Finite Group Databasebeta

← C59×#13082 #28425191

Subgroups — C59×#13082 #28425191

Order 15104.

1088 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#100×C59C211yesmaximal, characteristic, complemented
2C59×#2403C211yesmaximal, characteristic
3C2×C59×AΣL(1,𝔽16)C212yesmaximal, complemented
4C59×#1781C211yesmaximal, characteristic, complemented
5C59×#1390C212yesmaximal, complemented
6C23×D4×C59C411yescharacteristic, complemented
7C23×D4×C59C2211yescharacteristic
8C22×M16×C59—21no—
9C2×#120×C59—21no—
10C2×#120×C59C411yescharacteristic, complemented
11C2×#120×C59C2211yescharacteristic
12C2×#100×C59—21no—
13C2×#100×C59—24no—
14C2×#100×C59C2212yes—
15C2×#99×C59—21no—
16C2×#99×C59C2212yes—
17C59×#392—21no—
18C59×#392—21no—
19C59×#386—21no—
20C59×#386C411yescharacteristic, complemented
21C59×#386C2211yescharacteristic
22C59×#379—21no—
23C59×#379C411yescharacteristic, complemented
24C59×AΣL(1,𝔽16)—24no—
25C25×C59C2×C411yescharacteristic
26C25×C59C2×C411yescharacteristic
27C25×C59D411yescharacteristic
28C22×D4×C59—21no—
29C22×D4×C59—22no—
30C22×D4×C59—22no—
31C22×D4×C59—21no—
32C22×D4×C59—21no—
33C22×D4×C59—21no—
34C22×D4×C59—42no—
35C22×D4×C59—41no—
36C22×D4×C59—41no—
37C22×D4×C59—44no—
38C22×D4×C59—41no—
39C22×D4×C59—41no—
40C22×D4×C59C2×C411yescharacteristic
41C22×D4×C59D411yescharacteristic
42C22×D4×C59D411yescharacteristic
43C22×D4×C59C2311yescharacteristic
44C23×C4×C59C2×C411yescharacteristic
45C23×C4×C59D411yescharacteristic
46C2×M16×C59—24no—
47C2×M16×C59—22no—
48C2×M16×C59—41no—
49C2×M16×C59—42no—
50C22×C8×C59—41no—
51#120×C59—22no—
52#120×C59—22no—
53#120×C59—44no—
54#120×C59—42no—
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—22no—
61C2×C22⋊C4×C59—21no—
62C2×C22⋊C4×C59—41no—
63C2×C22⋊C4×C59—41no—
64C2×C22⋊C4×C59C2×C411yescharacteristic
65C2×C22⋊C4×C59C2×C411yescharacteristic
66#100×C59—24no—
67#100×C59—22no—
68#100×C59D414yescomplemented
69#99×C59—22no—
70#99×C59—22no—
71#99×C59—42no—
72#95×C59—21no—
73#95×C59—21no—
74C24×C59—21no—
75C24×C59—21no—
76C24×C59—21no—
77C24×C59—21no—
78C24×C59—21no—
79C24×C59—22no—
80C24×C59—22no—
81C24×C59—22no—
82C24×C59—41no—
83C24×C59—41no—
84C24×C59—42no—
85C24×C59—41no—
86C24×C59—42no—
87C24×C59—42no—
88C24×C59—41no—
89C24×C59—81no—
90C24×C59—81no—
91C24×C59—81no—
92C24×C59C22⋊C411yescharacteristic
93C24×C59C22⋊C411yescharacteristic
94C24×C59C22⋊C411yescharacteristic
95C24×C59C22×C411yescharacteristic
96C24×C59C2×D411yescharacteristic
97C2×D4×C59—24no—
98C2×D4×C59—22no—
99C2×D4×C59—22no—
100C2×D4×C59—22no—
101C2×D4×C59—22no—
102C2×D4×C59—21no—
103C2×D4×C59—21no—
104C2×D4×C59—41no—
105C2×D4×C59—41no—
106C2×D4×C59—41no—
107C2×D4×C59—41no—
108C2×D4×C59—41no—
109C2×D4×C59—41no—
110C2×D4×C59—44no—
111C2×D4×C59—44no—
112C2×D4×C59—44no—
113C2×D4×C59—44no—
114C2×D4×C59—42no—
115C2×D4×C59—42no—
116C2×D4×C59—42no—
117C2×D4×C59—42no—
118C2×D4×C59—44no—
119C2×D4×C59—44no—
120C2×D4×C59—44no—
121C2×D4×C59—41no—
122C2×D4×C59—41no—
123C2×D4×C59—44no—
124C2×D4×C59—42no—
125C2×D4×C59—42no—
126C2×D4×C59—42no—
127C2×D4×C59—42no—
128C2×D4×C59—81no—
129C2×D4×C59—81no—
130C2×D4×C59C2×D412yes—
131C2×D4×C59#4112yes—
132C22×C4×C59—21no—
133C22×C4×C59—21no—
134C22×C4×C59—22no—
135C22×C4×C59—21no—
136C22×C4×C59—21no—
137C22×C4×C59—21no—
138C22×C4×C59—21no—
139C22×C4×C59—21no—
140C22×C4×C59—42no—
141C22×C4×C59—41no—
142C22×C4×C59—42no—
143C22×C4×C59C22⋊C411yescharacteristic
144C22×C4×C59C2×D411yescharacteristic
145M16×C59—24no—
146M16×C59—44no—
147M16×C59—42no—
148C2×C8×C59—44no—
149C2×C8×C59—42no—
150C22⋊C4×C59—22no—
151C22⋊C4×C59—42no—
152C22⋊C4×C59—42no—
153C22⋊C4×C59—42no—
154C22⋊C4×C59—42no—
155C22⋊C4×C59—41no—
156C22⋊C4×C59—41no—
157C22⋊C4×C59—41no—
158C22⋊C4×C59—42no—
159C22⋊C4×C59—42no—
160C22⋊C4×C59—81no—
161C22⋊C4×C59—82no—
162C22⋊C4×C59—82no—
163C23×C59—22no—
164C23×C59—21no—
165C23×C59—21no—
166C23×C59—21no—
167C23×C59—21no—
168C23×C59—21no—
169C23×C59—21no—
170C23×C59—22no—
171C23×C59—21no—
172C23×C59—21no—
173C23×C59—21no—
174C23×C59—21no—
175C23×C59—21no—
176C23×C59—21no—
177C23×C59—41no—
178C23×C59—42no—
179C23×C59—42no—
180C23×C59—42no—
181C23×C59—42no—
182C23×C59—41no—
183C23×C59—41no—
184C23×C59—41no—
185C23×C59—41no—
186C23×C59—41no—
187C23×C59—41no—
188C23×C59—42no—
189C23×C59—41no—
190C23×C59—42no—
191C23×C59—41no—
192C23×C59—41no—
193C23×C59—41no—
194C23×C59—41no—
195C23×C59—42no—
196C23×C59—42no—
197C23×C59—42no—
198C23×C59—42no—
199C23×C59—41no—
200C23×C59—41no—
201C23×C59—41no—
202C23×C59—81no—
203C23×C59—81no—
204C23×C59—81no—
205C23×C59—81no—
206C23×C59—82no—
207C23×C59—84no—
208C23×C59—84no—
209C23×C59—84no—
210C23×C59—84no—
211C23×C59—84no—
212C23×C59—84no—
213C23×C59—82no—
214C23×C59#9911yescharacteristic
215C23×C59#9911yescharacteristic
216C23×C59C2×C22⋊C411yescharacteristic
217C23×C59C4×D412yes—
218C23×C59#12112yes—
219D4×C59—42no—
220D4×C59—42no—
221D4×C59—44no—
222D4×C59—44no—
223D4×C59—42no—
224D4×C59—42no—
225D4×C59—44no—
226D4×C59—48no—
227D4×C59—44no—
228D4×C59—84no—
229D4×C59—84no—
230C2×C4×C59—22no—
231C2×C4×C59—22no—
232C2×C4×C59—22no—
233C2×C4×C59—22no—
234C2×C4×C59—21no—
235C2×C4×C59—21no—
236C2×C4×C59—21no—
237C2×C4×C59—21no—
238C2×C4×C59—22no—
239C2×C4×C59—41no—
240C2×C4×C59—42no—
241C2×C4×C59—41no—
242C2×C4×C59—42no—
243C2×C4×C59—41no—
244C2×C4×C59—41no—
245C2×C4×C59—41no—
246C2×C4×C59—41no—
247C2×C4×C59—41no—
248C2×C4×C59—41no—
249C2×C4×C59—82no—
250C2×C4×C59—82no—
251C2×C4×C59—82no—
252C2×C4×C59#9912yes—
253C2×C4×C59#12011yescharacteristic
254C2×C4×C59#12311yescharacteristic
255C8×C59—44no—
256#13082C5911yesmaximal, characteristic, direct product factor, Sylow
257C22×C59—21no—
258C22×C59—21no—
259C22×C59—21no—
260C22×C59—21no—
261C22×C59—21no—
262C22×C59—21no—
263C22×C59—21no—
264C22×C59—22no—
265C22×C59—22no—
266C22×C59—42no—
267C22×C59—42no—
268C22×C59—42no—
269C22×C59—42no—
270C22×C59—42no—
271C22×C59—42no—
272C22×C59—42no—
273C22×C59—42no—
274C22×C59—41no—
275C22×C59—41no—
276C22×C59—41no—
277C22×C59—41no—
278C22×C59—42no—
279C22×C59—41no—
280C22×C59—41no—
281C22×C59—41no—
282C22×C59—41no—
283C22×C59—41no—
284C22×C59—41no—
285C22×C59—81no—
286C22×C59—84no—
287C22×C59—84no—
288C22×C59—81no—
289C22×C59—81no—
290C22×C59—81no—
291C22×C59—81no—
292C22×C59—81no—
293C22×C59—84no—
294C22×C59—84no—
295C22×C59—84no—
296C22×C59—84no—
297C22×C59—81no—
298C22×C59—81no—
299C22×C59AΣL(1,𝔽16)12yescomplemented
300C22×C59#38611yescharacteristic
301C22×C59C2×#9911yescharacteristic
302C22×C59C2×#9911yescharacteristic
303C4×C59—21no—
304C4×C59—22no—
305C4×C59—21no—
306C4×C59—42no—
307C4×C59—81no—
308C4×C59—81no—
309C4×C59—162no—
310C22×#100C2×C5911yescharacteristic, complemented
311#2403C2×C5911yescharacteristic
312C2×AΣL(1,𝔽16)C2×C5912yescomplemented
313#1781C2×C5911yescharacteristic, complemented
314#1390C2×C5912yescomplemented
315C2×C59—21no—
316C2×C59—21no—
317C2×C59—22no—
318C2×C59—42no—
319C2×C59—41no—
320C2×C59—42no—
321C2×C59—81no—
322C2×C59—82no—
323C2×C59—81no—
324C2×C59#189811yescharacteristic
325C2×C59C2×AΣL(1,𝔽16)11yescharacteristic
326C2×C59#212111yescharacteristic
327C23×D4C4×C5911yescharacteristic, complemented
328C23×D4C22×C5911yescharacteristic
329C22×M16—21no—
330C2×#120—21no—
331C2×#120C4×C5911yescharacteristic, complemented
332C2×#120C22×C5911yescharacteristic
333C2×#100—21no—
334C2×#100—24no—
335C2×#100C22×C5912yes—
336C2×#99—21no—
337C2×#99C22×C5912yes—
338#392—21no—
339#392—21no—
340#386—21no—
341#386C4×C5911yescharacteristic, complemented
342#386C22×C5911yescharacteristic
343#379—21no—
344#379C4×C5911yescharacteristic, complemented
345AΣL(1,𝔽16)—24no—
346C59#1308211yescharacteristic, direct product factor, Sylow
347C25C2×C4×C5911yescharacteristic
348C25C2×C4×C5911yescharacteristic
349C25D4×C5911yescharacteristic
350C22×D4—21no—
351C22×D4—22no—
352C22×D4—22no—
353C22×D4—21no—
354C22×D4—21no—
355C22×D4—21no—
356C22×D4—42no—
357C22×D4—41no—
358C22×D4—41no—
359C22×D4—44no—
360C22×D4—41no—
361C22×D4—41no—
362C22×D4C2×C4×C5911yescharacteristic
363C22×D4D4×C5911yescharacteristic
364C22×D4D4×C5911yescharacteristic
365C22×D4C23×C5911yescharacteristic
366C23×C4C2×C4×C5911yescharacteristic
367C23×C4D4×C5911yescharacteristic
368C2×M16—24no—
369C2×M16—22no—
370C2×M16—41no—
371C2×M16—42no—
372C22×C8—41no—
373#120—22no—
374#120—22no—
375#120—44no—
376#120—42no—
377C2×C22⋊C4—21no—
378C2×C22⋊C4—21no—
379C2×C22⋊C4—21no—
380C2×C22⋊C4—21no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—22no—
383C2×C22⋊C4—21no—
384C2×C22⋊C4—41no—
385C2×C22⋊C4—41no—
386C2×C22⋊C4C2×C4×C5911yescharacteristic
387C2×C22⋊C4C2×C4×C5911yescharacteristic
388#100—24no—
389#100—22no—
390#100D4×C5914yescomplemented
391#99—22no—
392#99—22no—
393#99—42no—
394#95—21no—
395#95—21no—
396C24—21no—
397C24—21no—
398C24—21no—
399C24—21no—
400C24—21no—
401C24—22no—
402C24—22no—
403C24—22no—
404C24—41no—
405C24—41no—
406C24—42no—
407C24—41no—
408C24—42no—
409C24—42no—
410C24—41no—
411C24—81no—
412C24—81no—
413C24—81no—
414C24C22⋊C4×C5911yescharacteristic
415C24C22⋊C4×C5911yescharacteristic
416C24C22⋊C4×C5911yescharacteristic
417C24C22×C4×C5911yescharacteristic
418C24C2×D4×C5911yescharacteristic
419C2×D4—24no—
420C2×D4—22no—
421C2×D4—22no—
422C2×D4—22no—
423C2×D4—22no—
424C2×D4—21no—
425C2×D4—21no—
426C2×D4—41no—
427C2×D4—41no—
428C2×D4—41no—
429C2×D4—41no—
430C2×D4—41no—
431C2×D4—41no—
432C2×D4—44no—
433C2×D4—44no—
434C2×D4—44no—
435C2×D4—44no—
436C2×D4—42no—
437C2×D4—42no—
438C2×D4—42no—
439C2×D4—42no—
440C2×D4—44no—
441C2×D4—44no—
442C2×D4—44no—
443C2×D4—41no—
444C2×D4—41no—
445C2×D4—44no—
446C2×D4—42no—
447C2×D4—42no—
448C2×D4—42no—
449C2×D4—42no—
450C2×D4—81no—
451C2×D4—81no—
452C2×D4C2×D4×C5912yes—
453C2×D4#41×C5912yes—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—22no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—42no—
463C22×C4—41no—
464C22×C4—42no—
465C22×C4C22⋊C4×C5911yescharacteristic
466C22×C4C2×D4×C5911yescharacteristic
467M16—24no—
468M16—44no—
469M16—42no—
470C2×C8—44no—
471C2×C8—42no—
472C22⋊C4—22no—
473C22⋊C4—42no—
474C22⋊C4—42no—
475C22⋊C4—42no—
476C22⋊C4—42no—
477C22⋊C4—41no—
478C22⋊C4—41no—
479C22⋊C4—41no—
480C22⋊C4—42no—
481C22⋊C4—42no—
482C22⋊C4—81no—
483C22⋊C4—82no—
484C22⋊C4—82no—
485C23—22no—
486C23—21no—
487C23—21no—
488C23—21no—
489C23—21no—
490C23—21no—
491C23—21no—
492C23—22no—
493C23—21no—
494C23—21no—
495C23—21no—
496C23—21no—
497C23—21no—
498C23—21no—
499C23—41no—
500C23—42no—
501C23—42no—
502C23—42no—
503C23—42no—
504C23—41no—
505C23—41no—
506C23—41no—
507C23—41no—
508C23—41no—
509C23—41no—
510C23—42no—
511C23—41no—
512C23—42no—
513C23—41no—
514C23—41no—
515C23—41no—
516C23—41no—
517C23—42no—
518C23—42no—
519C23—42no—
520C23—42no—
521C23—41no—
522C23—41no—
523C23—41no—
524C23—81no—
525C23—81no—
526C23—81no—
527C23—81no—
528C23—82no—
529C23—84no—
530C23—84no—
531C23—84no—
532C23—84no—
533C23—84no—
534C23—84no—
535C23—82no—
536C23#99×C5911yescharacteristic
537C23#99×C5911yescharacteristic
538C23C2×C22⋊C4×C5911yescharacteristic
539C23C4×D4×C5912yes—
540C23#121×C5912yes—
541D4—42no—
542D4—42no—
543D4—44no—
544D4—44no—
545D4—42no—
546D4—42no—
547D4—44no—
548D4—48no—
549D4—44no—
550D4—84no—
551D4—84no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—22no—
561C2×C4—41no—
562C2×C4—42no—
563C2×C4—41no—
564C2×C4—42no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—82no—
572C2×C4—82no—
573C2×C4—82no—
574C2×C4#99×C5912yes—
575C2×C4#120×C5911yescharacteristic
576C2×C4#123×C5911yescharacteristic
577C8—44no—
578C22—21no—
579C22—21no—
580C22—21no—
581C22—21no—
582C22—21no—
583C22—21no—
584C22—21no—
585C22—22no—
586C22—22no—
587C22—42no—
588C22—42no—
589C22—42no—
590C22—42no—
591C22—42no—
592C22—42no—
593C22—42no—
594C22—42no—
595C22—41no—
596C22—41no—
597C22—41no—
598C22—41no—
599C22—42no—
600C22—41no—
601C22—41no—
602C22—41no—
603C22—41no—
604C22—41no—
605C22—41no—
606C22—81no—
607C22—84no—
608C22—84no—
609C22—81no—
610C22—81no—
611C22—81no—
612C22—81no—
613C22—81no—
614C22—84no—
615C22—84no—
616C22—84no—
617C22—84no—
618C22—81no—
619C22—81no—
620C22C59×AΣL(1,𝔽16)12yescomplemented
621C22C59×#38611yescharacteristic
622C22C2×#99×C5911yescharacteristic
623C22C2×#99×C5911yescharacteristic
624C4—21no—
625C4—22no—
626C4—21no—
627C4—42no—
628C4—81no—
629C4—81no—
630C4—162no—
631C2—21no—
632C2—21no—
633C2—22no—
634C2—42no—
635C2—41no—
636C2—42no—
637C2—81no—
638C2—82no—
639C2—81no—
640C2C59×#189811yescharacteristic
641C2C2×C59×AΣL(1,𝔽16)11yescharacteristic
642C2C59×#212111yescharacteristic
subgroupG/H
center, socleC22×C59C2×#99
commutatorC24C22×C4×C59
Frattini, cosocleC22×D4C23×C59
prime radicalC59×#2403C2
LCSG ▷ C24 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C59 ◁ C24×C59 ◁ C23×D4×C59 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×#100×C59C2semidirect
3. C2×C59×AΣL(1,𝔽16)C2semidirect
4. C59×#1781C2semidirect
5. C59×#1390C2semidirect
6. C23×D4×C59C4semidirect
10. C2×#120×C59C4semidirect
20. C59×#386C4semidirect
23. C59×#379C4semidirect
68. #100×C59D4semidirect
256. #13082C59direct (N × H)
299. C22×C59AΣL(1,𝔽16)semidirect
310. C22×#100C2×C59semidirect
312. C2×AΣL(1,𝔽16)C2×C59semidirect
313. #1781C2×C59semidirect
314. #1390C2×C59semidirect
327. C23×D4C4×C59semidirect
331. C2×#120C4×C59semidirect
341. #386C4×C59semidirect
344. #379C4×C59semidirect
346. C59#13082direct (N × H)
390. #100D4×C59semidirect
620. C22C59×AΣL(1,𝔽16)semidirect

Maximal subgroups

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

subgroupindex
C22×#100×C592
C59×#24032
C2×C59×AΣL(1,𝔽16)2
C59×#17812
C59×#13902
#1308259