Finite Group Databasebeta

← C59×#16803 #28428912

Subgroups — C59×#16803 #28428912

Order 15104.

1402 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C59×#399C211yesmaximal, characteristic
2C2×C59×#393C211yesmaximal, characteristic
3C2×C59×#391C211yesmaximal, characteristic, complemented
4C2×C59×#388C211yesmaximal, characteristic
5C59×#1446C211yesmaximal, characteristic, complemented
6C59×#1445C211yesmaximal, characteristic, complemented
7C59×#1442C212yesmaximal, complemented
8C59×#1441C212yesmaximal, complemented
9C59×#1440C212yesmaximal
10C59×#1440C212yesmaximal
11C59×#1434C211yesmaximal, characteristic, complemented
12C23×Q8×C59C2211yescharacteristic
13C22×C4⋊C4×C59C2211yescharacteristic
14C22×C4⋊C4×C59C2212yes—
15C22×C4⋊C4×C59C2211yescharacteristic
16C22×C22⋊C4×C59C2212yes—
17C22×C22⋊C4×C59C2212yes—
18C22×C22⋊C4×C59C2211yescharacteristic
19C22×C22⋊C4×C59C2211yescharacteristic
20C22×C22⋊C4×C59C2211yescharacteristic
21C22×C42×C59C2211yescharacteristic
22C59×#399—24no—
23C59×#393—24no—
24C59×#391—24no—
25C59×#388—24no—
26C2×#95×C59C2211yescharacteristic
27C2×#95×C59C2211yescharacteristic
28C2×#95×C59C2212yes—
29C2×#95×C59C2212yes—
30C2×#95×C59C2211yescharacteristic
31C2×#95×C59C2212yes—
32C2×#95×C59C2211yescharacteristic
33C2×#95×C59C2212yes—
34C2×#95×C59C2212yes—
35C2×#95×C59C2212yes—
36C2×#95×C59C2212yes—
37C2×#95×C59C2212yes—
38C2×#95×C59C2212yes—
39C25×C59C2311yescharacteristic
40C22×Q8×C59—22no—
41C22×Q8×C59—22no—
42C22×Q8×C59—24no—
43C22×Q8×C59—22no—
44C22×Q8×C59—42no—
45C23×C4×C59C2311yescharacteristic
46C23×C4×C59C2312yes—
47C23×C4×C59C2311yescharacteristic
48C23×C4×C59C2312yes—
49C23×C4×C59C2311yescharacteristic
50C23×C4×C59C2311yescharacteristic
51C23×C4×C59C2311yescharacteristic
52C23×C4×C59C2312yes—
53C23×C4×C59C2312yes—
54C23×C4×C59C2311yescharacteristic
55C2×C4⋊C4×C59—22no—
56C2×C4⋊C4×C59—22no—
57C2×C4⋊C4×C59—24no—
58C2×C4⋊C4×C59—22no—
59C2×C4⋊C4×C59—24no—
60C2×C4⋊C4×C59—22no—
61C2×C4⋊C4×C59—42no—
62C2×C4⋊C4×C59—42no—
63C2×C22⋊C4×C59—22no—
64C2×C22⋊C4×C59—22no—
65C2×C22⋊C4×C59—24no—
66C2×C22⋊C4×C59—24no—
67C2×C22⋊C4×C59—22no—
68C2×C22⋊C4×C59—22no—
69C2×C22⋊C4×C59—24no—
70C2×C22⋊C4×C59—24no—
71C2×C22⋊C4×C59—42no—
72C2×C22⋊C4×C59—42no—
73C2×C22⋊C4×C59—42no—
74C2×C22⋊C4×C59—42no—
75C2×C22⋊C4×C59D414yes—
76C2×C42×C59—42no—
77C2×C42×C59D414yes—
78#95×C59—22no—
79#95×C59—22no—
80#95×C59—24no—
81#95×C59—24no—
82#95×C59—24no—
83#95×C59—22no—
84#95×C59—22no—
85#95×C59—24no—
86#95×C59—24no—
87#95×C59—42no—
88#95×C59—42no—
89#95×C59—42no—
90#95×C59—42no—
91C24×C59—21no—
92C24×C59—21no—
93C24×C59—22no—
94C24×C59—22no—
95C24×C59—22no—
96C24×C59—22no—
97C24×C59—21no—
98C24×C59—21no—
99C24×C59—21no—
100C24×C59—21no—
101C24×C59C2×D412yes—
102C24×C59C2411yescharacteristic
103C2×Q8×C59—28no—
104C2×Q8×C59—48no—
105C2×Q8×C59—48no—
106C2×Q8×C59—44no—
107C2×Q8×C59—44no—
108C22×C4×C59—22no—
109C22×C4×C59—22no—
110C22×C4×C59—22no—
111C22×C4×C59—21no—
112C22×C4×C59—22no—
113C22×C4×C59—22no—
114C22×C4×C59—22no—
115C22×C4×C59—22no—
116C22×C4×C59—21no—
117C22×C4×C59—22no—
118C22×C4×C59—22no—
119C22×C4×C59—22no—
120C22×C4×C59—22no—
121C22×C4×C59—22no—
122C22×C4×C59—22no—
123C22×C4×C59—22no—
124C22×C4×C59—22no—
125C22×C4×C59—22no—
126C22×C4×C59—22no—
127C22×C4×C59—22no—
128C22×C4×C59—21no—
129C22×C4×C59—21no—
130C22×C4×C59—21no—
131C22×C4×C59—21no—
132C22×C4×C59—22no—
133C22×C4×C59—22no—
134C22×C4×C59—21no—
135C22×C4×C59—22no—
136C22×C4×C59—22no—
137C22×C4×C59—21no—
138C22×C4×C59—22no—
139C22×C4×C59—22no—
140C22×C4×C59—22no—
141C22×C4×C59—22no—
142C22×C4×C59—22no—
143C22×C4×C59—22no—
144C22×C4×C59—22no—
145C22×C4×C59—22no—
146C22×C4×C59—22no—
147C22×C4×C59—22no—
148C22×C4×C59—22no—
149C22×C4×C59—22no—
150C22×C4×C59—22no—
151C22×C4×C59—22no—
152C22×C4×C59—21no—
153C22×C4×C59—21no—
154C22×C4×C59—22no—
155C22×C4×C59—22no—
156C22×C4×C59—21no—
157C22×C4×C59—21no—
158C22×C4×C59C2×D412yes—
159C22×C4×C59C2×D412yes—
160C22×C4×C59C2×D412yes—
161C22×C4×C59C2×D412yes—
162C22×C4×C59C2×D412yes—
163C22×C4×C59#4114yes—
164C22×C4×C59#4114yes—
165C22×C4×C59#4112yes—
166C4⋊C4×C59—48no—
167C4⋊C4×C59—44no—
168C4⋊C4×C59—44no—
169C22⋊C4×C59—28no—
170C22⋊C4×C59—48no—
171C22⋊C4×C59—48no—
172C22⋊C4×C59—44no—
173C22⋊C4×C59—44no—
174C42×C59—44no—
175C23×C59—22no—
176C23×C59—22no—
177C23×C59—22no—
178C23×C59—24no—
179C23×C59—24no—
180C23×C59—41no—
181C23×C59—41no—
182C23×C59—41no—
183C23×C59—41no—
184C23×C59—41no—
185C23×C59—41no—
186C23×C59—42no—
187C23×C59—41no—
188C23×C59—41no—
189C23×C59—42no—
190C23×C59—42no—
191C23×C59—42no—
192C23×C59—42no—
193C23×C59—42no—
194C23×C59—42no—
195C23×C59—42no—
196C23×C59—42no—
197C23×C59—42no—
198C23×C59C22×D411yescharacteristic
199C23×C59C22×D411yescharacteristic
200C23×C59C2×#4111yescharacteristic
201C23×C59C2×#4112yes—
202C23×C59C2×#4112yes—
203C23×C59H(5,𝔽2)12yes—
204C23×C59H(5,𝔽2)12yes—
205C23×C592−1+411yescharacteristic
206C23×C592−1+411yescharacteristic
207C23×C592−1+411yescharacteristic
208C23×C592−1+411yescharacteristic
209Q8×C59—416no—
210C2×C4×C59—22no—
211C2×C4×C59—22no—
212C2×C4×C59—24no—
213C2×C4×C59—24no—
214C2×C4×C59—22no—
215C2×C4×C59—24no—
216C2×C4×C59—22no—
217C2×C4×C59—22no—
218C2×C4×C59—22no—
219C2×C4×C59—22no—
220C2×C4×C59—22no—
221C2×C4×C59—22no—
222C2×C4×C59—24no—
223C2×C4×C59—24no—
224C2×C4×C59—24no—
225C2×C4×C59—24no—
226C2×C4×C59—24no—
227C2×C4×C59—24no—
228C2×C4×C59—42no—
229C2×C4×C59—41no—
230C2×C4×C59—42no—
231C2×C4×C59—41no—
232C2×C4×C59—42no—
233C2×C4×C59—42no—
234C2×C4×C59—42no—
235C2×C4×C59—42no—
236C2×C4×C59—42no—
237C2×C4×C59—42no—
238C2×C4×C59—42no—
239C2×C4×C59—42no—
240C2×C4×C59—42no—
241C2×C4×C59—42no—
242C2×C4×C59—42no—
243C2×C4×C59—42no—
244C2×C4×C59—41no—
245C2×C4×C59—42no—
246C2×C4×C59—41no—
247C2×C4×C59—41no—
248C2×C4×C59—41no—
249C2×C4×C59—42no—
250C2×C4×C59—41no—
251C2×C4×C59—41no—
252C2×C4×C59—42no—
253C2×C4×C59—42no—
254C2×C4×C59—42no—
255C2×C4×C59—42no—
256C2×C4×C59—42no—
257C2×C4×C59—42no—
258C2×C4×C59—42no—
259C2×C4×C59—42no—
260C2×C4×C59—42no—
261C2×C4×C59—42no—
262C2×C4×C59—42no—
263C2×C4×C59—42no—
264C2×C4×C59—42no—
265C2×C4×C59—42no—
266C2×C4×C59—42no—
267C2×C4×C59#12114yes—
268#16803C5911yesmaximal, characteristic, direct product factor, Sylow
269C22×C59—42no—
270C22×C59—44no—
271C22×C59—44no—
272C22×C59—42no—
273C22×C59—42no—
274C22×C59—81no—
275C22×C59—81no—
276C22×C59—81no—
277C22×C59—81no—
278C22×C59—82no—
279C22×C59—82no—
280C22×C59C2×#12111yescharacteristic
281C22×C59#52511yescharacteristic
282C22×C59#53211yescharacteristic
283C22×C59#53411yescharacteristic
284C22×C59#53511yescharacteristic
285C22×C59#53611yescharacteristic
286C22×C59#53611yescharacteristic
287C22×C59#53611yescharacteristic
288C22×C59#53611yescharacteristic
289C22×C59#53912yes—
290C22×C59#54111yescharacteristic
291C22×C59#54111yescharacteristic
292C22×C59#54212yes—
293C22×C59#54212yes—
294C22×C59#54212yes—
295C22×C59#54612yes—
296C22×C59#54612yes—
297C22×C59#55112yes—
298C22×C59#55212yes—
299C22×C59#55612yes—
300C22×C59#55912yes—
301C22×C59#56212yes—
302C22×C59#56212yes—
303C4×C59—24no—
304C4×C59—42no—
305C4×C59—42no—
306C4×C59—44no—
307C4×C59—44no—
308C4×C59—42no—
309C4×C59—81no—
310C4×C59—81no—
311C4×C59—82no—
312C4×C59—82no—
313C2×#399C2×C5911yescharacteristic
314C2×#393C2×C5911yescharacteristic
315C2×#391C2×C5911yescharacteristic, complemented
316C2×#388C2×C5911yescharacteristic
317#1446C2×C5911yescharacteristic, complemented
318#1445C2×C5911yescharacteristic, complemented
319#1442C2×C5912yescomplemented
320#1441C2×C5912yescomplemented
321#1440C2×C5912yes—
322#1440C2×C5912yes—
323#1434C2×C5911yescharacteristic, complemented
324C2×C59—82no—
325C2×C59#253411yescharacteristic
326C2×C59#254411yescharacteristic
327C2×C59#260411yescharacteristic
328C2×C59#262111yescharacteristic
329C2×C59#263211yescharacteristic
330C2×C59#266311yescharacteristic
331C2×C59#268712yes—
332C2×C59#270012yes—
333C2×C59#275412yes—
334C2×C59#279812yes—
335C2×C59#281611yescharacteristic
336C23×Q8C22×C5911yescharacteristic
337C22×C4⋊C4C22×C5911yescharacteristic
338C22×C4⋊C4C22×C5912yes—
339C22×C4⋊C4C22×C5911yescharacteristic
340C22×C22⋊C4C22×C5912yes—
341C22×C22⋊C4C22×C5912yes—
342C22×C22⋊C4C22×C5911yescharacteristic
343C22×C22⋊C4C22×C5911yescharacteristic
344C22×C22⋊C4C22×C5911yescharacteristic
345C22×C42C22×C5911yescharacteristic
346#399—24no—
347#393—24no—
348#391—24no—
349#388—24no—
350C2×#95C22×C5911yescharacteristic
351C2×#95C22×C5912yes—
352C2×#95C22×C5911yescharacteristic
353C2×#95C22×C5912yes—
354C2×#95C22×C5912yes—
355C2×#95C22×C5912yes—
356C2×#95C22×C5912yes—
357C2×#95C22×C5911yescharacteristic
358C2×#95C22×C5911yescharacteristic
359C2×#95C22×C5912yes—
360C2×#95C22×C5912yes—
361C2×#95C22×C5912yes—
362C2×#95C22×C5912yes—
363C59#1680311yescharacteristic, direct product factor, Sylow
364C25C23×C5911yescharacteristic
365C22×Q8—22no—
366C22×Q8—22no—
367C22×Q8—24no—
368C22×Q8—22no—
369C22×Q8—42no—
370C23×C4C23×C5912yes—
371C23×C4C23×C5911yescharacteristic
372C23×C4C23×C5911yescharacteristic
373C23×C4C23×C5912yes—
374C23×C4C23×C5911yescharacteristic
375C23×C4C23×C5911yescharacteristic
376C23×C4C23×C5911yescharacteristic
377C23×C4C23×C5912yes—
378C23×C4C23×C5912yes—
379C23×C4C23×C5911yescharacteristic
380C2×C4⋊C4—22no—
381C2×C4⋊C4—22no—
382C2×C4⋊C4—24no—
383C2×C4⋊C4—22no—
384C2×C4⋊C4—24no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4—42no—
387C2×C4⋊C4—42no—
388C2×C22⋊C4—22no—
389C2×C22⋊C4—22no—
390C2×C22⋊C4—24no—
391C2×C22⋊C4—24no—
392C2×C22⋊C4—22no—
393C2×C22⋊C4—22no—
394C2×C22⋊C4—24no—
395C2×C22⋊C4—24no—
396C2×C22⋊C4—42no—
397C2×C22⋊C4—42no—
398C2×C22⋊C4—42no—
399C2×C22⋊C4—42no—
400C2×C22⋊C4D4×C5914yes—
401C2×C42—42no—
402C2×C42D4×C5914yes—
403#95—22no—
404#95—22no—
405#95—24no—
406#95—24no—
407#95—24no—
408#95—22no—
409#95—22no—
410#95—24no—
411#95—24no—
412#95—42no—
413#95—42no—
414#95—42no—
415#95—42no—
416C24—21no—
417C24—21no—
418C24—22no—
419C24—22no—
420C24—22no—
421C24—22no—
422C24—21no—
423C24—21no—
424C24—21no—
425C24—21no—
426C24C2×D4×C5912yes—
427C24C24×C5911yescharacteristic
428C2×Q8—28no—
429C2×Q8—48no—
430C2×Q8—48no—
431C2×Q8—44no—
432C2×Q8—44no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—21no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—21no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—21no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—21no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4C2×D4×C5912yes—
484C22×C4C2×D4×C5912yes—
485C22×C4C2×D4×C5912yes—
486C22×C4C2×D4×C5912yes—
487C22×C4C2×D4×C5912yes—
488C22×C4#41×C5914yes—
489C22×C4#41×C5914yes—
490C22×C4#41×C5912yes—
491C4⋊C4—48no—
492C4⋊C4—44no—
493C4⋊C4—44no—
494C22⋊C4—28no—
495C22⋊C4—48no—
496C22⋊C4—48no—
497C22⋊C4—44no—
498C22⋊C4—44no—
499C42—44no—
500C23—22no—
501C23—22no—
502C23—22no—
503C23—24no—
504C23—24no—
505C23—41no—
506C23—41no—
507C23—41no—
508C23—41no—
509C23—41no—
510C23—41no—
511C23—42no—
512C23—41no—
513C23—41no—
514C23—42no—
515C23—42no—
516C23—42no—
517C23—42no—
518C23—42no—
519C23—42no—
520C23—42no—
521C23—42no—
522C23—42no—
523C23C22×D4×C5911yescharacteristic
524C23C22×D4×C5911yescharacteristic
525C23C2×#41×C5911yescharacteristic
526C23C2×#41×C5912yes—
527C23C2×#41×C5912yes—
528C23H(5,𝔽2)×C5912yes—
529C23H(5,𝔽2)×C5912yes—
530C232−1+4×C5911yescharacteristic
531C232−1+4×C5911yescharacteristic
532C232−1+4×C5911yescharacteristic
533C232−1+4×C5911yescharacteristic
534Q8—416no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—24no—
538C2×C4—24no—
539C2×C4—22no—
540C2×C4—24no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—24no—
548C2×C4—24no—
549C2×C4—24no—
550C2×C4—24no—
551C2×C4—24no—
552C2×C4—24no—
553C2×C4—42no—
554C2×C4—41no—
555C2×C4—42no—
556C2×C4—41no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—42no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—42no—
563C2×C4—42no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—41no—
570C2×C4—42no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—42no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—42no—
580C2×C4—42no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4#121×C5914yes—
593C22—42no—
594C22—42no—
595C22—42no—
596C22—44no—
597C22—44no—
598C22—82no—
599C22—82no—
600C22—81no—
601C22—81no—
602C22—81no—
603C22—81no—
604C22C2×#121×C5911yescharacteristic
605C22C59×#52511yescharacteristic
606C22C59×#53211yescharacteristic
607C22C59×#53411yescharacteristic
608C22C59×#53511yescharacteristic
609C22C59×#53611yescharacteristic
610C22C59×#53611yescharacteristic
611C22C59×#53611yescharacteristic
612C22C59×#53611yescharacteristic
613C22C59×#53912yes—
614C22C59×#54111yescharacteristic
615C22C59×#54111yescharacteristic
616C22C59×#54212yes—
617C22C59×#54212yes—
618C22C59×#54212yes—
619C22C59×#54612yes—
620C22C59×#54612yes—
621C22C59×#55112yes—
622C22C59×#55212yes—
623C22C59×#55612yes—
624C22C59×#55912yes—
625C22C59×#56212yes—
626C22C59×#56212yes—
627C4—24no—
628C4—44no—
629C4—42no—
630C4—42no—
631C4—42no—
632C4—44no—
633C4—82no—
634C4—81no—
635C4—81no—
636C4—82no—
637C2—82no—
638C2C59×#253411yescharacteristic
639C2C59×#254411yescharacteristic
640C2C59×#260411yescharacteristic
641C2C59×#262111yescharacteristic
642C2C59×#263211yescharacteristic
643C2C59×#266311yescharacteristic
644C2C59×#268712yes—
645C2C59×#270012yes—
646C2C59×#275412yes—
647C2C59×#279812yes—
648C2C59×#281611yescharacteristic
subgroupG/H
center, socleC24×C59C24
commutator, Frattini, cosocleC24C24×C59
prime radicalC25×C59C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C59 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C59×#391C2semidirect
5. C59×#1446C2semidirect
6. C59×#1445C2semidirect
7. C59×#1442C2semidirect
8. C59×#1441C2semidirect
11. C59×#1434C2semidirect
268. #16803C59direct (N × H)
315. C2×#391C2×C59semidirect
317. #1446C2×C59semidirect
318. #1445C2×C59semidirect
319. #1442C2×C59semidirect
320. #1441C2×C59semidirect
323. #1434C2×C59semidirect
363. C59#16803direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C59×#3992
C2×C59×#3932
C2×C59×#3912
C2×C59×#3882
C59×#14462
C59×#14452
C59×#14422
C59×#14412
C59×#14402
C59×#14342
#1680359