Finite Group Databasebeta

← #14458485

Subgroups — #14458485

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#11754514C211yesmaximal, characteristic, complemented
3C2×#91105C211yesmaximal, characteristic, complemented
4C5×C8×#67C211yesmaximal, characteristic, complemented
5C3×#65403C211yesmaximal, characteristic, complemented
6#11748551C211yesmaximal, characteristic, complemented
7#11748375C211yesmaximal, characteristic, complemented
8#11748110C211yesmaximal, characteristic, complemented
9D3×#3953C211yesmaximal, characteristic, complemented
10#11748003C211yesmaximal, characteristic, complemented
11#11747946C211yesmaximal, characteristic, complemented
12#11747839C211yesmaximal, characteristic, complemented
13#11747830C211yesmaximal, characteristic, complemented
14#11747790C211yesmaximal, characteristic, complemented
15#11747625C211yesmaximal, characteristic, complemented
16#10611170—31nomaximal, Hall
17C22×D60C2211yescharacteristic
18C2×#6790—21no—
19C2×D3×D20C2211yescharacteristic
20C22×C3×C5×C8C2211yescharacteristic, complemented
21C2×C4⋊Dic15C2211yescharacteristic, complemented
22C4×C5×#67C2211yescharacteristic
23C2×C5×D3×C8C2211yescharacteristic, complemented
24C3×#4076C2211yescharacteristic
25C3×#4070C2211yescharacteristic, complemented
26C2×C3×#677C2211yescharacteristic, complemented
27#91576—21no—
28#91572—21no—
29#67⋊Dic5—21no—
30#91476—21no—
31#91469C2211yescharacteristic, complemented
32#91460C2211yescharacteristic
33#91459—21no—
34#91458C2211yescharacteristic
35#91428C2211yescharacteristic
36D3×C4⋊Dic5C2211yescharacteristic, complemented
37#91417—21no—
38#91369C2211yescharacteristic, complemented
39#91343—21no—
40Dic3×Dic10C2211yescharacteristic, complemented
41C2×#6658C2211yescharacteristic
42C2×#6658C2211yescharacteristic, complemented
43#91105C2211yescharacteristic
44#91105C2211yescharacteristic
45#91105C2211yescharacteristic, complemented
46#91105C2211yescharacteristic, complemented
47C5×#830C2211yescharacteristic, complemented
48C5×(C2×D3)⋊C8C2211yescharacteristic, complemented
49C5×Dic3⋊C8C2211yescharacteristic, complemented
50C5×C8×Dic3C2211yescharacteristic, complemented
51C3×#3953C2211yescharacteristic, complemented
52C3×#3949C2211yescharacteristic, complemented
53C3×#3948C2211yescharacteristic, complemented
54#90987C2211yescharacteristic, complemented
55#90987C2211yescharacteristic, complemented
56#90968C2211yescharacteristic
57#90968C2211yescharacteristic, complemented
58#90965C2211yescharacteristic, complemented
59#90965C2211yescharacteristic, complemented
60#80680—51nomaximal, Hall
61D4×D20—31no—
62#65877—31no—
63C5×C8×D4—31no—
64#65403—31no—
65#65403D311yescharacteristic, complemented
66C2×#3953—31no—
67C2×#3953—31no—
68#65137—31no—
69#65131—31no—
70#65024—31no—
71#65024—31no—
72#65020—31no—
73#65020—31no—
74#64983—31no—
75C4×#677—31no—
76C23×D15—21no—
77C22×D3×D5—21no—
78C22×C3×C4×C5C2311yescharacteristic
79C22×Dic15—21no—
80C2×D60—22no—
81C2×D60—21no—
82C2×D60—41no—
83C2×D60C2311yescharacteristic
84C2×D60C2311yescharacteristic
85C2×C5×#67D411yescharacteristic
86C2×C4×C5×D3C2311yescharacteristic
87C2×C3×C22⋊D5—21no—
88C2×C3×D20C2311yescharacteristic
89C2×C3×Dic10C2311yescharacteristic
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×C8—41no—
101C2×C3×C5×C8C2311yescharacteristic
102C2×C3×C5×C8C2311yescharacteristic
103C4⋊Dic15—21no—
104C4⋊Dic15C2311yescharacteristic
105C4⋊Dic15C2311yescharacteristic
106C5×#217D411yescharacteristic
107C5×(C2×D3)⋊C4D411yescharacteristic
108C5×Dic3⋊C4D411yescharacteristic
109C4×C5×Dic3C2311yescharacteristic
110C2×C5×C3⋊C8C2311yescharacteristic
111C2×C5×C3⋊C8C2311yescharacteristic
112C5×D3×C8—41no—
113C3×C22⋊Dic5—21no—
114C3×#685—21no—
115C3×C4⋊Dic5C2311yescharacteristic
116C3×C4⋊Dic5C2311yescharacteristic
117C3×#683—21no—
118C3×#677—41no—
119Dic3⋊Dic5—21no—
120Dic3⋊Dic5—21no—
121#6669—21no—
122#6668—21no—
123#6667—21no—
124#6667—21no—
125(C2×D3)⋊Dic5—21no—
126Dic3×Dic5—21no—
127#6658—22no—
128#6658—41no—
129#5635—51no—
130#5609—51no—
131C3×#465—51no—
132#5169—51no—
133#5163—51no—
134C2×#821—51no—
135C8×#67D511yescharacteristic, complemented
136#5046—51no—
137#5034—51no—
138#4870—51no—
139#4863—51no—
140#4807—51no—
141#4788—51no—
142D3×#102—51no—
143#4760—51no—
144C2×D4×D5—61no—
145C22×D20—31no—
146C22×D20—31no—
147C22×C5×C8—31no—
148C22×C5×C8C2×D311yescharacteristic, complemented
149C4×C5×D4—31no—
150D4×Dic5—61no—
151#4076—31no—
152#4076C2×D311yescharacteristic
153C2×C4⋊Dic5—31no—
154C2×C4⋊Dic5—31no—
155#4070—31no—
156#4070C2×D311yescharacteristic, complemented
157C2×#677—31no—
158C2×#677—31no—
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⋊C8—31no—
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#3953—31no—
182#3953C2×D311yescharacteristic, complemented
183#3949—31no—
184#3949—31no—
185#3949C2×D311yescharacteristic, complemented
186#3948C2×D311yescharacteristic, complemented
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—
205C2×Dic15—81no—
206D60—21no—
207D60—21no—
208D60—21no—
209D60—42no—
210D60#4112yes—
211C5×#67SD1614yescomplemented
212C2×C5×Dic3C2×D411yescharacteristic
213C2×C5×Dic3C2×D411yescharacteristic
214C2×C5×Dic3C2×D411yescharacteristic
215C4×C5×D3—21no—
216C4×C5×D3—21no—
217C3×C22⋊D5—42no—
218C2×C3×Dic5—21no—
219C2×C3×Dic5—21no—
220C2×C3×Dic5—21no—
221C3×D20—21no—
222C3×D20—21no—
223C3×Dic10—21no—
224C3×Dic10—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—
239C2×C3×SD16—51no—
240C22×C3×C8C2×D511yescharacteristic, complemented
241C3×C22⋊Q8—51no—
242C3×#121—51no—
243#946—51no—
244Q8×Dic3—51no—
245C2×#215—51no—
246C2×#215—51no—
247#940—51no—
248#937—101no—
249C4×#67C2×D511yescharacteristic
250C2×C4⋊Dic3—51no—
251C2×D3×C8C2×D511yescharacteristic, complemented
252#897—101no—
253#895—51no—
254#893—51no—
255D3×C4⋊C4—51no—
256#889—101no—
257#888—51no—
258#884—101no—
259#882—101no—
260#67⋊C4—101no—
261#878—101no—
262C3×#106—51no—
263C3×#103—51no—
264C3×#102—51no—
265#832—51no—
266#832—51no—
267#830C2×D511yescharacteristic, complemented
268#821—51no—
269#821—51no—
270#821—51no—
271#821—51no—
272(C2×D3)⋊C8C2×D511yescharacteristic, complemented
273Dic3⋊C8C2×D511yescharacteristic, complemented
274C8×Dic3C2×D511yescharacteristic, complemented
275#809—51no—
276#809—51no—
277#808—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—61no—
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—61no—
302C2×Dic10C22×D311yescharacteristic
303C2×C5×C8—31no—
304C2×C5×C8—31no—
305C2×C5×C8—41no—
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—21no—
316#685—61no—
317#685—61no—
318C4⋊Dic5—31no—
319C4⋊Dic5—31no—
320C4⋊Dic5—61no—
321C4⋊Dic5—61no—
322C4⋊Dic5—61no—
323C4⋊Dic5C22×D311yescharacteristic
324C4⋊Dic5C22×D311yescharacteristic
325#683—21no—
326#683—61no—
327#683—61no—
328C4×Dic5—61no—
329#677—41no—
330#677—62no—
331#677—121no—
332#554—151no—
333D42—151no—
334#486—151no—
335#481—151no—
336#481—151no—
337#476—151no—
338#465—51no—
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×Q8—51no—
379C2×C3×D4—51no—
380C2×C3×D4—101no—
381C22×C3×C4C22×D511yescharacteristic
382C2×#67—101no—
383C2×#67—101no—
384C2×#67—101no—
385C2×#67D2011yescharacteristic
386C22×Dic3—101no—
387D3×D4—102no—
388D3×D4—201no—
389D3×D4—204no—
390C2×D12—51no—
391C2×D12—51no—
392C2×D12—102no—
393C2×D12—101no—
394C2×D12—101no—
395C2×D12—201no—
396C2×C4×D3—101no—
397C2×C4×D3—101no—
398C2×C4×D3C22×D511yescharacteristic
399C2×Dic6—101no—
400C3×SD16—201no—
401C2×C3×C8—41no—
402C2×C3×C8C22×D511yescharacteristic
403C2×C3×C8C22×D511yescharacteristic
404C3×C4⋊C4—51no—
405C3×C4⋊C4—51no—
406C3×C4⋊C4—101no—
407C3×C22⋊C4—101no—
408C3×C22⋊C4—101no—
409#217D2011yescharacteristic
410#215—102no—
411#215—201no—
412(C2×D3)⋊C4—101no—
413(C2×D3)⋊C4—101no—
414(C2×D3)⋊C4—101no—
415(C2×D3)⋊C4D2011yescharacteristic
416C4⋊Dic3—51no—
417C4⋊Dic3—51no—
418C4⋊Dic3—101no—
419C4⋊Dic3—101no—
420Dic3⋊C4—101no—
421Dic3⋊C4—101no—
422Dic3⋊C4—101no—
423Dic3⋊C4D2011yescharacteristic
424C4×Dic3—101no—
425C4×Dic3C22×D511yescharacteristic
426C2×C3⋊C8C22×D511yescharacteristic
427C2×C3⋊C8C22×D511yescharacteristic
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—241no—
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—21no—
471Dic10—21no—
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—51no—
481C2×SD16—151no—
482C2×SD16—151no—
483C22×C8—31no—
484C22×C8D3×D511yescharacteristic, complemented
485C4⋊Q8—151no—
486#127—151no—
487#125—301no—
488C22⋊Q8—51no—
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—151no—
502C2×C4⋊C4—151no—
503#106—51no—
504#106—151no—
505#106—151no—
506C4⋊C8—31no—
507#103—51no—
508#102—51no—
509#102—151no—
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⋊C8—31no—
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×Q8—101no—
540C3×Q8—101no—
541C3×D4—101no—
542C3×D4—101no—
543C3×D4—202no—
544C2×C3×C4—21no—
545C2×C3×C4—21no—
546C2×C3×C4—101no—
547C2×C3×C4—101no—
548C2×C3×C4—101no—
549C2×C3×C4C2×D2011yescharacteristic
550C2×C3×C4C23×D511yescharacteristic
551#67—202no—
552#67—202no—
553#67—401no—
554#67#67714yescomplemented
555C2×Dic3—101no—
556C2×Dic3—101no—
557C2×Dic3—401no—
558C2×Dic3C2×D2011yescharacteristic
559C2×Dic3C2×D2011yescharacteristic
560C2×Dic3C2×D2011yescharacteristic
561D12—52no—
562D12—101no—
563D12—101no—
564D12—101no—
565D12—202no—
566D12—202no—
567C4×D3—21no—
568C4×D3—21no—
569C4×D3—202no—
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—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×C5#100411yescharacteristic
599C4×C5D3×#4111yescharacteristic
600Dic5—41no—
601Dic5—41no—
602Dic5—41no—
603Dic5—121no—
604Dic5—121no—
605C24—301no—
606C24—301no—
607C2×Q8—51no—
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—301no—
626C22×C4—301no—
627C22×C4—301no—
628C22×C4C2×D3×D511yescharacteristic
629SD16—201no—
630SD16—302no—
631SD16—601no—
632C2×C8—31no—
633C2×C8—31no—
634C2×C8—41no—
635C2×C8—121no—
636C2×C8C2×D3×D511yescharacteristic
637C2×C8C2×D3×D511yescharacteristic
638C4⋊C4—31no—
639C4⋊C4—51no—
640C4⋊C4—51no—
641C4⋊C4—101no—
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—101no—
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#561011yescharacteristic
691C2×C5C2×D3×SD1611yescharacteristic
692C2×C5#576911yescharacteristic
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—101no—
708Q8—101no—
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—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—401no—
746C2×C3#6588811yescharacteristic
747C2×C3C22×#67711yescharacteristic
748C2×C3#6608611yescharacteristic
749D3—22no—
750D3—202no—
751D3—401no—
752C5#8068011yescharacteristic, 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#9201611yescharacteristic
781C4#9204911yescharacteristic
782C3#1061117011yescharacteristic, complemented, Sylow
783C2—22no—
784C2—62no—
785C2—401no—
786C2—602no—
787C2—1201no—
788C2C2×D3×#67711yescharacteristic
789C2#1175397311yescharacteristic
790C2#1175466211yescharacteristic
subgroupG/H
centerC22C2×D3×D20
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×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. #11754514C2semidirect
3. C2×#91105C2semidirect
4. C5×C8×#67C2semidirect
5. C3×#65403C2semidirect
6. #11748551C2semidirect
7. #11748375C2semidirect
8. #11748110C2semidirect
9. D3×#3953C2semidirect
10. #11748003C2semidirect
11. #11747946C2semidirect
12. #11747839C2semidirect
13. #11747830C2semidirect
14. #11747790C2semidirect
15. #11747625C2semidirect
20. C22×C3×C5×C8C22semidirect
21. C2×C4⋊Dic15C22semidirect
23. C2×C5×D3×C8C22semidirect
25. C3×#4070C22semidirect
26. C2×C3×#677C22semidirect
31. #91469C22semidirect
36. D3×C4⋊Dic5C22semidirect
38. #91369C22semidirect
40. Dic3×Dic10C22semidirect
42. C2×#6658C22semidirect
45. #91105C22semidirect
46. #91105C22semidirect
47. C5×#830C22semidirect
48. C5×(C2×D3)⋊C8C22semidirect
49. C5×Dic3⋊C8C22semidirect
50. C5×C8×Dic3C22semidirect
51. C3×#3953C22semidirect
52. C3×#3949C22semidirect
53. C3×#3948C22semidirect
54. #90987C22semidirect
55. #90987C22semidirect
57. #90968C22semidirect
58. #90965C22semidirect
59. #90965C22semidirect
65. #65403D3semidirect
135. C8×#67D5semidirect
148. C22×C5×C8C2×D3semidirect
156. #4070C2×D3semidirect
159. C2×#677C2×D3semidirect
182. #3953C2×D3semidirect
185. #3949C2×D3semidirect
186. #3948C2×D3semidirect
211. C5×#67SD16semidirect
240. C22×C3×C8C2×D5semidirect
251. C2×D3×C8C2×D5semidirect
267. #830C2×D5semidirect
272. (C2×D3)⋊C8C2×D5semidirect
273. Dic3⋊C8C2×D5semidirect
274. C8×Dic3C2×D5semidirect
484. C22×C8D3×D5semidirect
554. #67#677semidirect
658. C3×C5#3295semidirect
752. C5#80680semidirect
782. C3#10611170semidirect

Maximal subgroups

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

subgroupindex
#117546612
#117545142
C2×#911052
C5×C8×#672
C3×#654032
#117485512
#117483752
#117481102
D3×#39532
#117480032
#117479462
#117478392
#117478302
#117477902
#117476252
#106111703
#806805