Finite Group Databasebeta

← #14453113

Subgroups — #14453113

Order 1920.

692 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756293C211yesmaximal, characteristic, complemented
2C5×#5534C211yesmaximal, characteristic, complemented
3C3×#65288C211yesmaximal, characteristic, complemented
4#11748558C211yesmaximal, characteristic, complemented
5#11748535C211yesmaximal, characteristic, complemented
6#11748533C211yesmaximal, characteristic, complemented
7#11748515C211yesmaximal, characteristic
8#11747102C211yesmaximal, characteristic, complemented
9#11747046C211yesmaximal, characteristic, complemented
10#11747038C211yesmaximal, characteristic, complemented
11#11746946C211yesmaximal, characteristic, complemented
12#11746945C211yesmaximal, characteristic, complemented
13#11746885C211yesmaximal, characteristic, complemented
14#11746884C211yesmaximal, characteristic, complemented
15#11746883C211yesmaximal, characteristic, complemented
16#10615200—31nomaximal, Hall
17C3×C5×#117C2211yescharacteristic
18#91819C2211yescharacteristic
19#91813C2211yescharacteristic
20#91787—21no—
21#91785—21no—
22#91774—21no—
23#91772—21no—
24#91764C2211yescharacteristic
25C4×D60C2211yescharacteristic
26#91758C2211yescharacteristic
27C4×Dic30C2211yescharacteristic
28C5×#930C2211yescharacteristic
29C5×#924C2211yescharacteristic
30C5×#898—21no—
31C5×#896—21no—
32C5×#885—21no—
33C5×#883—21no—
34C5×#875C2211yescharacteristic
35C4×C5×D12C2211yescharacteristic
36C5×#869C2211yescharacteristic
37C4×C5×Dic6C2211yescharacteristic
38C2×C3×#681C2211yescharacteristic
39C22×C3×#168C2211yescharacteristic
40C2×#6663C2211yescharacteristic
41C2×#6660C2211yescharacteristic
42C2×#6659C2211yescharacteristic
43C2×#6654C2211yescharacteristic
44C3×C4⋊#168C2211yescharacteristic
45C3×C4⋊#168C2211yescharacteristic
46C3×C4⋊#168C2211yescharacteristic
47C3×C4⋊#168C2211yescharacteristic
48#90985C2211yescharacteristic
49#90985C2211yescharacteristic
50#90985C2211yescharacteristic
51#90985C2211yescharacteristic
52#90975C2211yescharacteristic
53#90975C2211yescharacteristic
54#90973C2211yescharacteristic
55#90973C2211yescharacteristic
56#90969C2211yescharacteristic
57#90969C2211yescharacteristic
58#90967C2211yescharacteristic
59#90967C2211yescharacteristic
60#79098—51nomaximal, Hall
61C5×#542—31no—
62#65868—31no—
63#65383—31no—
64#65373—31no—
65#65346—31no—
66#65343—31no—
67#65341—31no—
68#65337—31no—
69#65330—31no—
70#65328—31no—
71#65317—31no—
72#65309—31no—
73#65305—31no—
74#65297—31no—
75#65288D311yescharacteristic, complemented
76C22×C3×C4×C5C2311yescharacteristic
77C2×#1220—21no—
78C2×D60C2311yescharacteristic
79C2×C4×D15—21no—
80C2×Dic30—21no—
81C2×Dic30C2311yescharacteristic
82C2×C5×#67—21no—
83C2×C5×D12C2311yescharacteristic
84C2×C4×C5×D3—21no—
85C2×C5×Dic6—21no—
86C2×C5×Dic6C2311yescharacteristic
87C3×C5×C4⋊C4D411yescharacteristic
88C3×C5×C4⋊C4D411yescharacteristic
89C3×C5×C22⋊C4D411yescharacteristic
90C3×C5×C22⋊C4D411yescharacteristic
91C3×C42×C5C2311yescharacteristic
92C3×C42×C5C2311yescharacteristic
93#6719—21no—
94#6714—21no—
95#6714—21no—
96#6714—21no—
97#6714—21no—
98C4⋊Dic15—21no—
99C4⋊Dic15C2311yescharacteristic
100C4⋊Dic15C2311yescharacteristic
101#6712—21no—
102#6712—21no—
103C4×Dic15—21no—
104C5×#217—21no—
105C5×(C2×D3)⋊C4—21no—
106C5×(C2×D3)⋊C4—21no—
107C5×(C2×D3)⋊C4—21no—
108C5×(C2×D3)⋊C4—21no—
109C5×C4⋊Dic3—21no—
110C5×C4⋊Dic3C2311yescharacteristic
111C5×C4⋊Dic3C2311yescharacteristic
112C5×Dic3⋊C4—21no—
113C5×Dic3⋊C4—21no—
114C4×C5×Dic3—21no—
115C3×#681—41no—
116C2×C3×#168—41no—
117C2×C3×#168C2311yescharacteristic
118C2×C3×#168C2311yescharacteristic
119C2×C3×#168C2311yescharacteristic
120C2×C3×#168C2311yescharacteristic
121#6663—41no—
122#6660—41no—
123#6659—41no—
124#6654—41no—
125#5534—51no—
126#5534D511yescharacteristic, complemented
127C3×#424—51no—
128#5137—51no—
129#5135—51no—
130#5114—51no—
131#5114—51no—
132#4851—51no—
133#4851—51no—
134#4845—51no—
135#4845—51no—
136#4844—51no—
137#4844—51no—
138#4842—51no—
139#4842—51no—
140C5×C4⋊Q8—31no—
141C5×#126—61no—
142C5×#124—31no—
143C5×#124—61no—
144C5×#123—61no—
145C5×C22⋊Q8—31no—
146C5×C22⋊Q8—61no—
147C5×#121—31no—
148C4×C5×Q8—31no—
149C4×C5×D4—31no—
150C5×#117C2×D311yescharacteristic
151C2×#689—31no—
152C2×#688—31no—
153C2×#687—31no—
154C2×#686—31no—
155#4076—31no—
156#4070—31no—
157C2×#681C2×D311yescharacteristic
158C22×#168C2×D311yescharacteristic
159#4044—61no—
160#4042—61no—
161#4031—61no—
162#4029—61no—
163#4021—31no—
164C4×D20—31no—
165#4015—31no—
166C4×Dic10—31no—
167#3967—31no—
168#3967—31no—
169#3964—31no—
170#3964—31no—
171#3942—31no—
172#3942—31no—
173#3941—31no—
174#3941—31no—
175#3940—31no—
176#3940—31no—
177#3940—31no—
178#3940—31no—
179C4⋊#168C2×D311yescharacteristic
180C4⋊#168C2×D311yescharacteristic
181C4⋊#168C2×D311yescharacteristic
182C4⋊#168C2×D311yescharacteristic
183#3263—151noSylow
184C23×C3×C5C2×D411yescharacteristic
185C22×D15—21no—
186C22×C5×D3—21no—
187C2×C3×C4×C5—21no—
188C2×C3×C4×C5—21no—
189C2×C3×C4×C5C2×D411yescharacteristic
190C2×C3×C4×C5C2×D411yescharacteristic
191C2×C3×C4×C5C2×D411yescharacteristic
192C2×C3×C4×C5C2×D411yescharacteristic
193C2×C3×C4×C5C2×D411yescharacteristic
194C2×C3×C4×C5C2411yescharacteristic
195#1220—81no—
196C2×Dic15—21no—
197C2×Dic15—21no—
198C2×Dic15—21no—
199D60—21no—
200D60—21no—
201C4×D15—81no—
202Dic30—21no—
203Dic30—21no—
204Dic30—81no—
205C5×#67—81no—
206C2×C5×Dic3—21no—
207C2×C5×Dic3—21no—
208C2×C5×Dic3—21no—
209C5×D12—21no—
210C5×D12—21no—
211C4×C5×D3—81no—
212C5×Dic6—21no—
213C5×Dic6—21no—
214C5×Dic6—81no—
215C3×#168—21no—
216C3×#168—21no—
217C3×#168—21no—
218C3×#168—21no—
219C2×C3×M16—51no—
220C22×C3×C8—51no—
221C3×#117C2×D511yescharacteristic
222#930—51no—
223#930C2×D511yescharacteristic
224#924—51no—
225#924C2×D511yescharacteristic
226C2×Dic12—51no—
227C2×D24—51no—
228C2×#204—51no—
229C2×#204—51no—
230#898—21no—
231#898—101no—
232#896—21no—
233#896—101no—
234#885—21no—
235#885—101no—
236#883—21no—
237#883—101no—
238#875—51no—
239#875C2×D511yescharacteristic
240C4×D12—51no—
241C4×D12C2×D511yescharacteristic
242#869—51no—
243#869C2×D511yescharacteristic
244C4×Dic6—51no—
245C4×Dic6C2×D511yescharacteristic
246C3×C4⋊C8—51no—
247C3×C4⋊C8—51no—
248C3×C4⋊C8—51no—
249C3×C4⋊C8—51no—
250#821—51no—
251#821—51no—
252#821—51no—
253#821—51no—
254#817—51no—
255#817—51no—
256#817—51no—
257#817—51no—
258#816—51no—
259#816—51no—
260#816—51no—
261#816—51no—
262C2×C5×Q8—31no—
263C2×C5×Q8—61no—
264C2×C5×D4—31no—
265C2×C5×D4—61no—
266C22×C4×C5—61no—
267C22×C4×C5C22×D311yescharacteristic
268C2×C22⋊D5—61no—
269C2×D20—31no—
270C2×C4×D5—61no—
271C2×Dic10—31no—
272C2×Dic10—61no—
273C5×C4⋊C4—31no—
274C5×C4⋊C4—31no—
275C5×C4⋊C4—61no—
276C5×C4⋊C4—61no—
277C5×C4⋊C4—61no—
278C5×C4⋊C4D1211yescharacteristic
279C5×C4⋊C4D1211yescharacteristic
280C5×C22⋊C4—61no—
281C5×C22⋊C4—61no—
282C5×C22⋊C4—61no—
283C5×C22⋊C4—61no—
284C5×C22⋊C4—61no—
285C5×C22⋊C4D1211yescharacteristic
286C5×C22⋊C4D1211yescharacteristic
287C42×C5—61no—
288C42×C5C22×D311yescharacteristic
289C42×C5C22×D311yescharacteristic
290C22⋊Dic5—61no—
291#689—121no—
292#688—121no—
293#687—121no—
294#686—121no—
295#685—61no—
296#685—61no—
297#685—61no—
298#685—61no—
299C4⋊Dic5—31no—
300C4⋊Dic5—31no—
301C4⋊Dic5—61no—
302#683—61no—
303#683—61no—
304C4×Dic5—61no—
305#681—41no—
306C2×#168—41no—
307C2×#168C22×D311yescharacteristic
308C2×#168C22×D311yescharacteristic
309C2×#168C22×D311yescharacteristic
310C2×#168C22×D311yescharacteristic
311#542—31no—
312#542—151no—
313#476—151no—
314#476—151no—
315#475—151no—
316#475—151no—
317#470—151no—
318#469—151no—
319#465—151no—
320#465—151no—
321#464—151no—
322#464—151no—
323#463—151no—
324#463—151no—
325#424—51no—
326C22×C3×C5—21no—
327C22×C3×C5—21no—
328C22×C3×C5—21no—
329C22×C3×C5C22×D411yescharacteristic
330C2×D15—41no—
331C2×D15—41no—
332C2×D15—41no—
333C2×C5×D3—41no—
334C2×C5×D3—41no—
335C2×C5×D3—41no—
336C3×C4×C5—21no—
337C3×C4×C5—21no—
338C3×C4×C5—21no—
339C3×C4×C5—21no—
340C3×C4×C5—21no—
341C3×C4×C5H(5,𝔽2)11yescharacteristic
342C3×C4×C52−1+411yescharacteristic
343Dic15—41no—
344Dic15—41no—
345Dic15—41no—
346C5×Dic3—41no—
347C5×Dic3—41no—
348C5×Dic3—41no—
349C22×C3×C4C22×D511yescharacteristic
350C2×#67—21no—
351C2×#67—101no—
352C2×D12—51no—
353C2×D12C22×D511yescharacteristic
354C2×C4×D3—21no—
355C2×C4×D3—101no—
356C2×Dic6—21no—
357C2×Dic6—51no—
358C2×Dic6—101no—
359C2×Dic6C22×D511yescharacteristic
360C3×M16—201no—
361C2×C3×C8—51no—
362C2×C3×C8—51no—
363C2×C3×C8—51no—
364C2×C3×C8—51no—
365C2×C3×C8—201no—
366C3×C4⋊C4C22⋊D511yescharacteristic
367C3×C4⋊C4C22⋊D511yescharacteristic
368C3×C22⋊C4C22⋊D511yescharacteristic
369C3×C22⋊C4C22⋊D511yescharacteristic
370C3×C42C22×D511yescharacteristic
371C3×C42C22×D511yescharacteristic
372#217—21no—
373#217—101no—
374(C2×D3)⋊C4—21no—
375(C2×D3)⋊C4—21no—
376(C2×D3)⋊C4—21no—
377(C2×D3)⋊C4—21no—
378(C2×D3)⋊C4—101no—
379(C2×D3)⋊C4—101no—
380(C2×D3)⋊C4—101no—
381(C2×D3)⋊C4—101no—
382C4⋊Dic3—21no—
383C4⋊Dic3—51no—
384C4⋊Dic3—51no—
385C4⋊Dic3—101no—
386C4⋊Dic3C22×D511yescharacteristic
387C4⋊Dic3C22×D511yescharacteristic
388Dic3⋊C4—21no—
389Dic3⋊C4—21no—
390Dic3⋊C4—101no—
391Dic3⋊C4—101no—
392C4×Dic3—21no—
393C4×Dic3—101no—
394Dic12—201no—
395D24—201no—
396#204—201no—
397#204—201no—
398C23×C5—61no—
399C23×C5C2×D1211yescharacteristic
400C22×D5—61no—
401C5×Q8—61no—
402C5×Q8—61no—
403C5×Q8—241no—
404C5×D4—61no—
405C5×D4—61no—
406C5×D4—241no—
407C2×C4×C5—21no—
408C2×C4×C5—21no—
409C2×C4×C5—61no—
410C2×C4×C5—61no—
411C2×C4×C5—61no—
412C2×C4×C5—241no—
413C2×C4×C5C2×D1211yescharacteristic
414C2×C4×C5C2×D1211yescharacteristic
415C2×C4×C5C2×D1211yescharacteristic
416C2×C4×C5C2×D1211yescharacteristic
417C2×C4×C5C2×D1211yescharacteristic
418C2×C4×C5C23×D311yescharacteristic
419C22⋊D5—241no—
420C2×Dic5—61no—
421C2×Dic5—61no—
422C2×Dic5—61no—
423D20—61no—
424D20—61no—
425C4×D5—241no—
426Dic10—61no—
427Dic10—61no—
428Dic10—241no—
429#168—21no—
430#168—21no—
431#168—21no—
432#168—21no—
433C2×Q16—151no—
434C2×SD16—151no—
435C2×SD16—151no—
436C2×D8—151no—
437C2×M16—51no—
438C22×C8—51no—
439C4⋊Q8—31no—
440C4⋊Q8—151no—
441#126—61no—
442#126—301no—
443#124—31no—
444#124—61no—
445#124—151no—
446#124—301no—
447#123—61no—
448#123—301no—
449C22⋊Q8—31no—
450C22⋊Q8—61no—
451C22⋊Q8—151no—
452C22⋊Q8—301no—
453#121—31no—
454#121—151no—
455C4×Q8—31no—
456C4×Q8—151no—
457C4×D4—31no—
458C4×D4—151no—
459#117D3×D511yescharacteristic
460#106—151no—
461#106—151no—
462#106—151no—
463#106—151no—
464C4⋊C8—51no—
465C4⋊C8—51no—
466C4⋊C8—51no—
467C4⋊C8—51no—
468#103—151no—
469#103—151no—
470#103—151no—
471#103—151no—
472#102—151no—
473#102—151no—
474#102—151no—
475#102—151no—
476C2×C3×C5—41no—
477C2×C3×C5#53711yescharacteristic
478C2×C3×C5#57711yescharacteristic
479C2×C3×C5#57711yescharacteristic
480D15—81no—
481C5×D3—81no—
482C23×C3C2×C22⋊D511yescharacteristic
483C22×D3—21no—
484C22×D3—101no—
485C2×C3×C4—21no—
486C2×C3×C4—21no—
487C2×C3×C4C2×C22⋊D511yescharacteristic
488C2×C3×C4C2×C22⋊D511yescharacteristic
489C2×C3×C4C2×C22⋊D511yescharacteristic
490C2×C3×C4C2×C22⋊D511yescharacteristic
491C2×C3×C4C2×C22⋊D511yescharacteristic
492C2×C3×C4C23×D511yescharacteristic
493#67—81no—
494#67—401no—
495C2×Dic3—21no—
496C2×Dic3—21no—
497C2×Dic3—21no—
498C2×Dic3—101no—
499C2×Dic3—101no—
500C2×Dic3—101no—
501D12—21no—
502D12—21no—
503D12—101no—
504D12—101no—
505C4×D3—81no—
506C4×D3—401no—
507Dic6—21no—
508Dic6—21no—
509Dic6—81no—
510Dic6—101no—
511Dic6—101no—
512Dic6—401no—
513C3×C8—101no—
514C3×C8—101no—
515C3×C8—101no—
516C3×C8—101no—
517C22×C5—21no—
518C22×C5—21no—
519C22×C5—21no—
520C22×C5—121no—
521C22×C5—121no—
522C22×C5—121no—
523C22×C5C22×D1211yescharacteristic
524C2×D5—121no—
525C2×D5—121no—
526C2×D5—121no—
527C4×C5—21no—
528C4×C5—21no—
529C4×C5—21no—
530C4×C5—21no—
531C4×C5—21no—
532C4×C5—121no—
533C4×C5—121no—
534C4×C5—121no—
535C4×C5#100411yescharacteristic
536C4×C5#100711yescharacteristic
537Dic5—121no—
538Dic5—121no—
539Dic5—121no—
540C2×Q8—31no—
541C2×Q8—61no—
542C2×Q8—151no—
543C2×Q8—301no—
544C2×D4—31no—
545C2×D4—61no—
546C2×D4—151no—
547C2×D4—301no—
548C22×C4—61no—
549C22×C4—301no—
550C22×C4C2×D3×D511yescharacteristic
551Q16—601no—
552SD16—601no—
553SD16—601no—
554D8—601no—
555M16—201no—
556C2×C8—51no—
557C2×C8—51no—
558C2×C8—51no—
559C2×C8—51no—
560C2×C8—201no—
561C4⋊C4—31no—
562C4⋊C4—31no—
563C4⋊C4—61no—
564C4⋊C4—61no—
565C4⋊C4—61no—
566C4⋊C4—151no—
567C4⋊C4—151no—
568C4⋊C4—301no—
569C4⋊C4—301no—
570C4⋊C4—301no—
571C4⋊C4#120311yescharacteristic
572C4⋊C4#120311yescharacteristic
573C22⋊C4—61no—
574C22⋊C4—61no—
575C22⋊C4—61no—
576C22⋊C4—61no—
577C22⋊C4—61no—
578C22⋊C4—301no—
579C22⋊C4—301no—
580C22⋊C4—301no—
581C22⋊C4—301no—
582C22⋊C4—301no—
583C22⋊C4#120311yescharacteristic
584C22⋊C4#120311yescharacteristic
585C42—61no—
586C42—301no—
587C42C2×D3×D511yescharacteristic
588C42C2×D3×D511yescharacteristic
589C3×C5#326311yescharacteristic, complemented, Hall
590C22×C3—21no—
591C22×C3—21no—
592C22×C3—21no—
593C22×C3C22×C22⋊D511yescharacteristic
594C2×D3—41no—
595C2×D3—41no—
596C2×D3—41no—
597C2×D3—201no—
598C2×D3—201no—
599C2×D3—201no—
600C3×C4—21no—
601C3×C4—21no—
602C3×C4—21no—
603C3×C4—21no—
604C3×C4—21no—
605C3×C4#414911yescharacteristic
606C3×C4#415011yescharacteristic
607Dic3—41no—
608Dic3—41no—
609Dic3—41no—
610Dic3—201no—
611Dic3—201no—
612Dic3—201no—
613C2×C5—41no—
614C2×C5—241no—
615C2×C5#551011yescharacteristic
616C2×C5#575111yescharacteristic
617C2×C5#575111yescharacteristic
618D5—241no—
619C23—61no—
620C23—301no—
621C23C2×#120311yescharacteristic
622Q8—61no—
623Q8—61no—
624Q8—241no—
625Q8—301no—
626Q8—301no—
627Q8—1201no—
628D4—61no—
629D4—61no—
630D4—241no—
631D4—301no—
632D4—301no—
633D4—1201no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—61no—
637C2×C4—61no—
638C2×C4—61no—
639C2×C4—241no—
640C2×C4—301no—
641C2×C4—301no—
642C2×C4—301no—
643C2×C4—1201no—
644C2×C4C2×#120311yescharacteristic
645C2×C4C2×#120311yescharacteristic
646C2×C4C2×#120311yescharacteristic
647C2×C4C2×#120311yescharacteristic
648C2×C4C2×#120311yescharacteristic
649C2×C4C22×D3×D511yescharacteristic
650C8—101no—
651C8—101no—
652C8—101no—
653C8—101no—
654C2×C3—41no—
655C2×C3#6616711yescharacteristic
656C2×C3#6617011yescharacteristic
657C2×C3#6617111yescharacteristic
658D3—81no—
659D3—401no—
660C5#7909811yescharacteristic, complemented, Sylow
661C22—21no—
662C22—21no—
663C22—21no—
664C22—121no—
665C22—121no—
666C22—121no—
667C22—601no—
668C22—601no—
669C22—601no—
670C22C22×#120311yescharacteristic
671C4—21no—
672C4—21no—
673C4—21no—
674C4—21no—
675C4—21no—
676C4—121no—
677C4—121no—
678C4—121no—
679C4—601no—
680C4—601no—
681C4—601no—
682C4#9200411yescharacteristic
683C4#9201711yescharacteristic
684C3#1061520011yescharacteristic, complemented, Sylow
685C2—41no—
686C2—241no—
687C2—1201no—
688C2#1175460311yescharacteristic
689C2#1175530711yescharacteristic
690C2#1175530811yescharacteristic
subgroupG/H
centerC22C22×#1203
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#117C22
socleC22×C3×C5C22×D4
prime radical#11748515C2
hypercenter#117D3×D5
hypocenterC3×C5#3263
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ #117

Complements

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

NH ≅ G/Ntype
1. #11756293C2semidirect
2. C5×#5534C2semidirect
3. C3×#65288C2semidirect
4. #11748558C2semidirect
5. #11748535C2semidirect
6. #11748533C2semidirect
8. #11747102C2semidirect
9. #11747046C2semidirect
10. #11747038C2semidirect
11. #11746946C2semidirect
12. #11746945C2semidirect
13. #11746885C2semidirect
14. #11746884C2semidirect
15. #11746883C2semidirect
75. #65288D3semidirect
126. #5534D5semidirect
589. C3×C5#3263semidirect
660. C5#79098semidirect
684. C3#10615200semidirect

Maximal subgroups

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

subgroupindex
#117562932
C5×#55342
C3×#652882
#117485582
#117485352
#117485332
#117485152
#117471022
#117470462
#117470382
#117469462
#117469452
#117468852
#117468842
#117468832
#106152003
#790985