Finite Group Databasebeta

← #14458472

Subgroups — #14458472

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#67×D20C211yesmaximal, characteristic
2#11754514C211yesmaximal, characteristic, complemented
3#11750836C211yesmaximal, characteristic, complemented
4C5×#67⋊C8C211yesmaximal, characteristic, complemented
5C3×#65020C211yesmaximal, characteristic, complemented
6#11748541C211yesmaximal, characteristic, complemented
7C2×#90965C211yesmaximal, characteristic, complemented
8#11748110C211yesmaximal, characteristic, complemented
9D3×#3953C211yesmaximal, characteristic, complemented
10#11748003C211yesmaximal, characteristic, complemented
11#11747913C211yesmaximal, characteristic, complemented
12#11747912C211yesmaximal, characteristic, complemented
13#11747839C211yesmaximal, characteristic, complemented
14Dic3×#677C211yesmaximal, characteristic, complemented
15#11747781C211yesmaximal, characteristic, complemented
16#10611170—31nomaximal, Hall
17C22×C3×D20C2211yescharacteristic
18C2×D5×#67—21no—
19C2×D3×D20C2211yescharacteristic
20#91819C2211yescharacteristic
21C2×C4⋊Dic15C2211yescharacteristic, complemented
22C4×C5×#67C2211yescharacteristic
23C22×C5×C3⋊C8C2211yescharacteristic, complemented
24C2×C5×D3×C8C2211yescharacteristic, complemented
25C3×#4070C2211yescharacteristic, complemented
26C2×C3×#677C2211yescharacteristic
27C2×C3×#677C2211yescharacteristic, complemented
28#91576—21no—
29#91564—21no—
30#67⋊Dic5—21no—
31#91474—21no—
32#91469C2211yescharacteristic, complemented
33#91458C2211yescharacteristic
34#91456C2211yescharacteristic
35D3×C4⋊Dic5C2211yescharacteristic, complemented
36Dic3×D20C2211yescharacteristic
37#91417—21no—
38#91409—21no—
39#91369C2211yescharacteristic, complemented
40#91343—21no—
41Dic3×Dic10C2211yescharacteristic, complemented
42C2×#6658C2211yescharacteristic, complemented
43C3×C5×C22⋊C8C2211yescharacteristic, complemented
44#91105C2211yescharacteristic, complemented
45#91105C2211yescharacteristic, complemented
46#91101C2211yescharacteristic, complemented
47#91101C2211yescharacteristic, complemented
48C5×(C2×D3)⋊C8C2211yescharacteristic, complemented
49C5×Dic3⋊C8C2211yescharacteristic, complemented
50C5×C8×Dic3C2211yescharacteristic, complemented
51C3×#3953C2211yescharacteristic
52C3×#3953C2211yescharacteristic, complemented
53#90987C2211yescharacteristic, complemented
54#90971C2211yescharacteristic, complemented
55#90968C2211yescharacteristic, complemented
56#90965C2211yescharacteristic
57#90965C2211yescharacteristic
58#90965C2211yescharacteristic, complemented
59#90965C2211yescharacteristic, complemented
60#80158—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#65024—31no—
72#65020—31no—
73#65020D311yescharacteristic, complemented
74#64983—31no—
75C4×#677—31no—
76C23×C3×D5—21no—
77C22×D3×D5—21no—
78C22×C3×C4×C5C2311yescharacteristic
79C2×#1220—21no—
80C22×Dic15—21no—
81C2×D60C2311yescharacteristic
82C2×C5×#67D411yescharacteristic
83C2×C4×C5×D3C2311yescharacteristic
84C2×C3×D20—22no—
85C2×C3×D20—21no—
86C2×C3×D20—41no—
87C2×C3×D20C2311yescharacteristic
88C2×C3×D20C2311yescharacteristic
89C2×C3×Dic10C2311yescharacteristic
90D5×#67—44no—
91C2×#1204—21no—
92C2×#1202—21no—
93C2×#1202—21no—
94C2×#1202—21no—
95C2×#1201—21no—
96C2×D3×Dic5—21no—
97C2×D5×Dic3—21no—
98D3×D20—22no—
99D3×D20—41no—
100C2×C3×C5×C8C2311yescharacteristic
101C2×C3×C5×C8C2311yescharacteristic
102#6714—21no—
103C4⋊Dic15—21no—
104C4⋊Dic15C2311yescharacteristic
105C4⋊Dic15C2311yescharacteristic
106C4⋊Dic15C2311yescharacteristic
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×C22⋊Dic5—21no—
116C3×C4⋊Dic5C2311yescharacteristic
117C3×#683—21no—
118C3×#677—22no—
119C3×#677—41no—
120Dic3⋊Dic5—21no—
121Dic3⋊Dic5—21no—
122#6669—21no—
123#6668—21no—
124(C2×D3)⋊Dic5—21no—
125#6665—21no—
126#6665—21no—
127Dic3×Dic5—21no—
128#6658—41no—
129D4×#67—51no—
130#5635—51no—
131C3×#450—51no—
132C2×#832—51no—
133#5171—51no—
134#5169—51no—
135#5163—51no—
136Dic3×SD16—51no—
137#5048—51no—
138#4777—51no—
139D3×#102—51no—
140#4761—51no—
141#4760—51no—
142#4735—51no—
143#67⋊C8D511yescharacteristic, complemented
144C2×D4×D5—61no—
145C22×D20—31no—
146C22×D20C2×D311yescharacteristic
147C22×C5×C8—31no—
148C22×C5×C8—31no—
149C4×C5×D4—31no—
150D4×Dic5—61no—
151#4076—31no—
152#4076—31no—
153C2×C4⋊Dic5—31no—
154C2×C4⋊Dic5—31no—
155#4070—31no—
156#4070C2×D311yescharacteristic, complemented
157C2×#677—31no—
158C2×#677C2×D311yescharacteristic
159C2×#677C2×D311yescharacteristic, complemented
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
182#3953C2×D311yescharacteristic, complemented
183#3949—31no—
184#3949—31no—
185#3949—31no—
186#3948—31no—
187#3295—151noSylow
188C23×C3×C5C2×D411yescharacteristic
189C22×D15—21no—
190C22×C5×D3C2×D411yescharacteristic
191C22×C3×D5—21no—
192C22×C3×D5—21no—
193C22×C3×D5—42no—
194C22×C3×D5—42no—
195C22×C3×D5—81no—
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
203#1220—42no—
204C2×Dic15—21no—
205C2×Dic15—21no—
206C2×Dic15—21no—
207C2×Dic15—81no—
208D60—21no—
209D60—21no—
210C5×#67SD1614yescomplemented
211C2×C5×Dic3C2×D411yescharacteristic
212C2×C5×Dic3C2×D411yescharacteristic
213C2×C5×Dic3C2×D411yescharacteristic
214C4×C5×D3—21no—
215C4×C5×D3—21no—
216C2×C3×Dic5—21no—
217C2×C3×Dic5—21no—
218C3×D20—21no—
219C3×D20—21no—
220C3×D20—21no—
221C3×D20—42no—
222C3×D20#4112yes—
223C3×Dic10—21no—
224C3×Dic10—21no—
225#1204—81no—
226#1202—42no—
227#1202—42no—
228#1202—81no—
229#1201—42no—
230D3×Dic5—81no—
231D5×Dic3—42no—
232C3×C5×C8—21no—
233C3×C5×C8—21no—
234C5×C3⋊C8—21no—
235C5×C3⋊C8—21no—
236C22×C3×D4—51no—
237C22×#67—101no—
238C2×D3×D4—51no—
239C2×C3×SD16—51no—
240C2×C3×SD16—51no—
241C3×C22⋊Q8—51no—
242#953—101no—
243#946—51no—
244Q8×Dic3—51no—
245C2×#215—51no—
246#940—51no—
247#939—101no—
248#938—51no—
249#937—101no—
250D4×Dic3—51no—
251#930—51no—
252C4×#67C2×D511yescharacteristic
253C2×C4⋊Dic3—51no—
254C22×C3⋊C8C2×D511yescharacteristic, complemented
255C2×D3×C8C2×D511yescharacteristic, complemented
256#897—101no—
257D3×C4⋊C4—51no—
258#889—101no—
259#888—51no—
260#67⋊C4—101no—
261#878—101no—
262C3×#102—51no—
263C3×#102—51no—
264C3×C22⋊C8C2×D511yescharacteristic, complemented
265#835—51no—
266#832—51no—
267#832—51no—
268#832—51no—
269#832—51no—
270#821—51no—
271#821—51no—
272(C2×D3)⋊C8C2×D511yescharacteristic, complemented
273#817—51no—
274#817—51no—
275Dic3⋊C8C2×D511yescharacteristic, complemented
276C8×Dic3C2×D511yescharacteristic, complemented
277#809—51no—
278#808—51no—
279C23×D5—21no—
280C23×D5—61no—
281C2×C5×D4—31no—
282C22×C4×C5—31no—
283C22×C4×C5C22×D311yescharacteristic
284C2×C22⋊D5—61no—
285C2×C22⋊D5—61no—
286C22×Dic5—61no—
287C22×Dic5—61no—
288D4×D5—124no—
289C2×D20—22no—
290C2×D20—21no—
291C2×D20—31no—
292C2×D20—41no—
293C2×D20—62no—
294C2×D20—61no—
295C2×D20—61no—
296C2×D20—61no—
297C2×D20—121no—
298C2×D20C22×D311yescharacteristic
299C2×D20C22×D311yescharacteristic
300C2×C4×D5—61no—
301C2×Dic10—61no—
302C2×Dic10C22×D311yescharacteristic
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—21no—
314C22⋊Dic5—61no—
315#685—61no—
316#685—61no—
317#685—61no—
318C4⋊Dic5—31no—
319C4⋊Dic5—31no—
320C4⋊Dic5—31no—
321C4⋊Dic5—61no—
322C4⋊Dic5—61no—
323C4⋊Dic5—61no—
324C4⋊Dic5C22×D311yescharacteristic
325#683—21no—
326#683—61no—
327#683—61no—
328C4×Dic5—61no—
329#677—22no—
330#677—41no—
331#677—121no—
332#554—151no—
333D42—151no—
334#486—151no—
335#481—151no—
336#481—151no—
337#476—151no—
338#465—151no—
339#465—151no—
340#460—151no—
341#450—51no—
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—41no—
352C2×D15—41no—
353C2×D15—41no—
354C2×C5×D3—21no—
355C2×C5×D3—21no—
356C2×C5×D3C2×SD1612yes—
357C2×C3×D5—22no—
358C2×C3×D5—41no—
359C2×C3×D5—41no—
360C2×C3×D5—41no—
361C2×C3×D5—41no—
362C2×C3×D5—41no—
363C2×C3×D5—84no—
364D3×D5—84no—
365C3×C4×C5—21no—
366C3×C4×C5C2×#4111yescharacteristic
367C3×C4×C5H(5,𝔽2)11yescharacteristic
368Dic15—41no—
369Dic15—41no—
370Dic15—41no—
371C3×Dic5—41no—
372C3×Dic5—41no—
373C5×Dic3—21no—
374C5×Dic3—21no—
375C5×Dic3C2×SD1612yes—
376C24×C3—101no—
377C23×D3—101no—
378C2×C3×Q8—51no—
379C2×C3×D4—51no—
380C2×C3×D4—51no—
381C2×C3×D4—102no—
382C2×C3×D4—101no—
383C2×C3×D4—201no—
384C22×C3×C4C22×D511yescharacteristic
385C2×#67—101no—
386C2×#67—101no—
387C2×#67—101no—
388C2×#67—101no—
389C2×#67—101no—
390C2×#67—204no—
391C2×#67D2011yescharacteristic
392C22×Dic3—101no—
393C22×Dic3—101no—
394D3×D4—102no—
395D3×D4—201no—
396C2×D12—51no—
397C2×C4×D3—101no—
398C2×C4×D3C22×D511yescharacteristic
399C2×Dic6—101no—
400C3×SD16—102no—
401C3×SD16—201no—
402C2×C3×C8C22×D511yescharacteristic
403C2×C3×C8C22×D511yescharacteristic
404C3×C4⋊C4—51no—
405C3×C4⋊C4—101no—
406C3×C22⋊C4—101no—
407#217—101no—
408#217—101no—
409#217D2011yescharacteristic
410#215—201no—
411(C2×D3)⋊C4—101no—
412(C2×D3)⋊C4—101no—
413(C2×D3)⋊C4D2011yescharacteristic
414C4⋊Dic3—51no—
415C4⋊Dic3—51no—
416C4⋊Dic3—51no—
417C4⋊Dic3—101no—
418C4⋊Dic3—101no—
419Dic3⋊C4—101no—
420Dic3⋊C4—101no—
421Dic3⋊C4—101no—
422Dic3⋊C4D2011yescharacteristic
423C4×Dic3—101no—
424C4×Dic3C22×D511yescharacteristic
425C2×C3⋊C8—41no—
426C2×C3⋊C8C22×D511yescharacteristic
427C2×C3⋊C8C22×D511yescharacteristic
428D3×C8—41no—
429C23×C5—31no—
430C23×C5D3×D411yescharacteristic
431C22×D5—21no—
432C22×D5—21no—
433C22×D5—42no—
434C22×D5—42no—
435C22×D5—61no—
436C22×D5—81no—
437C22×D5—122no—
438C22×D5—122no—
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—122no—
451C22⋊D5—122no—
452C2×Dic5—21no—
453C2×Dic5—21no—
454C2×Dic5—61no—
455C2×Dic5—61no—
456C2×Dic5—61no—
457C2×Dic5—241no—
458C2×Dic5—241no—
459D20—21no—
460D20—21no—
461D20—21no—
462D20—42no—
463D20—61no—
464D20—61no—
465D20—122no—
466D20—122no—
467D20—241no—
468D20#23712yes—
469C4×D5—122no—
470Dic10—21no—
471Dic10—21no—
472Dic10—241no—
473C5×C8—21no—
474C5×C8—21no—
475C5×C8—61no—
476C5×C8—61no—
477C22×D4—51no—
478C22×D4—151no—
479C22×D4—301no—
480C2×SD16—51no—
481C2×SD16—51no—
482C2×SD16—151no—
483C22×C8—31no—
484C22×C8—31no—
485C4⋊Q8—151no—
486#127—151no—
487#125—301no—
488C22⋊Q8—51no—
489C22⋊Q8—151no—
490C22⋊Q8—301no—
491C22⋊Q8—301no—
492#121—151no—
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—151no—
502C2×C4⋊C4—151no—
503#106—151no—
504#106—151no—
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—81no—
525C3×D5—42no—
526C3×D5—81no—
527C5×D3—22no—
528C23×C3—101no—
529C23×C3—101no—
530C23×C3—202no—
531C23×C3—202no—
532C23×C3—401no—
533C23×C3C2×D2011yescharacteristic
534C22×D3—101no—
535C22×D3—202no—
536C22×D3—202no—
537C22×D3—401no—
538C22×D3C2×D2011yescharacteristic
539C3×Q8—101no—
540C3×Q8—101no—
541C3×D4—52no—
542C3×D4—101no—
543C3×D4—101no—
544C3×D4—101no—
545C3×D4—202no—
546C2×C3×C4—21no—
547C2×C3×C4—21no—
548C2×C3×C4—101no—
549C2×C3×C4—101no—
550C2×C3×C4C2×D2011yescharacteristic
551C2×C3×C4C23×D511yescharacteristic
552#67—202no—
553#67—202no—
554#67—202no—
555#67—202no—
556#67—401no—
557#67#67714yescomplemented
558C2×Dic3—101no—
559C2×Dic3—101no—
560C2×Dic3—101no—
561C2×Dic3—202no—
562C2×Dic3—401no—
563C2×Dic3C2×D2011yescharacteristic
564C2×Dic3C2×D2011yescharacteristic
565C2×Dic3C2×D2011yescharacteristic
566D12—101no—
567D12—101no—
568C4×D3—21no—
569C4×D3—21no—
570C4×D3—401no—
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—22no—
584C2×D5—41no—
585C2×D5—41no—
586C2×D5—41no—
587C2×D5—41no—
588C2×D5—41no—
589C2×D5—84no—
590C2×D5—121no—
591C2×D5—121no—
592C2×D5—121no—
593C2×D5—244no—
594C4×C5—21no—
595C4×C5—32no—
596C4×C5—61no—
597C4×C5—61no—
598C4×C5C2×#23711yescharacteristic
599C4×C5#100411yescharacteristic
600Dic5—41no—
601Dic5—41no—
602Dic5—121no—
603Dic5—121no—
604Dic5—121no—
605C24—101no—
606C24—301no—
607C2×Q8—51no—
608C2×Q8—301no—
609C2×D4—31no—
610C2×D4—51no—
611C2×D4—51no—
612C2×D4—102no—
613C2×D4—101no—
614C2×D4—151no—
615C2×D4—201no—
616C2×D4—301no—
617C2×D4—301no—
618C2×D4—301no—
619C2×D4—302no—
620C2×D4—301no—
621C2×D4—301no—
622C2×D4—601no—
623C2×D4—604no—
624C22×C4—31no—
625C22×C4—301no—
626C22×C4—301no—
627C22×C4—301no—
628C22×C4C2×D3×D511yescharacteristic
629SD16—102no—
630SD16—201no—
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—101no—
641C4⋊C4—151no—
642C4⋊C4—151no—
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—102no—
662C22×C3—201no—
663C22×C3—201no—
664C22×C3—201no—
665C22×C3—201no—
666C22×C3—201no—
667C22×C3—404no—
668C22×C3C2×#67712yes—
669C22×C3C22×D2011yescharacteristic
670C2×D3—21no—
671C2×D3—21no—
672C2×D3—201no—
673C2×D3—201no—
674C2×D3—201no—
675C2×D3—404no—
676C2×D3C2×#67712yes—
677C3×C4—21no—
678C3×C4—201no—
679C3×C4—201no—
680C3×C4#414411yescharacteristic
681C3×C4D5×#4111yescharacteristic
682Dic3—21no—
683Dic3—21no—
684Dic3—201no—
685Dic3—201no—
686Dic3—201no—
687Dic3C2×#67712yes—
688C2×C5—22no—
689C2×C5—62no—
690C2×C5#559111yescharacteristic
691C2×C5C2×D3×SD1611yescharacteristic
692C2×C5#577411yescharacteristic
693D5—42no—
694D5—81no—
695D5—241no—
696C23—31no—
697C23—101no—
698C23—101no—
699C23—202no—
700C23—202no—
701C23—301no—
702C23—401no—
703C23—602no—
704C23—602no—
705C23—1201no—
706C23D3×D2011yescharacteristic
707Q8—101no—
708Q8—101no—
709Q8—1201no—
710D4—34no—
711D4—52no—
712D4—101no—
713D4—101no—
714D4—101no—
715D4—202no—
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—301no—
733C2×C4—301no—
734C2×C4—301no—
735C2×C4—602no—
736C2×C4—1201no—
737C2×C4—1201no—
738C2×C4D3×D2011yescharacteristic
739C2×C4C22×D3×D511yescharacteristic
740C8—21no—
741C8—21no—
742C8—61no—
743C8—61no—
744C2×C3—22no—
745C2×C3—202no—
746C2×C3—401no—
747C2×C3#6588811yescharacteristic
748C2×C3C22×#67711yescharacteristic
749C2×C3#6608611yescharacteristic
750D3—22no—
751D3—401no—
752C5#8015811yescharacteristic, complemented, Sylow
753C22—21no—
754C22—21no—
755C22—32no—
756C22—61no—
757C22—61no—
758C22—102no—
759C22—201no—
760C22—201no—
761C22—201no—
762C22—201no—
763C22—201no—
764C22—404no—
765C22—601no—
766C22—601no—
767C22—601no—
768C22—1204no—
769C22D3×#67712yes—
770C22C2×D3×D2011yescharacteristic
771C4—21no—
772C4—32no—
773C4—61no—
774C4—61no—
775C4—201no—
776C4—201no—
777C4—601no—
778C4—601no—
779C4—601no—
780C4D5×#23711yescharacteristic
781C4#9202511yescharacteristic
782C3#1061117011yescharacteristic, complemented, Sylow
783C2—22no—
784C2—62no—
785C2—202no—
786C2—401no—
787C2—1201no—
788C2#1175326711yescharacteristic
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#67×D20C2
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. #11754514C2semidirect
3. #11750836C2semidirect
4. C5×#67⋊C8C2semidirect
5. C3×#65020C2semidirect
6. #11748541C2semidirect
7. C2×#90965C2semidirect
8. #11748110C2semidirect
9. D3×#3953C2semidirect
10. #11748003C2semidirect
11. #11747913C2semidirect
12. #11747912C2semidirect
13. #11747839C2semidirect
14. Dic3×#677C2semidirect
15. #11747781C2semidirect
21. C2×C4⋊Dic15C22semidirect
23. C22×C5×C3⋊C8C22semidirect
24. C2×C5×D3×C8C22semidirect
25. C3×#4070C22semidirect
27. C2×C3×#677C22semidirect
32. #91469C22semidirect
35. D3×C4⋊Dic5C22semidirect
39. #91369C22semidirect
41. Dic3×Dic10C22semidirect
42. C2×#6658C22semidirect
43. C3×C5×C22⋊C8C22semidirect
44. #91105C22semidirect
45. #91105C22semidirect
46. #91101C22semidirect
47. #91101C22semidirect
48. C5×(C2×D3)⋊C8C22semidirect
49. C5×Dic3⋊C8C22semidirect
50. C5×C8×Dic3C22semidirect
52. C3×#3953C22semidirect
53. #90987C22semidirect
54. #90971C22semidirect
55. #90968C22semidirect
58. #90965C22semidirect
59. #90965C22semidirect
73. #65020D3semidirect
143. #67⋊C8D5semidirect
156. #4070C2×D3semidirect
159. C2×#677C2×D3semidirect
172. C5×C22⋊C8C2×D3semidirect
182. #3953C2×D3semidirect
210. C5×#67SD16semidirect
254. C22×C3⋊C8C2×D5semidirect
255. C2×D3×C8C2×D5semidirect
264. C3×C22⋊C8C2×D5semidirect
272. (C2×D3)⋊C8C2×D5semidirect
275. Dic3⋊C8C2×D5semidirect
276. C8×Dic3C2×D5semidirect
518. C22⋊C8D3×D5semidirect
557. #67#677semidirect
658. C3×C5#3295semidirect
752. C5#80158semidirect
782. C3#10611170semidirect

Maximal subgroups

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

subgroupindex
#67×D202
#117545142
#117508362
C5×#67⋊C82
C3×#650202
#117485412
C2×#909652
#117481102
D3×#39532
#117480032
#117479132
#117479122
#117478392
Dic3×#6772
#117477812
#106111703
#801585