Finite Group Databasebeta

← C59×#13043 #28425152

Subgroups — C59×#13043 #28425152

Order 15104.

844 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C59×B(4,𝔽2)C211yesmaximal, characteristic
2C59×#2375C211yesmaximal, characteristic, complemented
3C2×C59×AΣL(1,𝔽16)C211yesmaximal, characteristic, complemented
4C59×#1792C211yesmaximal, characteristic, complemented
5C59×#1790C211yesmaximal, characteristic, complemented
6C59×#1393C211yesmaximal, characteristic, complemented
7C59×#1390C211yesmaximal, characteristic, complemented
8C2×H(5,𝔽2)×C59C2211yescharacteristic
9C2×#120×C59—21no—
10C2×#120×C59C2211yescharacteristic
11C59×B(4,𝔽2)—22no—
12C59×B(4,𝔽2)C414yescomplemented
13C2×#104×C59—21no—
14C59×#417—21no—
15C2×#100×C59C2211yescharacteristic
16C2×#99×C59—21no—
17C2×#99×C59—21no—
18C2×#99×C59C2211yescharacteristic
19C2×#99×C59C2211yescharacteristic
20C59×#390—21no—
21C59×#390C2211yescharacteristic
22C59×#388—21no—
23C59×#388—21no—
24C59×#388—21no—
25C59×#386—21no—
26C59×#386—21no—
27C59×#386C2211yescharacteristic
28C59×#379—21no—
29C59×AΣL(1,𝔽16)—22no—
30C25×C59D411yescharacteristic
31H(5,𝔽2)×C59—21no—
32H(5,𝔽2)×C59—21no—
33H(5,𝔽2)×C59—21no—
34H(5,𝔽2)×C59—42no—
35H(5,𝔽2)×C59C2×C412yes—
36C2×#41×C59—21no—
37C2×#41×C59—41no—
38C22×D4×C59—21no—
39C22×D4×C59—21no—
40C22×D4×C59—21no—
41C22×D4×C59—41no—
42C22×D4×C59—41no—
43C22×D4×C59C2311yescharacteristic
44C23×C4×C59D411yescharacteristic, complemented
45C2×M16×C59—21no—
46#120×C59—21no—
47#120×C59—21no—
48#120×C59—24no—
49#120×C59—42no—
50#120×C59C2×C412yes—
51#120×C59D412yes—
52C2×C4⋊C4×C59—21no—
53C2×C4⋊C4×C59D411yescharacteristic, complemented
54C2×C22⋊C4×C59—21no—
55C2×C22⋊C4×C59—21no—
56C2×C22⋊C4×C59—21no—
57C2×C22⋊C4×C59—21no—
58C2×C22⋊C4×C59—21no—
59C2×C22⋊C4×C59—21no—
60C2×C22⋊C4×C59—21no—
61C2×C22⋊C4×C59—21no—
62C2×C22⋊C4×C59—21no—
63C2×C22⋊C4×C59—21no—
64C2×C22⋊C4×C59—41no—
65C2×C22⋊C4×C59—41no—
66C2×C22⋊C4×C59D411yescharacteristic
67C2×C22⋊C4×C59D411yescharacteristic, complemented
68C2×C42×C59—21no—
69C2×C42×C59D411yescharacteristic, complemented
70#104×C59—42no—
71#103×C59—41no—
72#102×C59—41no—
73#100×C59—21no—
74#100×C59—21no—
75#99×C59—21no—
76#99×C59—24no—
77#99×C59—21no—
78#99×C59—21no—
79#99×C59—42no—
80#99×C59C2×C412yes—
81#95×C59—21no—
82#95×C59—21no—
83#95×C59—21no—
84#95×C59—41no—
85C24×C59—21no—
86C24×C59—21no—
87C24×C59—21no—
88C24×C59—21no—
89C24×C59—41no—
90C24×C59—41no—
91C24×C59—81no—
92C24×C59—81no—
93C24×C59C22⋊C412yescomplemented
94C24×C59C2×D411yescharacteristic
95C24×C59C2×D411yescharacteristic
96#41×C59—22no—
97#41×C59—22no—
98#41×C59—42no—
99#41×C59—41no—
100#41×C59—42no—
101#41×C59—42no—
102#41×C59—42no—
103#41×C59—41no—
104C2×Q8×C59—21no—
105C2×D4×C59—21no—
106C2×D4×C59—22no—
107C2×D4×C59—22no—
108C2×D4×C59—22no—
109C2×D4×C59—22no—
110C2×D4×C59—22no—
111C2×D4×C59—22no—
112C2×D4×C59—41no—
113C2×D4×C59—41no—
114C2×D4×C59—42no—
115C2×D4×C59—42no—
116C2×D4×C59—41no—
117C2×D4×C59—41no—
118C2×D4×C59—41no—
119C2×D4×C59—41no—
120C2×D4×C59—42no—
121C2×D4×C59—42no—
122C2×D4×C59—41no—
123C2×D4×C59—41no—
124C2×D4×C59—41no—
125C2×D4×C59—44no—
126C2×D4×C59—81no—
127C2×D4×C59—81no—
128C2×D4×C59—82no—
129C2×D4×C59—82no—
130C2×D4×C59C22×C411yescharacteristic
131C2×D4×C59C2×D411yescharacteristic
132C2×D4×C59#4111yescharacteristic
133C2×D4×C59#4111yescharacteristic
134C22×C4×C59—21no—
135C22×C4×C59—21no—
136C22×C4×C59—21no—
137C22×C4×C59—21no—
138C22×C4×C59—21no—
139C22×C4×C59—21no—
140C22×C4×C59—21no—
141C22×C4×C59—41no—
142C22×C4×C59—41no—
143C22×C4×C59—41no—
144C22×C4×C59—41no—
145C22×C4×C59—81no—
146C22×C4×C59C2×D411yescharacteristic
147M16×C59—41no—
148M16×C59—41no—
149C2×C8×C59—41no—
150C4⋊C4×C59—41no—
151C4⋊C4×C59—81no—
152C22⋊C4×C59—21no—
153C22⋊C4×C59—22no—
154C22⋊C4×C59—22no—
155C22⋊C4×C59—22no—
156C22⋊C4×C59—44no—
157C22⋊C4×C59—41no—
158C22⋊C4×C59—41no—
159C22⋊C4×C59—41no—
160C22⋊C4×C59—41no—
161C22⋊C4×C59—81no—
162C22⋊C4×C59—81no—
163C22⋊C4×C59—81no—
164C22⋊C4×C59—81no—
165C22⋊C4×C59—81no—
166C22⋊C4×C59—81no—
167C22⋊C4×C59—81no—
168C22⋊C4×C59—82no—
169C22⋊C4×C59C22⋊C412yescomplemented
170C42×C59—41no—
171C42×C59—81no—
172C23×C59—21no—
173C23×C59—21no—
174C23×C59—21no—
175C23×C59—21no—
176C23×C59—22no—
177C23×C59—22no—
178C23×C59—22no—
179C23×C59—42no—
180C23×C59—41no—
181C23×C59—41no—
182C23×C59—41no—
183C23×C59—41no—
184C23×C59—41no—
185C23×C59—41no—
186C23×C59—41no—
187C23×C59—41no—
188C23×C59—41no—
189C23×C59—41no—
190C23×C59—42no—
191C23×C59—42no—
192C23×C59—41no—
193C23×C59—41no—
194C23×C59—41no—
195C23×C59—81no—
196C23×C59—82no—
197C23×C59—82no—
198C23×C59—81no—
199C23×C59—81no—
200C23×C59—84no—
201C23×C59—81no—
202C23×C59—81no—
203C23×C59—81no—
204C23×C59—81no—
205C23×C59C2×C22⋊C411yescharacteristic
206C23×C59C4×D411yescharacteristic
207C23×C59#12011yescharacteristic
208C23×C59#12111yescharacteristic
209C23×C59#12311yescharacteristic
210Q8×C59—22no—
211Q8×C59—41no—
212D4×C59—22no—
213D4×C59—41no—
214D4×C59—41no—
215D4×C59—41no—
216D4×C59—41no—
217D4×C59—41no—
218D4×C59—42no—
219D4×C59—42no—
220D4×C59—42no—
221D4×C59—42no—
222D4×C59—42no—
223D4×C59—42no—
224D4×C59—82no—
225D4×C59—82no—
226D4×C59—88no—
227C2×C4×C59—21no—
228C2×C4×C59—21no—
229C2×C4×C59—22no—
230C2×C4×C59—22no—
231C2×C4×C59—22no—
232C2×C4×C59—42no—
233C2×C4×C59—42no—
234C2×C4×C59—41no—
235C2×C4×C59—41no—
236C2×C4×C59—41no—
237C2×C4×C59—41no—
238C2×C4×C59—41no—
239C2×C4×C59—41no—
240C2×C4×C59—41no—
241C2×C4×C59—42no—
242C2×C4×C59—41no—
243C2×C4×C59—41no—
244C2×C4×C59—41no—
245C2×C4×C59—41no—
246C2×C4×C59—41no—
247C2×C4×C59—41no—
248C2×C4×C59—42no—
249C2×C4×C59—41no—
250C2×C4×C59—41no—
251C2×C4×C59—41no—
252C2×C4×C59—41no—
253C2×C4×C59—81no—
254C2×C4×C59—81no—
255C2×C4×C59—81no—
256C2×C4×C59—81no—
257C2×C4×C59—81no—
258C2×C4×C59—81no—
259C2×C4×C59C4×D411yescharacteristic
260C2×C4×C59#12111yescharacteristic
261C8×C59—81no—
262#13043C5911yesmaximal, characteristic, direct product factor, Sylow
263C22×C59—21no—
264C22×C59—21no—
265C22×C59—21no—
266C22×C59—21no—
267C22×C59—21no—
268C22×C59—21no—
269C22×C59—41no—
270C22×C59—41no—
271C22×C59—41no—
272C22×C59—41no—
273C22×C59—42no—
274C22×C59—42no—
275C22×C59—41no—
276C22×C59—41no—
277C22×C59—41no—
278C22×C59—41no—
279C22×C59—44no—
280C22×C59—42no—
281C22×C59—42no—
282C22×C59—81no—
283C22×C59—81no—
284C22×C59—81no—
285C22×C59—81no—
286C22×C59—82no—
287C22×C59—82no—
288C22×C59—82no—
289C22×C59—82no—
290C22×C59—82no—
291C22×C59—81no—
292C22×C59—81no—
293C22×C59—81no—
294C22×C59—81no—
295C22×C59—161no—
296C22×C59—161no—
297C22×C59#38611yescharacteristic
298C22×C59B(4,𝔽2)11yescharacteristic
299C22×C59B(4,𝔽2)11yescharacteristic
300C4×C59—21no—
301C4×C59—21no—
302C4×C59—42no—
303C4×C59—42no—
304C4×C59—81no—
305C4×C59—81no—
306C4×C59—82no—
307C4×C59—81no—
308C4×C59—81no—
309C4×C59—161no—
310C2×B(4,𝔽2)C2×C5911yescharacteristic
311#2375C2×C5911yescharacteristic, complemented
312C2×AΣL(1,𝔽16)C2×C5911yescharacteristic, complemented
313#1792C2×C5911yescharacteristic, complemented
314#1790C2×C5911yescharacteristic, complemented
315#1393C2×C5911yescharacteristic, complemented
316#1390C2×C5911yescharacteristic, complemented
317C2×C59—21no—
318C2×C59—21no—
319C2×C59—41no—
320C2×C59—41no—
321C2×C59—41no—
322C2×C59—41no—
323C2×C59—82no—
324C2×C59—82no—
325C2×C59#188911yescharacteristic
326C2×C59#219911yescharacteristic
327C2×C59#220011yescharacteristic
328C2×H(5,𝔽2)C22×C5911yescharacteristic
329C2×#120—21no—
330C2×#120C22×C5911yescharacteristic
331B(4,𝔽2)—22no—
332B(4,𝔽2)C4×C5914yescomplemented
333C2×#104—21no—
334#417—21no—
335C2×#100C22×C5911yescharacteristic
336C2×#99—21no—
337C2×#99—21no—
338C2×#99C22×C5911yescharacteristic
339C2×#99C22×C5911yescharacteristic
340#390—21no—
341#390C22×C5911yescharacteristic
342#388—21no—
343#388—21no—
344#388—21no—
345#386—21no—
346#386—21no—
347#386C22×C5911yescharacteristic
348#379—21no—
349AΣL(1,𝔽16)—22no—
350C59#1304311yescharacteristic, direct product factor, Sylow
351C25D4×C5911yescharacteristic
352H(5,𝔽2)—21no—
353H(5,𝔽2)—21no—
354H(5,𝔽2)—21no—
355H(5,𝔽2)—42no—
356H(5,𝔽2)C2×C4×C5912yes—
357C2×#41—21no—
358C2×#41—41no—
359C22×D4—21no—
360C22×D4—21no—
361C22×D4—21no—
362C22×D4—41no—
363C22×D4—41no—
364C22×D4C23×C5911yescharacteristic
365C23×C4D4×C5911yescharacteristic, complemented
366C2×M16—21no—
367#120—21no—
368#120—21no—
369#120—24no—
370#120—42no—
371#120C2×C4×C5912yes—
372#120D4×C5912yes—
373C2×C4⋊C4—21no—
374C2×C4⋊C4D4×C5911yescharacteristic, complemented
375C2×C22⋊C4—21no—
376C2×C22⋊C4—21no—
377C2×C22⋊C4—21no—
378C2×C22⋊C4—21no—
379C2×C22⋊C4—21no—
380C2×C22⋊C4—21no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—21no—
384C2×C22⋊C4—21no—
385C2×C22⋊C4—41no—
386C2×C22⋊C4—41no—
387C2×C22⋊C4D4×C5911yescharacteristic
388C2×C22⋊C4D4×C5911yescharacteristic, complemented
389C2×C42—21no—
390C2×C42D4×C5911yescharacteristic, complemented
391#104—42no—
392#103—41no—
393#102—41no—
394#100—21no—
395#100—21no—
396#99—21no—
397#99—24no—
398#99—21no—
399#99—21no—
400#99—42no—
401#99C2×C4×C5912yes—
402#95—21no—
403#95—21no—
404#95—21no—
405#95—41no—
406C24—21no—
407C24—21no—
408C24—21no—
409C24—21no—
410C24—41no—
411C24—41no—
412C24—81no—
413C24—81no—
414C24C22⋊C4×C5912yescomplemented
415C24C2×D4×C5911yescharacteristic
416C24C2×D4×C5911yescharacteristic
417#41—22no—
418#41—22no—
419#41—42no—
420#41—41no—
421#41—42no—
422#41—42no—
423#41—42no—
424#41—41no—
425C2×Q8—21no—
426C2×D4—21no—
427C2×D4—22no—
428C2×D4—22no—
429C2×D4—22no—
430C2×D4—22no—
431C2×D4—22no—
432C2×D4—22no—
433C2×D4—41no—
434C2×D4—41no—
435C2×D4—42no—
436C2×D4—42no—
437C2×D4—41no—
438C2×D4—41no—
439C2×D4—41no—
440C2×D4—41no—
441C2×D4—42no—
442C2×D4—42no—
443C2×D4—41no—
444C2×D4—41no—
445C2×D4—41no—
446C2×D4—44no—
447C2×D4—81no—
448C2×D4—81no—
449C2×D4—82no—
450C2×D4—82no—
451C2×D4C22×C4×C5911yescharacteristic
452C2×D4C2×D4×C5911yescharacteristic
453C2×D4#41×C5911yescharacteristic
454C2×D4#41×C5911yescharacteristic
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—41no—
463C22×C4—41no—
464C22×C4—41no—
465C22×C4—41no—
466C22×C4—81no—
467C22×C4C2×D4×C5911yescharacteristic
468M16—41no—
469M16—41no—
470C2×C8—41no—
471C4⋊C4—41no—
472C4⋊C4—81no—
473C22⋊C4—21no—
474C22⋊C4—22no—
475C22⋊C4—22no—
476C22⋊C4—22no—
477C22⋊C4—44no—
478C22⋊C4—41no—
479C22⋊C4—41no—
480C22⋊C4—41no—
481C22⋊C4—41no—
482C22⋊C4—81no—
483C22⋊C4—81no—
484C22⋊C4—81no—
485C22⋊C4—81no—
486C22⋊C4—81no—
487C22⋊C4—81no—
488C22⋊C4—81no—
489C22⋊C4—82no—
490C22⋊C4C22⋊C4×C5912yescomplemented
491C42—41no—
492C42—81no—
493C23—21no—
494C23—21no—
495C23—21no—
496C23—21no—
497C23—22no—
498C23—22no—
499C23—22no—
500C23—42no—
501C23—41no—
502C23—41no—
503C23—41no—
504C23—41no—
505C23—41no—
506C23—41no—
507C23—41no—
508C23—41no—
509C23—41no—
510C23—41no—
511C23—42no—
512C23—42no—
513C23—41no—
514C23—41no—
515C23—41no—
516C23—81no—
517C23—82no—
518C23—82no—
519C23—81no—
520C23—81no—
521C23—84no—
522C23—81no—
523C23—81no—
524C23—81no—
525C23—81no—
526C23C2×C22⋊C4×C5911yescharacteristic
527C23C4×D4×C5911yescharacteristic
528C23#120×C5911yescharacteristic
529C23#121×C5911yescharacteristic
530C23#123×C5911yescharacteristic
531Q8—22no—
532Q8—41no—
533D4—22no—
534D4—41no—
535D4—41no—
536D4—41no—
537D4—41no—
538D4—41no—
539D4—42no—
540D4—42no—
541D4—42no—
542D4—42no—
543D4—42no—
544D4—42no—
545D4—82no—
546D4—82no—
547D4—88no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—42no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—42no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—81no—
575C2×C4—81no—
576C2×C4—81no—
577C2×C4—81no—
578C2×C4—81no—
579C2×C4—81no—
580C2×C4C4×D4×C5911yescharacteristic
581C2×C4#121×C5911yescharacteristic
582C8—81no—
583C22—21no—
584C22—21no—
585C22—21no—
586C22—21no—
587C22—21no—
588C22—21no—
589C22—41no—
590C22—41no—
591C22—41no—
592C22—41no—
593C22—42no—
594C22—42no—
595C22—41no—
596C22—41no—
597C22—41no—
598C22—41no—
599C22—44no—
600C22—42no—
601C22—42no—
602C22—81no—
603C22—81no—
604C22—81no—
605C22—81no—
606C22—82no—
607C22—82no—
608C22—82no—
609C22—82no—
610C22—82no—
611C22—81no—
612C22—81no—
613C22—81no—
614C22—81no—
615C22—161no—
616C22—161no—
617C22C59×#38611yescharacteristic
618C22C59×B(4,𝔽2)11yescharacteristic
619C22C59×B(4,𝔽2)11yescharacteristic
620C4—21no—
621C4—21no—
622C4—42no—
623C4—42no—
624C4—81no—
625C4—81no—
626C4—82no—
627C4—81no—
628C4—81no—
629C4—161no—
630C2—21no—
631C2—21no—
632C2—41no—
633C2—41no—
634C2—41no—
635C2—41no—
636C2—82no—
637C2—82no—
638C2C59×#188911yescharacteristic
639C2C59×#219911yescharacteristic
640C2C59×#220011yescharacteristic
subgroupG/H
center, socleC22×C59B(4,𝔽2)
commutatorC2×D4C22×C4×C59
Frattini, cosocleC22×D4C23×C59
prime radicalC2×C59×B(4,𝔽2)C2
LCSG ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C59 ◁ C23×C59 ◁ C22×D4×C59 ◁ G

Complements

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

NH ≅ G/Ntype
2. C59×#2375C2semidirect
3. C2×C59×AΣL(1,𝔽16)C2semidirect
4. C59×#1792C2semidirect
5. C59×#1790C2semidirect
6. C59×#1393C2semidirect
7. C59×#1390C2semidirect
12. C59×B(4,𝔽2)C4semidirect
44. C23×C4×C59D4semidirect
53. C2×C4⋊C4×C59D4semidirect
67. C2×C22⋊C4×C59D4semidirect
69. C2×C42×C59D4semidirect
93. C24×C59C22⋊C4semidirect
169. C22⋊C4×C59C22⋊C4semidirect
262. #13043C59direct (N × H)
311. #2375C2×C59semidirect
312. C2×AΣL(1,𝔽16)C2×C59semidirect
313. #1792C2×C59semidirect
314. #1790C2×C59semidirect
315. #1393C2×C59semidirect
316. #1390C2×C59semidirect
332. B(4,𝔽2)C4×C59semidirect
350. C59#13043direct (N × H)
365. C23×C4D4×C59semidirect
374. C2×C4⋊C4D4×C59semidirect
388. C2×C22⋊C4D4×C59semidirect
390. C2×C42D4×C59semidirect
414. C24C22⋊C4×C59semidirect
490. C22⋊C4C22⋊C4×C59semidirect

Maximal subgroups

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

subgroupindex
C2×C59×B(4,𝔽2)2
C59×#23752
C2×C59×AΣL(1,𝔽16)2
C59×#17922
C59×#17902
C59×#13932
C59×#13902
#1304359