋊C4—153no—
479C4⋊C4—156no—
480C4⋊C4—156no—
481C4⋊C4C22×D1513yes—
482C4⋊C4C22×D1513yes—
483C22⋊C4—152no—
484C22⋊C4—156no—
485C22⋊C4—156no—
486C22⋊C4—156no—
487C22⋊C4—1512no—
488C22⋊C4C22×D1516yes—
489C42C22×D1513yes—
490C42C22×D1513yes—
491C42C22×D1511yescharacteristic
492C42C22×D1513yes—
493C3×C5D4×#4111yescharacteristic, complemented, Hall
494C22×C3—23no—
495C22×C3—23no—
496C22×C3C22×D2016yes—
497C22×C3C24×D511yescharacteristic
498C2×D3—54no—
499C2×D3—102no—
500C2×D3—102no—
501C2×D3—106no—
502C2×D3—106no—
503C2×D3—106no—
504C2×D3—2024no—
505C3×C4—23no—
506C3×C4—23no—
507C3×C4—21no—
508C3×C4C22×D2016yes—
509C3×C4C22×D2012yes—
510C3×C4D5×#4112yescomplemented
511Dic3—106no—
512Dic3—102no—
513C2×C5—26no—
514C2×C5C23×D1211yescharacteristic
515C2×C5C2×D3×#4111yescharacteristic
516C2×C5#596411yescharacteristic
517D5—64no—
518D5—126no—
519C23—152no—
520C23—156no—
521C23—3012no—
522C23—3012no—
523C23—606no—
524C23C23×D1513yes—
525Q8—3012no—
526Q8C2×D6014yescomplemented
527D4—154no—
528D4—3012no—
529D4—3024no—
530D4—3012no—
531D4—306no—
532D4—606no—
533D4C2×D60112yescomplemented
534C2×C4—26no—
535C2×C4—43no—
536C2×C4—152no—
537C2×C4—156no—
538C2×C4—3012no—
539C2×C4—304no—
540C2×C4—3012no—
541C2×C4—3012no—
542C2×C4—3012no—
543C2×C4C2×D60112yescomplemented
544C2×C4C23×D1511yescharacteristic
545C2×C4C23×D1513yes—
546C2×C4C23×D1513yes—
547C2×C4C23×D1513yes—
548C2×C4C23×D1511yescharacteristic
549C2×C4C23×D1511yescharacteristic
550C2×C3—26no—
551C2×C3C23×D2011yescharacteristic
552C2×C3C2×D5×#4111yescharacteristic
553C2×C3#6628311yescharacteristic
554D3—104no—
555D3—206no—
556C5#41×D1211yescharacteristic, complemented, Sylow
557C22—23no—
558C22—23no—
559C22—154no—
560C22—302no—
561C22—302no—
562C22—306no—
563C22—306no—
564C22—306no—
565C22—6024no—
566C22C22×D6016yes—
567C22C24×D1511yescharacteristic
568C4—23no—
569C4—21no—
570C4—23no—
571C4—302no—
572C4—306no—
573C4C22×D6012yes—
574C4C22×D6016yes—
575C4#41×D1512yescomplemented
576C3#41×D2011yescharacteristic, complemented, Sylow
577C2—26no—
578C2—304no—
579C2—606no—
580C2C23×D6011yescharacteristic
581C2C2×#41×D1511yescharacteristic
582C2#1175714611yescharacteristic
subgroupG/H
centerC2×C4C23×D15
commutator, socle, cosocleC22×C3×C5C25
FrattiniC22C24×D15
FittingC3×C4×C5×#41C2
hypercenterC4×#41D15
hypocenterC3×C5D4×#41
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C4×#41

Complements

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

NH ≅ G/Ntype
1. C2×#41×D15C2semidirect
2. C3×C4×C5×#41C2semidirect
3. #11756336C2semidirect
4. #11756335C2semidirect
5. Q8×D60C2semidirect
6. #11756314C2semidirect
7. #11756313C2semidirect
8. D4×D60C2semidirect
9. #11756283C2semidirect
10. #11756236C2semidirect
11. C2×C4×D60C2semidirect
15. C2×#6821C22semidirect
16. C2×Q8×D15C22semidirect
17. C2×#6819C22semidirect
18. C2×D4×D15C22semidirect
19. C2×#6817C22semidirect
21. C22×C4×D15C22semidirect
22. C3×C4×C5×Q8C22semidirect
23. C3×C4×C5×Q8C22semidirect
24. C3×C4×C5×D4C22semidirect
25. C3×C4×C5×D4C22semidirect
26. C3×C5×#117C22semidirect
27. C2×C3×C42×C5C22semidirect
28. #91819C22semidirect
29. #91819C22semidirect
30. C2×#6714C22semidirect
31. C2×C4⋊Dic15C22semidirect
32. #91786C22semidirect
33. #91786C22semidirect
34. #91784C22semidirect
35. #91784C22semidirect
36. #91775C22semidirect
37. #91771C22semidirect
38. #91764C22semidirect
39. #91763C22semidirect
42. C4×D60C22semidirect
43. C4×D60C22semidirect
44. C4×D60C22semidirect
45. C4×D60C22semidirect
46. C4×D60C22semidirect
47. #91758C22semidirect
50. C4×C5×#41D3semidirect
61. C3×C5×#41D4semidirect
103. C3×C4×#41D5semidirect
122. C4×C5×Q8C2×D3semidirect
123. C4×C5×Q8C2×D3semidirect
124. C4×C5×D4C2×D3semidirect
125. C4×C5×D4C2×D3semidirect
126. C5×#117C2×D3semidirect
127. C2×C42×C5C2×D3semidirect
155. C3×C5×Q8C2×D4semidirect
156. C3×C5×D4C2×D4semidirect
159. C2×C3×C4×C5C2×D4semidirect
174. D60#41direct (N × H)
189. C3×C4×Q8C2×D5semidirect
190. C3×C4×Q8C2×D5semidirect
191. C3×C4×D4C2×D5semidirect
192. C3×C4×D4C2×D5semidirect
193. C3×#117C2×D5semidirect
194. C2×C3×C42C2×D5semidirect
216. C5×#41D12semidirect
266. C4×#41D15semidirect
278. C2×D15C2×#41semidirect
284. C3×C4×C5C2×#41semidirect
288. C3×#41D20semidirect
335. C5×Q8C2×D12semidirect
336. C5×D4C2×D12semidirect
339. C2×C4×C5C2×D12semidirect
380. C4×Q8C2×D15semidirect
381. C4×Q8C2×D15semidirect
389. C4×D4C2×D15semidirect
390. C4×D4C2×D15semidirect
391. #117C2×D15semidirect
394. C2×C42C2×D15semidirect
407. C3×Q8C2×D20semidirect
408. C3×D4C2×D20semidirect
411. C2×C3×C4C2×D20semidirect
448. C4×C5D3×#41semidirect
455. #41D60direct (N × H)
493. C3×C5D4×#41semidirect
510. C3×C4D5×#41semidirect
526. Q8C2×D60semidirect
533. D4C2×D60semidirect
543. C2×C4C2×D60semidirect
556. C5#41×D12semidirect
575. C4#41×D15semidirect
576. C3#41×D20semidirect

Maximal subgroups

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

subgroupindex
C2×#41×D152
C3×C4×C5×#412
#117563362
#117563352
Q8×D602
#117563142
#117563132
D4×D602
#117562832
#117562362
C2×C4×D602
#41×D203
#41×D125