Finite Group Databasebeta

← #14484834

Subgroups — #14484834

Order 1920.

2224 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756335C211yesmaximal, characteristic, complemented
2C4×C5×#239C211yesmaximal, characteristic, complemented
3C3×#65903C211yesmaximal, characteristic, complemented
4#11755245C211yesmaximal, characteristic, complemented
5#11755200C211yesmaximal, characteristic, complemented
6Q8×#1200C211yesmaximal, characteristic, complemented
7#11755134C211yesmaximal, characteristic, complemented
8#11753622C213yesmaximal, complemented
9#11753582C213yesmaximal, complemented
10#11753424C213yesmaximal, complemented
11#11753311C213yesmaximal, complemented
12#11752701C213yesmaximal, complemented
13#11752633C213yesmaximal, complemented
14#11752593C213yesmaximal, complemented
15C4×#6769C213yesmaximal, complemented
16#10617743—31nomaximal, Hall
17C2×#6821C2211yescharacteristic
18C2×Q8×D15C2211yescharacteristic
19C2×C5×#239C2211yescharacteristic
20C2×#6769C2213yes—
21C3×C4×C5×Q8C2211yescharacteristic
22#91786C2213yes—
23#91784C2213yes—
24#91764C2213yes—
25C4×D60C2213yes—
26C5×Q8×Dic3C2211yescharacteristic
27C5×#893C2213yes—
28C5×#892C2213yes—
29C4×C5×D12C2213yes—
30C42×C5×D3C2213yes—
31C3×Q8×Dic5C2211yescharacteristic
32C3×Q8×Dic5C2211yescharacteristic
33C3×#4036C2213yes—
34C3×#4034C2213yes—
35C3×#4016C2213yes—
36C3×C4×Dic10C2213yes—
37#91466C2213yes—
38#91466C2213yes—
39#91460C2213yes—
40#91451C2213yes—
41#91446C2213yes—
42#91446C2213yes—
43#91446C2216yes—
44C4×#1203C2213yes—
45C4×#1203C2213yes—
46#91438C2216yes—
47#91437C2213yes—
48#91428C2213yes—
49#91428C2213yes—
50#91420C2216yes—
51#91418C2213yes—
52#91403C2211yescharacteristic
53#91403C2213yes—
54C4×#1200C2213yes—
55C4×#1200C2213yes—
56#91380C2216yes—
57#91373C2213yes—
58#91365C2213yes—
59#91351C2216yes—
60#91347C2213yes—
61#91342C2216yes—
62#91340C2213yes—
63#91338C2213yes—
64#91333C2213yes—
65Dic3×Dic10C2213yes—
66#91326C2216yes—
67#87016—51nomaximal, Hall
68C4×C5×#41—31no—
69#66168—31no—
70#66165—31no—
71#65910—31no—
72C4×#713—31no—
73C4×Q8×D5—31no—
74#65903D311yescharacteristic, complemented
75#65893—33no—
76#65892—33no—
77#65891—33no—
78#65882—33no—
79#65867—33no—
80#65864—33no—
81#65813—33no—
82C4×#709—33no—
83C2×C3×C5×Q8C2311yescharacteristic
84#6821—24no—
85Q8×D15—24no—
86C2×D60C2313yes—
87C2×D60C2313yes—
88C2×C4×D15C2313yes—
89C2×C4×D15C2313yes—
90C2×Dic30C2313yes—
91C5×#239—24no—
92C2×C5×D12C2313yes—
93C2×C4×C5×D3C2313yes—
94C2×C4×C5×D3C2313yes—
95C2×C4×C5×D3C2313yes—
96C2×C3×Dic10C2313yes—
97C2×#1203C2313yes—
98C2×#1203C2313yes—
99C2×#1203C2316yes—
100C2×#1200C2313yes—
101C2×#1200C2313yes—
102C2×#1200C2313yes—
103C2×#1200C2311yescharacteristic
104#6769—212no—
105C3×C5×C4⋊C4C2313yes—
106C3×C42×C5C2313yes—
107#6714C2311yescharacteristic
108#6714C2313yes—
109#6714C2316yes—
110C4⋊Dic15C2313yes—
111C5×(C2×D3)⋊C4C2316yes—
112C5×C4⋊Dic3C2313yes—
113C4×C5×Dic3C2313yes—
114C4×C5×Dic3C2311yescharacteristic
115C4×C5×Dic3C2313yes—
116C3×C4⋊Dic5C2313yes—
117C3×C4⋊Dic5C2313yes—
118C3×C4⋊Dic5C2313yes—
119C3×#683C2311yescharacteristic
120C3×#683C2313yes—
121C3×#683C2316yes—
122C3×C4×Dic5C2313yes—
123C3×C4×Dic5C2313yes—
124#6669C2316yes—
125#6668C2311yescharacteristic
126#6668C2313yes—
127#6667C2311yescharacteristic
128#6667C2313yes—
129#6667C2316yes—
130(C2×D3)⋊Dic5C2313yes—
131(C2×D3)⋊Dic5C2313yes—
132(C2×D3)⋊Dic5C2316yes—
133Dic3×Dic5C2311yescharacteristic
134Dic3×Dic5C2313yes—
135Dic3×Dic5C2313yes—
136Dic3×Dic5C2313yes—
137C3×#557—51no—
138#5732—53no—
139#5725—53no—
140#5695—53no—
141#5695—53no—
142#5691—53no—
143#5691—53no—
144#5585—53no—
145#5577—51no—
146#5576—51no—
147#5576—51no—
148C4×#239—51no—
149C4×#239—53no—
150C4×#239D511yescharacteristic, complemented
151C4×D3×Q8—51no—
152C2×C5×#41—31no—
153C2×#713—31no—
154C2×Q8×D5—31no—
155C2×#709—33no—
156C4×C5×Q8—31no—
157C4×C5×Q8C2×D311yescharacteristic
158C4×C5×D4—33no—
159C4×C5×D4—33no—
160C5×#117—33no—
161C2×C42×C5—33no—
162Q8×Dic5C2×D311yescharacteristic
163Q8×Dic5C2×D311yescharacteristic
164#4086—33no—
165#4084—33no—
166#4084—33no—
167#4082—33no—
168#4076—33no—
169#4075—36no—
170C4×C22⋊D5—33no—
171C4×C22⋊D5—33no—
172C4×C22⋊D5—36no—
173C4×C22⋊D5—33no—
174C4×C22⋊D5—33no—
175#4072—33no—
176#4070—33no—
177#4043—33no—
178#4041—33no—
179#4039—33no—
180#4038—33no—
181D5×C4⋊C4—33no—
182#4036C2×D313yes—
183#4034C2×D313yes—
184#4033—33no—
185#4031—36no—
186#4030—36no—
187#4029—36no—
188#4025—36no—
189#4022—36no—
190#4021—33no—
191C4×D20—33no—
192C4×D20—33no—
193C4×D20—33no—
194#4018—31no—
195#4018—33no—
196C42×D5—33no—
197C42×D5—33no—
198#4016C2×D313yes—
199C4×Dic10—33no—
200C4×Dic10—33no—
201C4×Dic10C2×D313yes—
202#3480—151noSylow
203C22×D15C2413yes—
204C22×D15C2411yescharacteristic
205C22×C5×D3C2413yes—
206C3×C5×Q8#4114yescomplemented
207C2×C3×C4×C5C2411yescharacteristic
208C2×C3×C4×C5C2413yes—
209C2×C3×C4×C5C2413yes—
210C2×Dic15C2411yescharacteristic
211C2×Dic15C2413yes—
212D60—26no—
213D60—26no—
214C4×D15—26no—
215C4×D15—26no—
216Dic30—26no—
217C2×C5×Dic3C2413yes—
218C2×C5×Dic3C2411yescharacteristic
219C2×C5×Dic3C2411yescharacteristic
220C5×D12—26no—
221C4×C5×D3—26no—
222C4×C5×D3—26no—
223C4×C5×D3—43no—
224C2×C3×Dic5C2411yescharacteristic
225C2×C3×Dic5C2413yes—
226C2×C3×Dic5C2413yes—
227C2×C3×Dic5C2411yescharacteristic
228C3×Dic10—26no—
229#1203—26no—
230#1203—26no—
231#1203—46no—
232#1200—26no—
233#1200—43no—
234#1200—43no—
235#1200#4114yescomplemented
236C2×#239—51no—
237C2×#239—53no—
238C2×#239C2×D511yescharacteristic
239C2×D3×Q8—51no—
240C3×C4⋊Q8—53no—
241C3×#125—53no—
242C3×#125—53no—
243C3×C4×Q8—51no—
244C3×C4×Q8—51no—
245C3×C4×Q8—53no—
246C3×C4×Q8C2×D511yescharacteristic
247#947—56no—
248Q8×Dic3—53no—
249Q8×Dic3C2×D511yescharacteristic
250#898—56no—
251#898—56no—
252#897—53no—
253#897—53no—
254#895—53no—
255#895—53no—
256#895—53no—
257#895—53no—
258#895—56no—
259#894—56no—
260#894—56no—
261#893—56no—
262#893—53no—
263#893—53no—
264#893—53no—
265#893—53no—
266#893C2×D513yes—
267#892—53no—
268#892—53no—
269#892—53no—
270#892—51no—
271#892C2×D513yes—
272D3×C4⋊C4—53no—
273#887—53no—
274#875—53no—
275#875—53no—
276#874—53no—
277C4×D12—53no—
278C4×D12—53no—
279C4×D12—53no—
280C4×D12—53no—
281C4×D12C2×D513yes—
282C42×D3—53no—
283C42×D3—53no—
284C42×D3C2×D513yes—
285C4×Dic6—53no—
286C5×#41—64no—
287C2×C5×Q8C22×D311yescharacteristic
288C2×C5×D4—33no—
289C22×C4×C5—33no—
290C22×C4×C5—33no—
291C22×C4×C5—33no—
292C2×C22⋊D5—33no—
293C2×C22⋊D5—33no—
294C2×C22⋊D5—36no—
295#713—64no—
296Q8×D5—64no—
297#709—612no—
298C2×D20—33no—
299C2×D20—33no—
300C2×C4×D5—31no—
301C2×C4×D5—33no—
302C2×C4×D5—33no—
303C2×C4×D5—33no—
304C2×C4×D5—33no—
305C2×C4×D5—33no—
306C2×Dic10—33no—
307C2×Dic10C22×D313yes—
308C5×C4⋊C4—33no—
309C5×C4⋊C4C22×D313yes—
310C5×C22⋊C4—36no—
311C42×C5—31no—
312C42×C5—33no—
313C42×C5—33no—
314C42×C5C22×D313yes—
315C22⋊Dic5—33no—
316C22⋊Dic5—36no—
317C22⋊Dic5—33no—
318#685—31no—
319#685—33no—
320#685—36no—
321#685—31no—
322#685—33no—
323#685—36no—
324C4⋊Dic5—33no—
325C4⋊Dic5C22×D313yes—
326C4⋊Dic5C22×D313yes—
327C4⋊Dic5C22×D313yes—
328#683—31no—
329#683—33no—
330#683—36no—
331#683C22×D311yescharacteristic
332#683C22×D313yes—
333#683C22×D316yes—
334C4×Dic5—33no—
335C4×Dic5—33no—
336C4×Dic5—33no—
337C4×Dic5—31no—
338C4×Dic5C22×D313yes—
339C4×Dic5C22×D313yes—
340#559—153no—
341#557—51no—
342#556—153no—
343#553—153no—
344#553—153no—
345#550—151no—
346#548—151no—
347#548—151no—
348#532—153no—
349#529—153no—
350#529—153no—
351C4×#41—31no—
352C4×#41—153no—
353C4×#41—151no—
354C2×C4×Q8—151no—
355C22×C3×C5C2511yescharacteristic
356C2×D15—21no—
357C2×D15—21no—
358C2×D15—23no—
359C2×D15—23no—
360C2×D15—23no—
361C2×D15C2×#4112yes—
362C2×C5×D3—23no—
363C2×C5×D3—23no—
364C2×C5×D3—23no—
365C3×C4×C5—23no—
366C3×C4×C5—21no—
367C3×C4×C5C2×#4116yes—
368Dic15—23no—
369Dic15—21no—
370C3×Dic5—23no—
371C3×Dic5—21no—
372C3×Dic5—23no—
373C3×Dic5C2×#4112yes—
374C5×Dic3—21no—
375C5×Dic3—23no—
376C5×Dic3C2×#4112yes—
377C2×C3×Q8—53no—
378C2×C3×Q8C22×D511yescharacteristic
379#239—24no—
380#239—1012no—
381#239—104no—
382D3×Q8—104no—
383C2×D12—53no—
384C2×D12—53no—
385C2×D12—53no—
386C2×D12—53no—
387C2×D12—56no—
388C2×D12C22×D513yes—
389C2×C4×D3—51no—
390C2×C4×D3—53no—
391C2×C4×D3—53no—
392C2×C4×D3—53no—
393C2×C4×D3—53no—
394C2×C4×D3—53no—
395C2×C4×D3C22×D513yes—
396C2×C4×D3C22×D513yes—
397C2×C4×D3C22×D513yes—
398C2×Dic6—53no—
399C3×C4⋊C4—51no—
400C3×C4⋊C4—53no—
401C3×C4⋊C4—56no—
402C3×C4⋊C4—53no—
403C3×C4⋊C4—53no—
404C3×C4⋊C4—53no—
405C3×C4⋊C4C22×D513yes—
406C3×C42—53no—
407C3×C42—53no—
408C3×C42C22×D513yes—
409(C2×D3)⋊C4—53no—
410(C2×D3)⋊C4—53no—
411(C2×D3)⋊C4—56no—
412(C2×D3)⋊C4—51no—
413(C2×D3)⋊C4—53no—
414(C2×D3)⋊C4—56no—
415(C2×D3)⋊C4—51no—
416(C2×D3)⋊C4—56no—
417(C2×D3)⋊C4—53no—
418(C2×D3)⋊C4C22×D516yes—
419C4⋊Dic3—53no—
420C4⋊Dic3—51no—
421C4⋊Dic3—53no—
422C4⋊Dic3C22×D513yes—
423Dic3⋊C4—56no—
424C4×Dic3—53no—
425C4×Dic3—51no—
426C4×Dic3—53no—
427C4×Dic3—53no—
428C4×Dic3C22×D513yes—
429C4×Dic3C22×D511yescharacteristic
430C4×Dic3C22×D513yes—
431C23×C5—33no—
432C22×D5—31no—
433C22×D5—33no—
434C5×Q8#23914yescomplemented
435C5×D4—66no—
436C2×C4×C5—31no—
437C2×C4×C5—33no—
438C2×C4×C5—31no—
439C2×C4×C5—66no—
440C2×C4×C5—66no—
441C2×C4×C5—123no—
442C2×C4×C5C23×D311yescharacteristic
443C2×C4×C5C23×D313yes—
444C2×C4×C5C23×D313yes—
445C22⋊D5—66no—
446C22⋊D5—66no—
447C22⋊D5—126no—
448C2×Dic5—31no—
449C2×Dic5—33no—
450C2×Dic5C23×D311yescharacteristic
451C2×Dic5C23×D313yes—
452C2×Dic5C23×D313yes—
453C2×Dic5C23×D311yescharacteristic
454D20—66no—
455D20—66no—
456C4×D5—34no—
457C4×D5—66no—
458C4×D5—66no—
459C4×D5—66no—
460C4×D5—123no—
461C4×D5—123no—
462Dic10—26no—
463Dic10—66no—
464C2×#41—31no—
465C2×#41—153no—
466C2×#41—151no—
467C22×Q8—151no—
468C4⋊Q8—53no—
469#127—153no—
470#126—156no—
471#126—156no—
472#125—53no—
473#125—53no—
474#124—153no—
475#124—156no—
476#124—153no—
477#123—156no—
478#123—156no—
479C22⋊Q8—153no—
480C22⋊Q8—153no—
481#121—156no—
482#121—153no—
483#121—153no—
484#121—153no—
485#121—153no—
486C4×Q8—31no—
487C4×Q8—51no—
488C4×Q8—51no—
489C4×Q8—53no—
490C4×Q8—153no—
491C4×Q8—153no—
492C4×Q8—153no—
493C4×Q8D3×D511yescharacteristic
494C4×D4—33no—
495C4×D4—33no—
496C4×D4—153no—
497C4×D4—153no—
498C4×D4—153no—
499C4×D4—153no—
500C4×D4—153no—
501C4×D4—153no—
502C4×D4—153no—
503C4×D4—156no—
504C4×D4—153no—
505#117—33no—
506#117—151no—
507#117—153no—
508#117—153no—
509#117—153no—
510C2×C4⋊C4—153no—
511C2×C42—33no—
512C2×C42—153no—
513C2×C42—153no—
514C2×C3×C5C22×#4111yescharacteristic
515C2×C3×C5C22×#4111yescharacteristic
516C2×C3×C5#58511yescharacteristic
517D15—22no—
518D15—43no—
519C5×D3—43no—
520C22×D3—51no—
521C22×D3—53no—
522C22×D3C23×D513yes—
523C3×Q8—106no—
524C3×Q8#70914yescomplemented
525C2×C3×C4—51no—
526C2×C3×C4—53no—
527C2×C3×C4—53no—
528C2×C3×C4—51no—
529C2×C3×C4C23×D513yes—
530C2×C3×C4C23×D511yescharacteristic
531C2×C3×C4C23×D513yes—
532C2×Dic3—51no—
533C2×Dic3—53no—
534C2×Dic3C23×D513yes—
535C2×Dic3C23×D511yescharacteristic
536C2×Dic3C23×D511yescharacteristic
537D12—26no—
538D12—106no—
539D12—106no—
540D12—106no—
541D12—106no—
542D12—206no—
543C4×D3—26no—
544C4×D3—26no—
545C4×D3—43no—
546C4×D3—54no—
547C4×D3—106no—
548C4×D3—106no—
549C4×D3—106no—
550C4×D3—203no—
551C4×D3—203no—
552Dic6—106no—
553C22×C5—63no—
554C22×C5—63no—
555C22×C5—63no—
556C22×C5C24×D311yescharacteristic
557C2×D5—32no—
558C2×D5—61no—
559C2×D5—61no—
560C2×D5—63no—
561C2×D5—63no—
562C2×D5—63no—
563C4×C5—23no—
564C4×C5—21no—
565C4×C5—32no—
566C4×C5—61no—
567C4×C5—63no—
568C4×C5C2×#23916yes—
569Dic5—23no—
570Dic5—21no—
571Dic5—23no—
572Dic5—63no—
573Dic5—61no—
574Dic5D3×#4112yes—
575#41—64no—
576#41—3012no—
577#41—304no—
578C2×Q8—53no—
579C2×Q8—153no—
580C2×Q8—304no—
581C2×Q8C2×D3×D511yescharacteristic
582C2×D4—33no—
583C2×D4—153no—
584C2×D4—153no—
585C2×D4—156no—
586C2×D4—153no—
587C2×D4—153no—
588C22×C4—33no—
589C22×C4—33no—
590C22×C4—33no—
591C22×C4—151no—
592C22×C4—153no—
593C22×C4—153no—
594C22×C4—153no—
595C22×C4—153no—
596C22×C4—153no—
597C4⋊C4—33no—
598C4⋊C4—53no—
599C4⋊C4—51no—
600C4⋊C4—53no—
601C4⋊C4—53no—
602C4⋊C4—53no—
603C4⋊C4—56no—
604C4⋊C4—156no—
605C4⋊C4—151no—
606C4⋊C4—153no—
607C4⋊C4—153no—
608C4⋊C4C2×D3×D513yes—
609C22⋊C4—36no—
610C22⋊C4—151no—
611C22⋊C4—153no—
612C22⋊C4—156no—
613C22⋊C4—153no—
614C22⋊C4—153no—
615C22⋊C4—156no—
616C22⋊C4—151no—
617C22⋊C4—153no—
618C22⋊C4—156no—
619C42—31no—
620C42—33no—
621C42—33no—
622C42—53no—
623C42—53no—
624C42—151no—
625C42—153no—
626C42—153no—
627C42—153no—
628C42C2×D3×D513yes—
629C3×C5#348011yescharacteristic, complemented, Hall
630C22×C3C24×D511yescharacteristic
631C2×D3—23no—
632C2×D3—23no—
633C2×D3—23no—
634C2×D3—52no—
635C2×D3—101no—
636C2×D3—101no—
637C2×D3—103no—
638C2×D3—103no—
639C2×D3—103no—
640C3×C4—23no—
641C3×C4—21no—
642C3×C4—52no—
643C3×C4—103no—
644C3×C4—101no—
645C3×C4—103no—
646C3×C4C2×#70916yes—
647Dic3—21no—
648Dic3—23no—
649Dic3—103no—
650Dic3—101no—
651Dic3D5×#4112yes—
652C2×C5—123no—
653C2×C5C22×#23911yescharacteristic
654C2×C5C2×D3×#4111yescharacteristic
655C2×C5#596811yescharacteristic
656D5—62no—
657D5—123no—
658C23—33no—
659C23—151no—
660C23—153no—
661Q8—106no—
662Q8—306no—
663Q8#676914yescomplemented
664D4—66no—
665D4—306no—
666D4—306no—
667D4—306no—
668D4—306no—
669D4—606no—
670C2×C4—31no—
671C2×C4—31no—
672C2×C4—33no—
673C2×C4—51no—
674C2×C4—51no—
675C2×C4—53no—
676C2×C4—53no—
677C2×C4—66no—
678C2×C4—66no—
679C2×C4—123no—
680C2×C4—154no—
681C2×C4—151no—
682C2×C4—153no—
683C2×C4—306no—
684C2×C4—306no—
685C2×C4—306no—
686C2×C4—603no—
687C2×C4—603no—
688C2×C4C22×D3×D511yescharacteristic
689C2×C4C22×D3×D513yes—
690C2×C4C22×D3×D513yes—
691C2×C3C22×#70911yescharacteristic
692C2×C3C2×D5×#4111yescharacteristic
693C2×C3#6628311yescharacteristic
694D3—43no—
695D3—102no—
696D3—203no—
697C5#8701611yescharacteristic, complemented, Sylow
698C22—63no—
699C22—63no—
700C22—63no—
701C22—152no—
702C22—301no—
703C22—301no—
704C22—303no—
705C22—303no—
706C22—303no—
707C22C23×D3×D511yescharacteristic
708C4—21no—
709C4—23no—
710C4—32no—
711C4—52no—
712C4—61no—
713C4—63no—
714C4—101no—
715C4—103no—
716C4—103no—
717C4—301no—
718C4—303no—
719C4C2×#676916yes—
720C3#1061774311yescharacteristic, complemented, Sylow
721C2—123no—
722C2—302no—
723C2—603no—
724C2C22×#676911yescharacteristic
725C2#1175704911yescharacteristic
726C2D3×D5×#4111yescharacteristic
subgroupG/H
center, FrattiniC22C23×D3×D5
commutator, socle, cosocleC22×C3×C5C25
FittingC3×C4×C5×Q8C22
hypercenterC4×Q8D3×D5
hypocenterC3×C5#3480
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. #11756335C2semidirect
2. C4×C5×#239C2semidirect
3. C3×#65903C2semidirect
4. #11755245C2semidirect
5. #11755200C2semidirect
6. Q8×#1200C2semidirect
7. #11755134C2semidirect
8. #11753622C2semidirect
9. #11753582C2semidirect
10. #11753424C2semidirect
11. #11753311C2semidirect
12. #11752701C2semidirect
13. #11752633C2semidirect
14. #11752593C2semidirect
15. C4×#6769C2semidirect
74. #65903D3semidirect
150. C4×#239D5semidirect
206. C3×C5×Q8#41semidirect
235. #1200#41semidirect
434. C5×Q8#239semidirect
524. C3×Q8#709semidirect
629. C3×C5#3480semidirect
663. Q8#6769semidirect
697. C5#87016semidirect
720. C3#10617743semidirect

Maximal subgroups

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

subgroupindex
#117563352
C4×C5×#2392
C3×#659032
#117552452
#117552002
Q8×#12002
#117551342
#117536222
#117535822
#117534242
#117533112
#117527012
#117526332
#117525932
C4×#67692
#106177433
#870165