Finite Group Databasebeta

← #14458473

Subgroups — #14458473

Order 1920.

924 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11754661C211yesmaximal, characteristic
2#11754494C211yesmaximal, characteristic, complemented
3#11750832C211yesmaximal, characteristic, complemented
4C5×#67⋊C8C211yesmaximal, characteristic, complemented
5C3×#65024C211yesmaximal, characteristic, complemented
6#11748539C211yesmaximal, characteristic, complemented
7C2×#90968C211yesmaximal, characteristic, complemented
8#11748120C211yesmaximal, characteristic, complemented
9D3×#3953C211yesmaximal, characteristic, complemented
10#11748004C211yesmaximal, characteristic, complemented
11#11748003C211yesmaximal, characteristic, complemented
12#11747914C211yesmaximal, characteristic, complemented
13#11747790C211yesmaximal, characteristic, complemented
14#11747789C211yesmaximal, characteristic, complemented
15#11747625C211yesmaximal, characteristic, complemented
16#10611170—31nomaximal, Hall
17C22×D60C2211yescharacteristic
18C2×#6790—21no—
19C2×D3×D20C2211yescharacteristic
20#91813C2211yescharacteristic, complemented
21C2×#6706C2211yescharacteristic
22C2×#6706C2211yescharacteristic, complemented
23C4×C5×#67C2211yescharacteristic
24C22×C5×C3⋊C8C2211yescharacteristic, complemented
25C2×C5×D3×C8C2211yescharacteristic, complemented
26C3×#4076C2211yescharacteristic
27C2×C3×C4⋊Dic5C2211yescharacteristic, complemented
28#91574—21no—
29#91572—21no—
30Dic5×#67—21no—
31#91476—21no—
32#91469C2211yescharacteristic, complemented
33#91460C2211yescharacteristic
34#91459—21no—
35#91458C2211yescharacteristic
36#91436—21no—
37#91428C2211yescharacteristic
38D3×C4⋊Dic5C2211yescharacteristic, complemented
39#91365C2211yescharacteristic, complemented
40#91346—21no—
41#91340C2211yescharacteristic, complemented
42C2×#6657C2211yescharacteristic, complemented
43C3×C5×C22⋊C8C2211yescharacteristic, complemented
44#91105C2211yescharacteristic
45#91105C2211yescharacteristic, complemented
46C5×(C2×D3)⋊C8C2211yescharacteristic, complemented
47C5×Dic3⋊C8C2211yescharacteristic, complemented
48C5×C8×Dic3C2211yescharacteristic, complemented
49C3×#3953C2211yescharacteristic, complemented
50C3×#3953C2211yescharacteristic, complemented
51C3×#3949C2211yescharacteristic, complemented
52C3×#3949C2211yescharacteristic, complemented
53#90987C2211yescharacteristic, complemented
54#90974C2211yescharacteristic, complemented
55#90968C2211yescharacteristic
56#90968C2211yescharacteristic
57#90968C2211yescharacteristic, complemented
58#90968C2211yescharacteristic, complemented
59#90965C2211yescharacteristic, complemented
60#81342—51nomaximal, Hall
61D4×D20—31no—
62#65877—31no—
63C5×C8×D4—31no—
64#65403—31no—
65#65403—31no—
66C2×#3953—31no—
67C2×#3953—31no—
68#65137—31no—
69#65131—31no—
70#65024—31no—
71#65024D311yescharacteristic, complemented
72#65020—31no—
73#65020—31no—
74#64983—31no—
75C4×#677—31no—
76C23×D15—21no—
77C22×D3×D5—21no—
78C22×C3×C4×C5C2311yescharacteristic
79C2×D60—22no—
80C2×D60—21no—
81C2×D60—41no—
82C2×D60C2311yescharacteristic
83C2×D60C2311yescharacteristic
84C2×Dic30C2311yescharacteristic
85C2×C5×#67D411yescharacteristic
86C2×C4×C5×D3C2311yescharacteristic
87C2×C3×C22⋊D5—21no—
88C22×C3×Dic5—21no—
89C2×C3×D20C2311yescharacteristic
90#6790—44no—
91C2×#1204—21no—
92C2×#1203—21no—
93C2×#1202—21no—
94C2×#1202—21no—
95C2×#1202—21no—
96C2×#1200—21no—
97C2×D3×Dic5—21no—
98D3×D20—22no—
99D3×D20—41no—
100C2×C3×C5×C8C2311yescharacteristic
101C2×C3×C5×C8C2311yescharacteristic
102#6719—21no—
103C4⋊Dic15C2311yescharacteristic
104#6712—21no—
105#6706—22no—
106#6706—41no—
107C5×#217D411yescharacteristic
108C5×(C2×D3)⋊C4D411yescharacteristic
109C5×Dic3⋊C4D411yescharacteristic
110C4×C5×Dic3C2311yescharacteristic
111C2×C5×C3⋊C8—41no—
112C2×C5×C3⋊C8C2311yescharacteristic
113C2×C5×C3⋊C8C2311yescharacteristic
114C5×D3×C8—41no—
115C3×#685—21no—
116C3×C4⋊Dic5—21no—
117C3×C4⋊Dic5C2311yescharacteristic
118C3×C4⋊Dic5C2311yescharacteristic
119C3×C4⋊Dic5C2311yescharacteristic
120Dic3⋊Dic5—21no—
121Dic3⋊Dic5—21no—
122#6669—21no—
123#6668—21no—
124#6667—21no—
125#6667—21no—
126(C2×D3)⋊Dic5—21no—
127Dic3×Dic5—21no—
128#6657—41no—
129#5609—51no—
130#5511—51no—
131C3×#481—51no—
132#5041—51no—
133C2×#809—51no—
134#4870—51no—
135#4864—51no—
136#4863—51no—
137#4852—51no—
138#4776—51no—
139D3×#102—51no—
140#4762—51no—
141#4760—51no—
142#4731—51no—
143#67⋊C8D511yescharacteristic, complemented
144C2×D4×D5—61no—
145C22×D20—31no—
146C22×D20—31no—
147C22×C5×C8—31no—
148C22×C5×C8—31no—
149C4×C5×D4—31no—
150D4×Dic5—61no—
151#4076—31no—
152#4076C2×D311yescharacteristic
153C2×C4⋊Dic5—31no—
154C2×C4⋊Dic5C2×D311yescharacteristic, complemented
155#4070—31no—
156#4070—31no—
157C2×#677—31no—
158C2×#677—31no—
159C2×#677—31no—
160#4041—61no—
161#4036—61no—
162#4028—61no—
163#4028—61no—
164#4024—61no—
165#4024—61no—
166#4020—31no—
167C4×D20—31no—
168#4015—31no—
169C4×Dic10—31no—
170C5×C4⋊C8—31no—
171C5×C22⋊C8—31no—
172C5×C22⋊C8C2×D311yescharacteristic, complemented
173C4×C5×C8—31no—
174#3953—31no—
175#3953—31no—
176#3953—31no—
177#3953—31no—
178#3953—31no—
179#3953—31no—
180#3953—31no—
181#3953C2×D311yescharacteristic, complemented
182#3953C2×D311yescharacteristic, complemented
183#3949—31no—
184#3949C2×D311yescharacteristic, complemented
185#3949C2×D311yescharacteristic, complemented
186#3948—31no—
187#3295—151noSylow
188C23×C3×C5C2×D411yescharacteristic
189C22×D15—21no—
190C22×D15—21no—
191C22×D15—42no—
192C22×D15—42no—
193C22×D15—81no—
194C22×C5×D3C2×D411yescharacteristic
195C22×C3×D5—21no—
196C2×D3×D5—42no—
197C2×D3×D5—42no—
198C2×D3×D5—81no—
199C2×C3×C4×C5—21no—
200C2×C3×C4×C5—21no—
201C2×C3×C4×C5C2×D411yescharacteristic
202C2×C3×C4×C5C2411yescharacteristic
203C2×Dic15—21no—
204C2×Dic15—21no—
205D60—21no—
206D60—21no—
207D60—21no—
208D60—42no—
209D60#4112yes—
210Dic30—21no—
211Dic30—21no—
212C5×#67SD1614yescomplemented
213C2×C5×Dic3C2×D411yescharacteristic
214C2×C5×Dic3C2×D411yescharacteristic
215C2×C5×Dic3C2×D411yescharacteristic
216C4×C5×D3—21no—
217C4×C5×D3—21no—
218C3×C22⋊D5—42no—
219C2×C3×Dic5—21no—
220C2×C3×Dic5—21no—
221C2×C3×Dic5—21no—
222C2×C3×Dic5—81no—
223C3×D20—21no—
224C3×D20—21no—
225#1204—81no—
226#1203—42no—
227#1202—42no—
228#1202—42no—
229#1202—81no—
230#1200—42no—
231D3×Dic5—81no—
232C3×C5×C8—21no—
233C3×C5×C8—21no—
234C5×C3⋊C8—21no—
235C5×C3⋊C8—21no—
236C2×D3×D4—51no—
237C2×D3×D4—101no—
238C22×D12—51no—
239C3×#121—51no—
240C2×C3×C4⋊C4—51no—
241#940—51no—
242#937—101no—
243C2×#214—51no—
244C4×#67—101no—
245C4×#67C2×D511yescharacteristic
246#924—51no—
247#924—101no—
248C22×C3⋊C8C2×D511yescharacteristic, complemented
249C2×#204—51no—
250C2×#204—51no—
251C2×D3×C8C2×D511yescharacteristic, complemented
252#897—51no—
253#896—101no—
254#895—51no—
255#893—51no—
256D3×C4⋊C4—51no—
257#889—101no—
258#888—51no—
259#887—51no—
260#884—101no—
261#882—101no—
262C3×#106—51no—
263C3×#106—51no—
264C3×#102—51no—
265C3×#102—51no—
266C3×C22⋊C8C2×D511yescharacteristic, complemented
267#832—51no—
268#821—51no—
269#821—51no—
270(C2×D3)⋊C8C2×D511yescharacteristic, complemented
271Dic3⋊C8C2×D511yescharacteristic, complemented
272C8×Dic3C2×D511yescharacteristic, complemented
273#810—51no—
274#809—51no—
275#809—51no—
276#809—51no—
277#809—51no—
278#808—51no—
279C23×D5—61no—
280C23×D5—61no—
281C2×C5×D4—31no—
282C22×C4×C5—31no—
283C22×C4×C5C22×D311yescharacteristic
284C2×C22⋊D5—21no—
285C2×C22⋊D5—61no—
286C22×Dic5—21no—
287C22×Dic5—61no—
288D4×D5—124no—
289C2×D20—31no—
290C2×D20—31no—
291C2×D20—62no—
292C2×D20—62no—
293C2×D20—61no—
294C2×D20—61no—
295C2×D20—61no—
296C2×D20—61no—
297C2×D20—121no—
298C2×D20—121no—
299C2×D20C22×D311yescharacteristic
300C2×C4×D5—61no—
301C2×Dic10—31no—
302C2×Dic10—61no—
303C2×C5×C8—31no—
304C2×C5×C8—31no—
305C2×C5×C8—121no—
306C2×C5×C8—121no—
307C2×C5×C8C22×D311yescharacteristic
308C2×C5×C8C22×D311yescharacteristic
309C5×C4⋊C4—31no—
310C5×C22⋊C4—31no—
311C5×C22⋊C4—31no—
312C42×C5—31no—
313C22⋊Dic5—61no—
314C22⋊Dic5—61no—
315#685—21no—
316#685—61no—
317#685—61no—
318C4⋊Dic5—21no—
319C4⋊Dic5—31no—
320C4⋊Dic5—61no—
321C4⋊Dic5—61no—
322C4⋊Dic5C22×D311yescharacteristic
323C4⋊Dic5C22×D311yescharacteristic
324C4⋊Dic5C22×D311yescharacteristic
325#683—61no—
326#683—61no—
327#683—61no—
328C4×Dic5—61no—
329#677—62no—
330#677—121no—
331#677—121no—
332#554—151no—
333D42—151no—
334#486—151no—
335#481—51no—
336#481—151no—
337#476—151no—
338#465—151no—
339#465—151no—
340#460—151no—
341#450—151no—
342#450—151no—
343C4×SD16—151no—
344C8×D4—31no—
345C2×#102—151no—
346C2×#102—151no—
347C22×C3×C5—21no—
348C22×C3×C5—21no—
349C22×C3×C5C2×SD1612yes—
350C22×C3×C5C22×D411yescharacteristic
351C2×D15—22no—
352C2×D15—41no—
353C2×D15—41no—
354C2×D15—41no—
355C2×D15—41no—
356C2×D15—41no—
357C2×D15—84no—
358C2×C5×D3—21no—
359C2×C5×D3—21no—
360C2×C5×D3C2×SD1612yes—
361C2×C3×D5—41no—
362C2×C3×D5—41no—
363C2×C3×D5—41no—
364D3×D5—84no—
365C3×C4×C5—21no—
366C3×C4×C5C2×#4111yescharacteristic
367C3×C4×C5H(5,𝔽2)11yescharacteristic
368Dic15—41no—
369Dic15—41no—
370C3×Dic5—41no—
371C3×Dic5—41no—
372C3×Dic5—41no—
373C5×Dic3—21no—
374C5×Dic3—21no—
375C5×Dic3C2×SD1612yes—
376C23×D3—101no—
377C23×D3—101no—
378C2×C3×D4—51no—
379C2×C3×D4—101no—
380C22×C3×C4—101no—
381C22×C3×C4C22×D511yescharacteristic
382C2×#67—101no—
383C2×#67—101no—
384C2×#67—101no—
385C2×#67D2011yescharacteristic
386D3×D4—102no—
387D3×D4—201no—
388D3×D4—204no—
389C2×D12—51no—
390C2×D12—51no—
391C2×D12—102no—
392C2×D12—101no—
393C2×D12—101no—
394C2×D12—201no—
395C2×C4×D3—101no—
396C2×C4×D3—101no—
397C2×C4×D3C22×D511yescharacteristic
398C2×Dic6—51no—
399C2×Dic6—101no—
400C2×C3×C8C22×D511yescharacteristic
401C2×C3×C8C22×D511yescharacteristic
402C3×C4⋊C4—51no—
403C3×C4⋊C4—51no—
404C3×C4⋊C4—51no—
405C3×C4⋊C4—101no—
406C3×C22⋊C4—101no—
407#217—101no—
408#217D2011yescharacteristic
409#214—201no—
410(C2×D3)⋊C4—101no—
411(C2×D3)⋊C4—101no—
412(C2×D3)⋊C4—101no—
413(C2×D3)⋊C4D2011yescharacteristic
414C4⋊Dic3—51no—
415C4⋊Dic3—101no—
416Dic3⋊C4—101no—
417Dic3⋊C4—101no—
418Dic3⋊C4—101no—
419Dic3⋊C4—101no—
420Dic3⋊C4D2011yescharacteristic
421C4×Dic3—101no—
422C4×Dic3C22×D511yescharacteristic
423C2×C3⋊C8—41no—
424C2×C3⋊C8C22×D511yescharacteristic
425C2×C3⋊C8C22×D511yescharacteristic
426#204—102no—
427#204—201no—
428D3×C8—41no—
429C23×C5—31no—
430C23×C5D3×D411yescharacteristic
431C22×D5—21no—
432C22×D5—61no—
433C22×D5—61no—
434C22×D5—122no—
435C22×D5—122no—
436C22×D5—122no—
437C22×D5—122no—
438C22×D5—241no—
439C22×D5—241no—
440C5×D4—34no—
441C2×C4×C5—21no—
442C2×C4×C5—21no—
443C2×C4×C5—31no—
444C2×C4×C5—31no—
445C2×C4×C5—31no—
446C2×C4×C5—61no—
447C2×C4×C5—61no—
448C2×C4×C5D3×D411yescharacteristic
449C2×C4×C5C23×D311yescharacteristic
450C22⋊D5—42no—
451C22⋊D5—122no—
452C2×Dic5—21no—
453C2×Dic5—21no—
454C2×Dic5—21no—
455C2×Dic5—61no—
456C2×Dic5—61no—
457C2×Dic5—81no—
458C2×Dic5—241no—
459D20—21no—
460D20—21no—
461D20—32no—
462D20—61no—
463D20—61no—
464D20—61no—
465D20—122no—
466D20—122no—
467D20—122no—
468D20—241no—
469C4×D5—122no—
470Dic10—61no—
471Dic10—61no—
472Dic10—241no—
473C5×C8—21no—
474C5×C8—21no—
475C5×C8—61no—
476C5×C8—61no—
477C22×D4—151no—
478C22×D4—151no—
479C22×D4—301no—
480C2×SD16—151no—
481C2×SD16—151no—
482C2×SD16—151no—
483C22×C8—31no—
484C22×C8—31no—
485C4⋊Q8—151no—
486#127—151no—
487#125—301no—
488C22⋊Q8—151no—
489C22⋊Q8—151no—
490C22⋊Q8—301no—
491C22⋊Q8—301no—
492#121—51no—
493#121—151no—
494#121—301no—
495#120—301no—
496#120—301no—
497C4×Q8—151no—
498C4×D4—31no—
499C4×D4—151no—
500C4×D4—301no—
501C2×C4⋊C4—51no—
502C2×C4⋊C4—151no—
503#106—51no—
504#106—51no—
505#106—151no—
506C4⋊C8—31no—
507#103—151no—
508#102—51no—
509#102—51no—
510#102—151no—
511#102—151no—
512#102—151no—
513#102—151no—
514#102—151no—
515#102—151no—
516#102—151no—
517C22⋊C8—31no—
518C22⋊C8D3×D511yescharacteristic, complemented
519C4×C8—31no—
520C2×C3×C5—22no—
521C2×C3×C5#54611yescharacteristic
522C2×C3×C5C22×SD1611yescharacteristic
523C2×C3×C5#57611yescharacteristic
524D15—42no—
525D15—81no—
526C3×D5—81no—
527C5×D3—22no—
528C23×C3—101no—
529C23×C3C2×D2011yescharacteristic
530C22×D3—101no—
531C22×D3—101no—
532C22×D3—202no—
533C22×D3—202no—
534C22×D3—202no—
535C22×D3—202no—
536C22×D3—401no—
537C22×D3—401no—
538C22×D3C2×D2011yescharacteristic
539C3×D4—101no—
540C3×D4—101no—
541C3×D4—202no—
542C2×C3×C4—21no—
543C2×C3×C4—21no—
544C2×C3×C4—101no—
545C2×C3×C4—101no—
546C2×C3×C4—101no—
547C2×C3×C4—401no—
548C2×C3×C4C2×D2011yescharacteristic
549C2×C3×C4C23×D511yescharacteristic
550#67—202no—
551#67—202no—
552#67—401no—
553#67#67714yescomplemented
554C2×Dic3—101no—
555C2×Dic3—101no—
556C2×Dic3C2×D2011yescharacteristic
557C2×Dic3C2×D2011yescharacteristic
558C2×Dic3C2×D2011yescharacteristic
559D12—52no—
560D12—101no—
561D12—101no—
562D12—101no—
563D12—202no—
564D12—202no—
565C4×D3—21no—
566C4×D3—21no—
567C4×D3—202no—
568C4×D3—401no—
569Dic6—101no—
570Dic6—101no—
571Dic6—401no—
572C3×C8—21no—
573C3×C8—21no—
574C3⋊C8—21no—
575C3⋊C8—21no—
576C22×C5—21no—
577C22×C5—21no—
578C22×C5—32no—
579C22×C5—61no—
580C22×C5—61no—
581C22×C5D3×SD1612yes—
582C22×C5C2×D3×D411yescharacteristic
583C2×D5—41no—
584C2×D5—41no—
585C2×D5—41no—
586C2×D5—62no—
587C2×D5—121no—
588C2×D5—121no—
589C2×D5—121no—
590C2×D5—121no—
591C2×D5—121no—
592C2×D5—244no—
593C2×D5—244no—
594C4×C5—21no—
595C4×C5—32no—
596C4×C5—61no—
597C4×C5—61no—
598C4×C5D3×#4111yescharacteristic
599C4×C5#100911yescharacteristic
600Dic5—41no—
601Dic5—41no—
602Dic5—41no—
603Dic5—121no—
604Dic5—121no—
605C24—301no—
606C24—301no—
607C2×Q8—151no—
608C2×Q8—301no—
609C2×D4—31no—
610C2×D4—51no—
611C2×D4—101no—
612C2×D4—151no—
613C2×D4—151no—
614C2×D4—302no—
615C2×D4—301no—
616C2×D4—301no—
617C2×D4—301no—
618C2×D4—302no—
619C2×D4—301no—
620C2×D4—301no—
621C2×D4—601no—
622C2×D4—601no—
623C2×D4—604no—
624C22×C4—31no—
625C22×C4—101no—
626C22×C4—301no—
627C22×C4—301no—
628C22×C4C2×D3×D511yescharacteristic
629SD16—302no—
630SD16—601no—
631SD16—601no—
632C2×C8—31no—
633C2×C8—31no—
634C2×C8—121no—
635C2×C8—121no—
636C2×C8C2×D3×D511yescharacteristic
637C2×C8C2×D3×D511yescharacteristic
638C4⋊C4—31no—
639C4⋊C4—51no—
640C4⋊C4—51no—
641C4⋊C4—51no—
642C4⋊C4—101no—
643C4⋊C4—151no—
644C4⋊C4—301no—
645C4⋊C4—301no—
646C4⋊C4—301no—
647C4⋊C4—301no—
648C4⋊C4—301no—
649C22⋊C4—31no—
650C22⋊C4—31no—
651C22⋊C4—101no—
652C22⋊C4—301no—
653C22⋊C4—301no—
654C22⋊C4—301no—
655C22⋊C4—301no—
656C42—31no—
657C42—301no—
658C3×C5#329511yescharacteristic, complemented, Hall
659C22×C3—21no—
660C22×C3—21no—
661C22×C3—201no—
662C22×C3—201no—
663C22×C3—201no—
664C22×C3C2×#67712yes—
665C22×C3C22×D2011yescharacteristic
666C2×D3—21no—
667C2×D3—21no—
668C2×D3—102no—
669C2×D3—201no—
670C2×D3—201no—
671C2×D3—201no—
672C2×D3—201no—
673C2×D3—201no—
674C2×D3—404no—
675C2×D3—404no—
676C2×D3C2×#67712yes—
677C3×C4—21no—
678C3×C4—201no—
679C3×C4—201no—
680C3×C4—201no—
681C3×C4#414411yescharacteristic
682C3×C4D5×#4111yescharacteristic
683Dic3—21no—
684Dic3—21no—
685Dic3—201no—
686Dic3—201no—
687Dic3C2×#67712yes—
688C2×C5—22no—
689C2×C5—62no—
690C2×C5#565411yescharacteristic
691C2×C5C2×D3×SD1611yescharacteristic
692C2×C5#577411yescharacteristic
693D5—81no—
694D5—122no—
695D5—241no—
696C23—31no—
697C23—101no—
698C23—301no—
699C23—301no—
700C23—602no—
701C23—602no—
702C23—602no—
703C23—602no—
704C23—1201no—
705C23—1201no—
706C23D3×D2011yescharacteristic
707Q8—301no—
708Q8—301no—
709Q8—1201no—
710D4—34no—
711D4—101no—
712D4—101no—
713D4—152no—
714D4—202no—
715D4—301no—
716D4—301no—
717D4—301no—
718D4—602no—
719D4—602no—
720D4—602no—
721D4—602no—
722D4—1201no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—31no—
726C2×C4—31no—
727C2×C4—31no—
728C2×C4—61no—
729C2×C4—61no—
730C2×C4—101no—
731C2×C4—101no—
732C2×C4—101no—
733C2×C4—301no—
734C2×C4—301no—
735C2×C4—401no—
736C2×C4—602no—
737C2×C4—1201no—
738C2×C4D3×D2011yescharacteristic
739C2×C4C22×D3×D511yescharacteristic
740C8—21no—
741C8—21no—
742C8—61no—
743C8—61no—
744C2×C3—22no—
745C2×C3—401no—
746C2×C3#6588811yescharacteristic
747C2×C3C22×#67711yescharacteristic
748C2×C3#6608611yescharacteristic
749D3—22no—
750D3—202no—
751D3—401no—
752C5#8134211yescharacteristic, complemented, Sylow
753C22—21no—
754C22—21no—
755C22—32no—
756C22—61no—
757C22—61no—
758C22—201no—
759C22—201no—
760C22—201no—
761C22—302no—
762C22—601no—
763C22—601no—
764C22—601no—
765C22—601no—
766C22—601no—
767C22—1204no—
768C22—1204no—
769C22D3×#67712yes—
770C22C2×D3×D2011yescharacteristic
771C4—21no—
772C4—32no—
773C4—61no—
774C4—61no—
775C4—201no—
776C4—201no—
777C4—201no—
778C4—601no—
779C4—601no—
780C4#9202411yescharacteristic
781C4#9202711yescharacteristic
782C3#1061117011yescharacteristic, complemented, Sylow
783C2—22no—
784C2—62no—
785C2—401no—
786C2—602no—
787C2—1201no—
788C2#1175327111yescharacteristic
789C2C2×D3×#67711yescharacteristic
790C2#1175403111yescharacteristic
subgroupG/H
centerC22C2×D3×D20
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×C22⋊C8C22
socleC22×C3×C5C22×D4
prime radical#11754661C2
hypercenterC22⋊C8D3×D5
hypocenterC3×C5#3295
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
2. #11754494C2semidirect
3. #11750832C2semidirect
4. C5×#67⋊C8C2semidirect
5. C3×#65024C2semidirect
6. #11748539C2semidirect
7. C2×#90968C2semidirect
8. #11748120C2semidirect
9. D3×#3953C2semidirect
10. #11748004C2semidirect
11. #11748003C2semidirect
12. #11747914C2semidirect
13. #11747790C2semidirect
14. #11747789C2semidirect
15. #11747625C2semidirect
20. #91813C22semidirect
22. C2×#6706C22semidirect
24. C22×C5×C3⋊C8C22semidirect
25. C2×C5×D3×C8C22semidirect
27. C2×C3×C4⋊Dic5C22semidirect
32. #91469C22semidirect
38. D3×C4⋊Dic5C22semidirect
39. #91365C22semidirect
41. #91340C22semidirect
42. C2×#6657C22semidirect
43. C3×C5×C22⋊C8C22semidirect
45. #91105C22semidirect
46. C5×(C2×D3)⋊C8C22semidirect
47. C5×Dic3⋊C8C22semidirect
48. C5×C8×Dic3C22semidirect
49. C3×#3953C22semidirect
50. C3×#3953C22semidirect
51. C3×#3949C22semidirect
52. C3×#3949C22semidirect
53. #90987C22semidirect
54. #90974C22semidirect
57. #90968C22semidirect
58. #90968C22semidirect
59. #90965C22semidirect
71. #65024D3semidirect
143. #67⋊C8D5semidirect
154. C2×C4⋊Dic5C2×D3semidirect
172. C5×C22⋊C8C2×D3semidirect
181. #3953C2×D3semidirect
182. #3953C2×D3semidirect
184. #3949C2×D3semidirect
185. #3949C2×D3semidirect
212. C5×#67SD16semidirect
248. C22×C3⋊C8C2×D5semidirect
251. C2×D3×C8C2×D5semidirect
266. C3×C22⋊C8C2×D5semidirect
270. (C2×D3)⋊C8C2×D5semidirect
271. Dic3⋊C8C2×D5semidirect
272. C8×Dic3C2×D5semidirect
518. C22⋊C8D3×D5semidirect
553. #67#677semidirect
658. C3×C5#3295semidirect
752. C5#81342semidirect
782. C3#10611170semidirect

Maximal subgroups

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

subgroupindex
#117546612
#117544942
#117508322
C5×#67⋊C82
C3×#650242
#117485392
C2×#909682
#117481202
D3×#39532
#117480042
#117480032
#117479142
#117477902
#117477892
#117476252
#106111703
#813425