Finite Group Databasebeta

← #14427788

Subgroups — #14427788

Order 1920.

1040 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91805C211yesmaximal, characteristic, complemented
2C22×C8×D15C211yesmaximal, characteristic, complemented
3#11756386C211yesmaximal, characteristic, complemented
4#11756365C211yesmaximal, characteristic, complemented
5C3×C5×#465C211yesmaximal, characteristic, complemented
6#11751272C211yesmaximal, characteristic, complemented
7#11751215C211yesmaximal, characteristic, complemented
8#11751152C211yesmaximal, characteristic, complemented
9#11751139C211yesmaximal, characteristic, complemented
10#11750965C211yesmaximal, characteristic, complemented
11#11750961C211yesmaximal, characteristic, complemented
12#11750914C211yesmaximal, characteristic, complemented
13#11750905C211yesmaximal, characteristic, complemented
14#11750876C211yesmaximal, characteristic, complemented
15#11750873C211yesmaximal, characteristic, complemented
16#10612387—31nomaximal, Hall
17C2×#6821C2211yescharacteristic
18C2×#6819C2211yescharacteristic
19C22×C4×D15C2211yescharacteristic
20C2×C3×C5×SD16C2211yescharacteristic, complemented
21C22×C3×C5×C8C2211yescharacteristic
22C3×C5×C22⋊Q8C2211yescharacteristic
23C3×C5×#121C2211yescharacteristic
24#91835C2211yescharacteristic
25C2×#6718C2211yescharacteristic, complemented
26#91827C2211yescharacteristic
27#91826—21no—
28D4×Dic15—21no—
29C2×#6715C2211yescharacteristic, complemented
30#91819C2211yescharacteristic
31#91813C2211yescharacteristic
32C22×C3⋊#168C2211yescharacteristic
33#91805—24no—
34C2×#6706C2211yescharacteristic, complemented
35C2×C8×D15—24no—
36C2×C8×D15C2211yescharacteristic
37C2×C8×D15C2211yescharacteristic
38C2×C8×D15C2211yescharacteristic
39C2×C8×D15C2211yescharacteristic
40#91786C2211yescharacteristic
41#91784C2211yescharacteristic
42#91783—21no—
43#91782—21no—
44#91781C2211yescharacteristic
45#91781C2211yescharacteristic
46#91772—21no—
47#91771—21no—
48#91770—21no—
49#91770—21no—
50C3×C5×#106C2211yescharacteristic, complemented
51C3×C5×#103C2211yescharacteristic, complemented
52C3×C5×#102C2211yescharacteristic, complemented
53#91119C2211yescharacteristic, complemented
54#91116C2211yescharacteristic, complemented
55#91105C2211yescharacteristic, complemented
56#91101C2211yescharacteristic, complemented
57#91100C2211yescharacteristic, complemented
58#91094C2211yescharacteristic, complemented
59#91093C2211yescharacteristic, complemented
60#91091C2211yescharacteristic, complemented
61#91091C2211yescharacteristic, complemented
62#80656—51nomaximal, Hall
63C2×#4062—31no—
64C22×C8×D5—31no—
65#65961—31no—
66#65940—31no—
67C5×#465D311yescharacteristic, complemented
68#65460—31no—
69#65403—31no—
70#65340—31no—
71#65327—31no—
72#65153—31no—
73#65149—31no—
74#65102—31no—
75#65093—31no—
76#65064—31no—
77#65061—31no—
78C23×D15D411yescharacteristic
79C2×C3×C5×Q8C2311yescharacteristic
80C2×C3×C5×D4—21no—
81C2×C3×C5×D4C2311yescharacteristic
82C22×C3×C4×C5C2311yescharacteristic
83C2×#1220—21no—
84C2×#1220—21no—
85C2×#1220—21no—
86C22×Dic15—21no—
87C22×Dic15D411yescharacteristic
88#6821—22no—
89#6821—22no—
90#6819—22no—
91#6819—22no—
92C2×D60—21no—
93C2×D60—21no—
94C2×D60C2311yescharacteristic
95C2×C4×D15—22no—
96C2×C4×D15—22no—
97C2×C4×D15—21no—
98C2×C4×D15D411yescharacteristic
99C2×C4×D15D411yescharacteristic
100C2×C4×D15C2311yescharacteristic
101C2×C4×D15C2311yescharacteristic
102C2×Dic30C2311yescharacteristic
103C3×C5×SD16—22no—
104C2×C3×C5×C8—22no—
105C2×C3×C5×C8C2311yescharacteristic
106C2×C3×C5×C8C2311yescharacteristic
107C3×C5×C4⋊C4—21no—
108C3×C5×C4⋊C4C2311yescharacteristic
109C3×C5×C4⋊C4C2311yescharacteristic
110C3×C5×C22⋊C4—21no—
111C3×C5×C22⋊C4—21no—
112#6719—21no—
113#6719—21no—
114#6718—22no—
115#6715—22no—
116#6714—21no—
117#6714—21no—
118#6714—21no—
119#6714—21no—
120#6714—21no—
121#6714—21no—
122C4⋊Dic15—21no—
123C4⋊Dic15C2311yescharacteristic
124C4⋊Dic15C2311yescharacteristic
125#6712—21no—
126#6712—21no—
127C4×Dic15—21no—
128C4×Dic15—21no—
129C2×C3⋊#168—22no—
130C2×C3⋊#168C2311yescharacteristic
131C2×C3⋊#168C2311yescharacteristic
132#6706—22no—
133C8×D15—22no—
134C8×D15—22no—
135C8×D15—22no—
136C8×D15D414yescomplemented
137C2×#916—51no—
138C22×D3×C8—51no—
139#5627—51no—
140#5606—51no—
141C3×#465D511yescharacteristic, complemented
142#5171—51no—
143#5114—51no—
144#5051—51no—
145#5038—51no—
146#4864—51no—
147#4860—51no—
148#4813—51no—
149#4804—51no—
150#4775—51no—
151#4772—51no—
152C2×#713—31no—
153C2×#711—31no—
154C22×C4×D5—31no—
155C2×C5×SD16C2×D311yescharacteristic, complemented
156C22×C5×C8C2×D311yescharacteristic
157C5×C22⋊Q8C2×D311yescharacteristic
158C5×#121C2×D311yescharacteristic
159#4092—31no—
160C2×#689—31no—
161#4084—31no—
162#4083—61no—
163D4×Dic5—61no—
164C2×#686—31no—
165#4076—31no—
166#4070—31no—
167C22×#168—31no—
168#4062—64no—
169C2×#677—31no—
170C2×C8×D5—31no—
171C2×C8×D5—31no—
172C2×C8×D5—31no—
173C2×C8×D5—31no—
174C2×C8×D5—64no—
175#4043—31no—
176#4041—31no—
177#4040—61no—
178#4039—61no—
179#4038—31no—
180#4038—31no—
181#4029—61no—
182#4028—61no—
183#4027—61no—
184#4027—61no—
185C5×#106C2×D311yescharacteristic, complemented
186C5×#103C2×D311yescharacteristic, complemented
187C5×#102C2×D311yescharacteristic, complemented
188#3967—31no—
189#3964—31no—
190#3953—31no—
191#3949—31no—
192#3948—31no—
193#3942—31no—
194#3941—31no—
195#3939—31no—
196#3939—31no—
197#3050—151noSylow
198C23×C3×C5—21no—
199C23×C3×C5C2×D411yescharacteristic
200C22×D15—22no—
201C22×D15—22no—
202C22×D15—22no—
203C22×D15—21no—
204C22×D15C2×D411yescharacteristic
205C22×D15C2×D411yescharacteristic
206C3×C5×Q8—21no—
207C3×C5×Q8—21no—
208C3×C5×D4—21no—
209C3×C5×D4—21no—
210C3×C5×D4—42no—
211C2×C3×C4×C5—21no—
212C2×C3×C4×C5—21no—
213C2×C3×C4×C5—21no—
214C2×C3×C4×C5—21no—
215C2×C3×C4×C5—21no—
216C2×C3×C4×C5C2×D411yescharacteristic
217C2×C3×C4×C5C2411yescharacteristic
218#1220—42no—
219#1220—42no—
220#1220—42no—
221C2×Dic15—22no—
222C2×Dic15—21no—
223C2×Dic15—21no—
224C2×Dic15—21no—
225C2×Dic15—42no—
226C2×Dic15C2×D411yescharacteristic
227C2×Dic15C2×D411yescharacteristic
228D60—21no—
229D60—21no—
230D60—42no—
231D60—42no—
232C4×D15—22no—
233C4×D15—21no—
234C4×D15—21no—
235C4×D15—22no—
236C4×D15—42no—
237C4×D15C2×D412yes—
238C4×D15#4112yes—
239Dic30—21no—
240Dic30—21no—
241C3×C5×C8—21no—
242C3×C5×C8C2×D412yes—
243C3⋊#168—21no—
244C3⋊#168C2×D412yes—
245C2×#239—51no—
246C2×#237—51no—
247C22×C4×D3—51no—
248C2×C3×SD16C2×D511yescharacteristic, complemented
249C22×C3×C8C2×D511yescharacteristic
250C3×C22⋊Q8C2×D511yescharacteristic
251C3×#121C2×D511yescharacteristic
252#946—51no—
253C2×#216—51no—
254#938—51no—
255#937—101no—
256D4×Dic3—101no—
257C2×#213—51no—
258#930—51no—
259#924—51no—
260C22×C3⋊C8—51no—
261#916—104no—
262C2×#204—51no—
263C2×D3×C8—51no—
264C2×D3×C8—51no—
265C2×D3×C8—51no—
266C2×D3×C8—51no—
267C2×D3×C8—104no—
268#897—51no—
269#895—51no—
270#894—101no—
271#893—101no—
272#892—51no—
273#892—51no—
274#883—101no—
275#882—101no—
276#67⋊C4—101no—
277#67⋊C4—101no—
278C3×#106C2×D511yescharacteristic, complemented
279C3×#103C2×D511yescharacteristic, complemented
280C3×#102C2×D511yescharacteristic, complemented
281#835—51no—
282#832—51no—
283#821—51no—
284#817—51no—
285#816—51no—
286#810—51no—
287#809—51no—
288#807—51no—
289#807—51no—
290C23×D5—31no—
291C2×C5×Q8C22×D311yescharacteristic
292C2×C5×D4—21no—
293C2×C5×D4C22×D311yescharacteristic
294C22×C4×C5C22×D311yescharacteristic
295C2×C22⋊D5—61no—
296C2×C22⋊D5—61no—
297C2×C22⋊D5—61no—
298C22×Dic5—31no—
299C22×Dic5—61no—
300#713—62no—
301#713—62no—
302#711—62no—
303#711—62no—
304C2×D20—31no—
305C2×D20—61no—
306C2×D20—61no—
307C2×C4×D5—31no—
308C2×C4×D5—31no—
309C2×C4×D5—31no—
310C2×C4×D5—31no—
311C2×C4×D5—62no—
312C2×C4×D5—62no—
313C2×C4×D5—61no—
314C2×Dic10—31no—
315C5×SD16—22no—
316C2×C5×C8—22no—
317C2×C5×C8C22×D311yescharacteristic
318C2×C5×C8C22×D311yescharacteristic
319C5×C4⋊C4—21no—
320C5×C4⋊C4C22×D311yescharacteristic
321C5×C4⋊C4C22×D311yescharacteristic
322C5×C22⋊C4—21no—
323C5×C22⋊C4—21no—
324C22⋊Dic5—61no—
325C22⋊Dic5—61no—
326#689—62no—
327#686—62no—
328#685—61no—
329#685—61no—
330#685—61no—
331#685—61no—
332#685—61no—
333#685—61no—
334C4⋊Dic5—31no—
335C4⋊Dic5—31no—
336C4⋊Dic5—61no—
337#683—61no—
338#683—61no—
339C4×Dic5—61no—
340C4×Dic5—61no—
341C2×#168—31no—
342C2×#168—31no—
343C2×#168—62no—
344#677—62no—
345C8×D5—34no—
346C8×D5—62no—
347C8×D5—62no—
348C8×D5—62no—
349C2×#135—151no—
350C23×C8—151no—
351#525—151no—
352#525—151no—
353#467—151no—
354#467—151no—
355#466—151no—
356#466—151no—
357#465—151no—
358#465—151no—
359#465—151no—
360#465D1511yescharacteristic, complemented
361#427—151no—
362#416—151no—
363#416—151no—
364C22×C3×C5—21no—
365C22×C3×C5—21no—
366C22×C3×C5—41no—
367C22×C3×C5—41no—
368C22×C3×C5—41no—
369C22×C3×C5#13512yescomplemented
370C22×C3×C5C22×D411yescharacteristic
371C2×D15—28no—
372C2×D15—21no—
373C2×D15—21no—
374C2×D15—21no—
375C2×D15—21no—
376C2×D15—41no—
377C2×D15—41no—
378C2×D15—41no—
379C2×D15#12112yes—
380C2×D15#13512yescomplemented
381C3×C4×C5—21no—
382C3×C4×C5—41no—
383C3×C4×C5—41no—
384C3×C4×C5—41no—
385C3×C4×C5C22×D411yescharacteristic
386C3×C4×C5C2×#4111yescharacteristic
387Dic15—21no—
388Dic15—41no—
389Dic15—41no—
390Dic15—41no—
391Dic15#12112yes—
392C23×D3—51no—
393C2×C3×Q8C22×D511yescharacteristic
394C2×C3×D4—21no—
395C2×C3×D4C22×D511yescharacteristic
396C22×C3×C4C22×D511yescharacteristic
397C2×#67—101no—
398C2×#67—101no—
399C2×#67—101no—
400C22×Dic3—51no—
401C22×Dic3—101no—
402#239—102no—
403#239—102no—
404#237—102no—
405#237—102no—
406C2×D12—51no—
407C2×D12—101no—
408C2×D12—101no—
409C2×C4×D3—51no—
410C2×C4×D3—51no—
411C2×C4×D3—51no—
412C2×C4×D3—51no—
413C2×C4×D3—102no—
414C2×C4×D3—102no—
415C2×C4×D3—101no—
416C2×Dic6—51no—
417C3×SD16—22no—
418C2×C3×C8—22no—
419C2×C3×C8C22×D511yescharacteristic
420C2×C3×C8C22×D511yescharacteristic
421C3×C4⋊C4—21no—
422C3×C4⋊C4C22×D511yescharacteristic
423C3×C4⋊C4C22×D511yescharacteristic
424C3×C22⋊C4—21no—
425C3×C22⋊C4—21no—
426#217—101no—
427#217—101no—
428#216—102no—
429#213—102no—
430(C2×D3)⋊C4—101no—
431(C2×D3)⋊C4—101no—
432(C2×D3)⋊C4—101no—
433(C2×D3)⋊C4—101no—
434(C2×D3)⋊C4—101no—
435(C2×D3)⋊C4—101no—
436C4⋊Dic3—51no—
437C4⋊Dic3—51no—
438C4⋊Dic3—101no—
439Dic3⋊C4—101no—
440Dic3⋊C4—101no—
441C4×Dic3—101no—
442C4×Dic3—101no—
443C2×C3⋊C8—51no—
444C2×C3⋊C8—51no—
445C2×C3⋊C8—102no—
446#204—102no—
447D3×C8—54no—
448D3×C8—102no—
449D3×C8—102no—
450D3×C8—102no—
451C23×C5—21no—
452C23×C5D3×D411yescharacteristic
453C22×D5—31no—
454C22×D5—31no—
455C22×D5—62no—
456C22×D5—62no—
457C22×D5—62no—
458C22×D5—61no—
459C5×Q8—21no—
460C5×Q8—21no—
461C5×D4—21no—
462C5×D4—21no—
463C5×D4—42no—
464C2×C4×C5—21no—
465C2×C4×C5—21no—
466C2×C4×C5—21no—
467C2×C4×C5—21no—
468C2×C4×C5—21no—
469C2×C4×C5D3×D411yescharacteristic
470C2×C4×C5C23×D311yescharacteristic
471C22⋊D5—122no—
472C22⋊D5—122no—
473C22⋊D5—122no—
474C2×Dic5—31no—
475C2×Dic5—31no—
476C2×Dic5—62no—
477C2×Dic5—61no—
478C2×Dic5—61no—
479C2×Dic5—61no—
480C2×Dic5—122no—
481D20—61no—
482D20—61no—
483D20—122no—
484D20—122no—
485C4×D5—32no—
486C4×D5—32no—
487C4×D5—62no—
488C4×D5—62no—
489C4×D5—61no—
490C4×D5—61no—
491C4×D5—122no—
492Dic10—61no—
493Dic10—61no—
494C5×C8—21no—
495C5×C8D3×D412yes—
496#168—32no—
497#168—61no—
498C2×#41—151no—
499C2×#41—151no—
500C23×C4—151no—
501#135—304no—
502C2×Q16—151no—
503C2×SD16—151no—
504C2×SD16C2×D1511yescharacteristic, complemented
505C2×D8—151no—
506C22×C8—151no—
507C22×C8—151no—
508C22×C8—151no—
509C22×C8—151no—
510C22×C8—151no—
511C22×C8—304no—
512C22×C8C2×D1511yescharacteristic
513#123—301no—
514#123—301no—
515C22⋊Q8—151no—
516C22⋊Q8—151no—
517C22⋊Q8—151no—
518C22⋊Q8C2×D1511yescharacteristic
519#121—151no—
520#121—151no—
521#121—151no—
522#121C2×D1511yescharacteristic
523#120—301no—
524#120—301no—
525C4×D4—301no—
526C4×D4—301no—
527C4×D4—301no—
528C4×D4—301no—
529#117—151no—
530#117—151no—
531#107—151no—
532#107—151no—
533#106—151no—
534#106C2×D1511yescharacteristic, complemented
535#103—151no—
536#103—151no—
537#103—151no—
538#103C2×D1511yescharacteristic, complemented
539#102—151no—
540#102—151no—
541#102—151no—
542#102C2×D1511yescharacteristic, complemented
543C2×C3×C5—22no—
544C2×C3×C5—81no—
545C2×C3×C5C2×#12111yescharacteristic
546C2×C3×C5C2×#13511yescharacteristic
547C2×C3×C5C2×#13511yescharacteristic
548D15—22no—
549D15—22no—
550D15—81no—
551C23×C3—21no—
552C23×C3D4×D511yescharacteristic
553C22×D3—51no—
554C22×D3—51no—
555C22×D3—102no—
556C22×D3—102no—
557C22×D3—102no—
558C22×D3—101no—
559C3×Q8—21no—
560C3×Q8—21no—
561C3×D4—21no—
562C3×D4—21no—
563C3×D4—42no—
564C2×C3×C4—21no—
565C2×C3×C4—21no—
566C2×C3×C4—21no—
567C2×C3×C4—21no—
568C2×C3×C4—21no—
569C2×C3×C4D4×D511yescharacteristic
570C2×C3×C4C23×D511yescharacteristic
571#67—202no—
572#67—202no—
573#67—202no—
574C2×Dic3—51no—
575C2×Dic3—51no—
576C2×Dic3—102no—
577C2×Dic3—101no—
578C2×Dic3—101no—
579C2×Dic3—101no—
580C2×Dic3—202no—
581D12—101no—
582D12—101no—
583D12—202no—
584D12—202no—
585C4×D3—52no—
586C4×D3—52no—
587C4×D3—102no—
588C4×D3—102no—
589C4×D3—101no—
590C4×D3—101no—
591C4×D3—202no—
592Dic6—101no—
593Dic6—101no—
594C3×C8—21no—
595C3×C8D4×D512yes—
596C3⋊C8—52no—
597C3⋊C8—101no—
598C22×C5—21no—
599C22×C5—21no—
600C22×C5—41no—
601C22×C5—41no—
602C22×C5—41no—
603C22×C5#91612yescomplemented
604C22×C5C2×D3×D411yescharacteristic
605C2×D5—32no—
606C2×D5—32no—
607C2×D5—68no—
608C2×D5—61no—
609C2×D5—61no—
610C2×D5—61no—
611C2×D5—61no—
612C2×D5—121no—
613C2×D5—121no—
614C2×D5—121no—
615C4×C5—21no—
616C4×C5—41no—
617C4×C5—41no—
618C4×C5—41no—
619C4×C5C2×D3×D411yescharacteristic
620C4×C5D3×#4111yescharacteristic
621Dic5—32no—
622Dic5—61no—
623Dic5—121no—
624Dic5—121no—
625Dic5—121no—
626C24—151no—
627#41—302no—
628#41—302no—
629#41—302no—
630#41—302no—
631C2×Q8—151no—
632C2×Q8C22×D1511yescharacteristic
633C2×D4—21no—
634C2×D4—151no—
635C2×D4—301no—
636C2×D4—301no—
637C2×D4—301no—
638C2×D4—301no—
639C2×D4—301no—
640C2×D4C22×D1511yescharacteristic
641C22×C4—151no—
642C22×C4—151no—
643C22×C4—151no—
644C22×C4—151no—
645C22×C4—151no—
646C22×C4—302no—
647C22×C4—302no—
648C22×C4—301no—
649C22×C4—301no—
650C22×C4C22×D1511yescharacteristic
651Q16—302no—
652SD16—22no—
653SD16—302no—
654D8—302no—
655C2×C8—22no—
656C2×C8—151no—
657C2×C8—154no—
658C2×C8—151no—
659C2×C8—302no—
660C2×C8—302no—
661C2×C8—302no—
662C2×C8—302no—
663C2×C8C22×D1511yescharacteristic
664C2×C8C22×D1511yescharacteristic
665C4⋊C4—21no—
666C4⋊C4—151no—
667C4⋊C4—151no—
668C4⋊C4—301no—
669C4⋊C4—301no—
670C4⋊C4—301no—
671C4⋊C4C22×D1511yescharacteristic
672C4⋊C4C22×D1511yescharacteristic
673C22⋊C4—21no—
674C22⋊C4—21no—
675C22⋊C4—301no—
676C22⋊C4—301no—
677C22⋊C4—301no—
678C22⋊C4—301no—
679C22⋊C4—301no—
680C22⋊C4—301no—
681C22⋊C4—301no—
682C22⋊C4—301no—
683C42—301no—
684C42—301no—
685C3×C5#305011yescharacteristic, complemented, Hall
686C22×C3—21no—
687C22×C3—21no—
688C22×C3—41no—
689C22×C3—41no—
690C22×C3—41no—
691C22×C3#406212yescomplemented
692C22×C3C2×D4×D511yescharacteristic
693C2×D3—52no—
694C2×D3—52no—
695C2×D3—108no—
696C2×D3—101no—
697C2×D3—101no—
698C2×D3—101no—
699C2×D3—101no—
700C2×D3—201no—
701C2×D3—201no—
702C2×D3—201no—
703C3×C4—21no—
704C3×C4—41no—
705C3×C4—41no—
706C3×C4—41no—
707C3×C4C2×D4×D511yescharacteristic
708C3×C4D5×#4111yescharacteristic
709Dic3—52no—
710Dic3—101no—
711Dic3—201no—
712Dic3—201no—
713Dic3—201no—
714C2×C5—22no—
715C2×C5—81no—
716C2×C5D3×#12111yescharacteristic
717C2×C5C2×#91611yescharacteristic
718C2×C5D3×#13511yescharacteristic
719D5—62no—
720D5—62no—
721D5—241no—
722C23—21no—
723C23—151no—
724C23—151no—
725C23—302no—
726C23—302no—
727C23—302no—
728C23—301no—
729C23D4×D1511yescharacteristic
730Q8—21no—
731Q8—21no—
732Q8—301no—
733Q8—301no—
734D4—21no—
735D4—21no—
736D4—42no—
737D4—301no—
738D4—301no—
739D4—602no—
740D4—602no—
741D4—602no—
742D4—602no—
743D4—602no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—151no—
750C2×C4—152no—
751C2×C4—152no—
752C2×C4—151no—
753C2×C4—302no—
754C2×C4—302no—
755C2×C4—302no—
756C2×C4—301no—
757C2×C4—301no—
758C2×C4—301no—
759C2×C4—301no—
760C2×C4—301no—
761C2×C4—602no—
762C2×C4—602no—
763C2×C4D4×D1511yescharacteristic
764C2×C4C23×D1511yescharacteristic
765C8—21no—
766C8—152no—
767C8—301no—
768C8D4×D1512yes—
769C2×C3—22no—
770C2×C3—81no—
771C2×C3D5×#12111yescharacteristic
772C2×C3C2×#406211yescharacteristic
773C2×C3D5×#13511yescharacteristic
774D3—102no—
775D3—102no—
776D3—401no—
777C5#8065611yescharacteristic, complemented, Sylow
778C22—21no—
779C22—21no—
780C22—41no—
781C22—41no—
782C22—41no—
783C22—152no—
784C22—152no—
785C22—308no—
786C22—301no—
787C22—301no—
788C22—301no—
789C22—301no—
790C22—601no—
791C22—601no—
792C22—601no—
793C22#9180512yescomplemented
794C22C2×D4×D1511yescharacteristic
795C4—21no—
796C4—41no—
797C4—41no—
798C4—41no—
799C4—152no—
800C4—301no—
801C4—601no—
802C4—601no—
803C4—601no—
804C4C2×D4×D1511yescharacteristic
805C4#41×D1511yescharacteristic
806C3#1061238711yescharacteristic, complemented, Sylow
807C2—22no—
808C2—81no—
809C2—302no—
810C2—302no—
811C2—1201no—
812C2D15×#12111yescharacteristic
813C2C2×#9180511yescharacteristic
814C2D15×#13511yescharacteristic
subgroupG/H
centerC22C2×D4×D15
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC3×C5×#465C2
socleC22×C3×C5C22×D4
hypercenter#465D15
hypocenterC3×C5#3050
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. C2×#91805C2semidirect
2. C22×C8×D15C2semidirect
3. #11756386C2semidirect
4. #11756365C2semidirect
5. C3×C5×#465C2semidirect
6. #11751272C2semidirect
7. #11751215C2semidirect
8. #11751152C2semidirect
9. #11751139C2semidirect
10. #11750965C2semidirect
11. #11750961C2semidirect
12. #11750914C2semidirect
13. #11750905C2semidirect
14. #11750876C2semidirect
15. #11750873C2semidirect
20. C2×C3×C5×SD16C22semidirect
25. C2×#6718C22semidirect
29. C2×#6715C22semidirect
34. C2×#6706C22semidirect
50. C3×C5×#106C22semidirect
51. C3×C5×#103C22semidirect
52. C3×C5×#102C22semidirect
53. #91119C22semidirect
54. #91116C22semidirect
55. #91105C22semidirect
56. #91101C22semidirect
57. #91100C22semidirect
58. #91094C22semidirect
59. #91093C22semidirect
60. #91091C22semidirect
61. #91091C22semidirect
67. C5×#465D3semidirect
136. C8×D15D4semidirect
141. C3×#465D5semidirect
155. C2×C5×SD16C2×D3semidirect
185. C5×#106C2×D3semidirect
186. C5×#103C2×D3semidirect
187. C5×#102C2×D3semidirect
248. C2×C3×SD16C2×D5semidirect
278. C3×#106C2×D5semidirect
279. C3×#103C2×D5semidirect
280. C3×#102C2×D5semidirect
360. #465D15semidirect
369. C22×C3×C5#135semidirect
380. C2×D15#135semidirect
504. C2×SD16C2×D15semidirect
534. #106C2×D15semidirect
538. #103C2×D15semidirect
542. #102C2×D15semidirect
603. C22×C5#916semidirect
685. C3×C5#3050semidirect
691. C22×C3#4062semidirect
777. C5#80656semidirect
793. C22#91805semidirect
806. C3#10612387semidirect

Maximal subgroups

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

subgroupindex
C2×#918052
C22×C8×D152
#117563862
#117563652
C3×C5×#4652
#117512722
#117512152
#117511522
#117511392
#117509652
#117509612
#117509142
#117509052
#117508762
#117508732
#106123873
#806565