Finite Group Databasebeta

← C59×#16812 #28428921

Subgroups — C59×#16812 #28428921

Order 15104.

1486 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C59×#398C211yesmaximal, characteristic, complemented
2C2×C59×#397C211yesmaximal, characteristic
3C2×C59×#395C211yesmaximal, characteristic, complemented
4C2×C59×#393C211yesmaximal, characteristic
5C2×C59×#391C211yesmaximal, characteristic, complemented
6C2×C59×#388C211yesmaximal, characteristic
7C59×#1445C212yesmaximal, complemented
8C59×#1445C212yesmaximal, complemented
9C59×#1439C212yesmaximal
10C59×#1439C212yesmaximal
11C59×#1434C211yesmaximal, characteristic, complemented
12C23×Q8×C59C2211yescharacteristic
13C22×C4⋊C4×C59C2211yescharacteristic
14C22×C4⋊C4×C59C2211yescharacteristic
15C22×C4⋊C4×C59C2212yes—
16C22×C4⋊C4×C59C2212yes—
17C22×C22⋊C4×C59C2211yescharacteristic
18C22×C22⋊C4×C59C2211yescharacteristic
19C22×C22⋊C4×C59C2212yes—
20C22×C22⋊C4×C59C2212yes—
21C22×C22⋊C4×C59C2211yescharacteristic
22C22×C42×C59C2211yescharacteristic
23C59×#398—24no—
24C59×#397—24no—
25C59×#395—24no—
26C59×#393—24no—
27C59×#391—24no—
28C59×#388—24no—
29C2×#95×C59C2211yescharacteristic
30C2×#95×C59C2211yescharacteristic
31C2×#95×C59C2212yes—
32C2×#95×C59C2212yes—
33C2×#95×C59C2212yes—
34C2×#95×C59C2212yes—
35C2×#95×C59C2212yes—
36C2×#95×C59C2212yes—
37C2×#95×C59C2212yes—
38C2×#95×C59C2212yes—
39C2×#95×C59C2211yescharacteristic
40C2×#95×C59C2211yescharacteristic
41C25×C59C2311yescharacteristic
42C22×Q8×C59—22no—
43C22×Q8×C59—22no—
44C22×Q8×C59—22no—
45C22×Q8×C59—24no—
46C22×Q8×C59—42no—
47C23×C4×C59C2311yescharacteristic
48C23×C4×C59C2312yes—
49C23×C4×C59C2311yescharacteristic
50C23×C4×C59C2311yescharacteristic
51C23×C4×C59C2311yescharacteristic
52C23×C4×C59C2312yes—
53C23×C4×C59C2312yes—
54C23×C4×C59C2312yes—
55C23×C4×C59C2311yescharacteristic
56C23×C4×C59C2311yescharacteristic
57C2×C4⋊C4×C59—22no—
58C2×C4⋊C4×C59—22no—
59C2×C4⋊C4×C59—24no—
60C2×C4⋊C4×C59—22no—
61C2×C4⋊C4×C59—22no—
62C2×C4⋊C4×C59—24no—
63C2×C4⋊C4×C59—22no—
64C2×C4⋊C4×C59—22no—
65C2×C4⋊C4×C59—24no—
66C2×C4⋊C4×C59—24no—
67C2×C4⋊C4×C59—42no—
68C2×C4⋊C4×C59—42no—
69C2×C22⋊C4×C59—22no—
70C2×C22⋊C4×C59—22no—
71C2×C22⋊C4×C59—22no—
72C2×C22⋊C4×C59—24no—
73C2×C22⋊C4×C59—22no—
74C2×C22⋊C4×C59—22no—
75C2×C22⋊C4×C59—24no—
76C2×C22⋊C4×C59—22no—
77C2×C22⋊C4×C59—24no—
78C2×C22⋊C4×C59—22no—
79C2×C22⋊C4×C59—24no—
80C2×C22⋊C4×C59—42no—
81C2×C22⋊C4×C59—42no—
82C2×C22⋊C4×C59—42no—
83C2×C42×C59—42no—
84C2×C42×C59D414yes—
85#95×C59—22no—
86#95×C59—22no—
87#95×C59—24no—
88#95×C59—24no—
89#95×C59—24no—
90#95×C59—24no—
91#95×C59—24no—
92#95×C59—24no—
93#95×C59—42no—
94#95×C59—42no—
95#95×C59D414yes—
96#95×C59D414yes—
97C24×C59—21no—
98C24×C59—21no—
99C24×C59—21no—
100C24×C59—21no—
101C24×C59—22no—
102C24×C59—22no—
103C24×C59—21no—
104C24×C59—22no—
105C24×C59—21no—
106C24×C59—22no—
107C24×C59#4112yes—
108C24×C59C2411yescharacteristic
109C2×Q8×C59—28no—
110C2×Q8×C59—48no—
111C2×Q8×C59—48no—
112C2×Q8×C59—44no—
113C2×Q8×C59—44no—
114C22×C4×C59—22no—
115C22×C4×C59—22no—
116C22×C4×C59—21no—
117C22×C4×C59—22no—
118C22×C4×C59—21no—
119C22×C4×C59—22no—
120C22×C4×C59—22no—
121C22×C4×C59—21no—
122C22×C4×C59—21no—
123C22×C4×C59—21no—
124C22×C4×C59—21no—
125C22×C4×C59—22no—
126C22×C4×C59—22no—
127C22×C4×C59—22no—
128C22×C4×C59—22no—
129C22×C4×C59—22no—
130C22×C4×C59—21no—
131C22×C4×C59—22no—
132C22×C4×C59—22no—
133C22×C4×C59—22no—
134C22×C4×C59—22no—
135C22×C4×C59—22no—
136C22×C4×C59—22no—
137C22×C4×C59—22no—
138C22×C4×C59—21no—
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—21no—
147C22×C4×C59—21no—
148C22×C4×C59—21no—
149C22×C4×C59—21no—
150C22×C4×C59—21no—
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—22no—
158C22×C4×C59—22no—
159C22×C4×C59—22no—
160C22×C4×C59—22no—
161C22×C4×C59—22no—
162C22×C4×C59—22no—
163C22×C4×C59—22no—
164C22×C4×C59—22no—
165C22×C4×C59C2×D412yes—
166C22×C4×C59C2×D412yes—
167C22×C4×C59C2×D414yes—
168C22×C4×C59C2×D414yes—
169C22×C4×C59C2×D412yes—
170C22×C4×C59C2×D412yes—
171C22×C4×C59C2×D412yes—
172C22×C4×C59#4112yes—
173C22×C4×C59#4114yes—
174C4⋊C4×C59—48no—
175C4⋊C4×C59—48no—
176C4⋊C4×C59—44no—
177C4⋊C4×C59—44no—
178C22⋊C4×C59—28no—
179C22⋊C4×C59—48no—
180C22⋊C4×C59—48no—
181C22⋊C4×C59—44no—
182C22⋊C4×C59—44no—
183C42×C59—44no—
184C23×C59—22no—
185C23×C59—24no—
186C23×C59—22no—
187C23×C59—22no—
188C23×C59—24no—
189C23×C59—41no—
190C23×C59—41no—
191C23×C59—41no—
192C23×C59—41no—
193C23×C59—41no—
194C23×C59—42no—
195C23×C59—42no—
196C23×C59—41no—
197C23×C59—42no—
198C23×C59—42no—
199C23×C59—42no—
200C23×C59—42no—
201C23×C59—42no—
202C23×C59—41no—
203C23×C59—41no—
204C23×C59—42no—
205C23×C59—42no—
206C23×C59—42no—
207C23×C59C22×D411yescharacteristic
208C23×C59C22×D411yescharacteristic
209C23×C59C22×D411yescharacteristic
210C23×C59C2×#4111yescharacteristic
211C23×C59C2×#4112yes—
212C23×C59C2×#4111yescharacteristic
213C23×C59H(5,𝔽2)12yes—
214C23×C59H(5,𝔽2)11yescharacteristic
215C23×C592−1+412yes—
216C23×C592−1+412yes—
217C23×C592−1+411yescharacteristic
218Q8×C59—416no—
219C2×C4×C59—22no—
220C2×C4×C59—22no—
221C2×C4×C59—24no—
222C2×C4×C59—24no—
223C2×C4×C59—22no—
224C2×C4×C59—22no—
225C2×C4×C59—24no—
226C2×C4×C59—22no—
227C2×C4×C59—22no—
228C2×C4×C59—22no—
229C2×C4×C59—24no—
230C2×C4×C59—24no—
231C2×C4×C59—22no—
232C2×C4×C59—22no—
233C2×C4×C59—24no—
234C2×C4×C59—24no—
235C2×C4×C59—24no—
236C2×C4×C59—22no—
237C2×C4×C59—24no—
238C2×C4×C59—24no—
239C2×C4×C59—24no—
240C2×C4×C59—22no—
241C2×C4×C59—41no—
242C2×C4×C59—42no—
243C2×C4×C59—42no—
244C2×C4×C59—41no—
245C2×C4×C59—42no—
246C2×C4×C59—42no—
247C2×C4×C59—42no—
248C2×C4×C59—42no—
249C2×C4×C59—42no—
250C2×C4×C59—42no—
251C2×C4×C59—41no—
252C2×C4×C59—42no—
253C2×C4×C59—42no—
254C2×C4×C59—41no—
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—41no—
262C2×C4×C59—42no—
263C2×C4×C59—41no—
264C2×C4×C59—41no—
265C2×C4×C59—42no—
266C2×C4×C59—41no—
267C2×C4×C59—41no—
268C2×C4×C59—41no—
269C2×C4×C59—42no—
270C2×C4×C59—42no—
271C2×C4×C59—42no—
272C2×C4×C59—42no—
273C2×C4×C59—42no—
274C2×C4×C59—42no—
275C2×C4×C59—42no—
276C2×C4×C59—42no—
277C2×C4×C59—42no—
278C2×C4×C59#12714yes—
279#16812C5911yesmaximal, characteristic, direct product factor, Sylow
280C22×C59—42no—
281C22×C59—42no—
282C22×C59—44no—
283C22×C59—44no—
284C22×C59—42no—
285C22×C59—81no—
286C22×C59—81no—
287C22×C59—82no—
288C22×C59—82no—
289C22×C59—81no—
290C22×C59—81no—
291C22×C59#52511yescharacteristic
292C22×C59#52511yescharacteristic
293C22×C59C2×#12711yescharacteristic
294C22×C59#53411yescharacteristic
295C22×C59#53611yescharacteristic
296C22×C59#53611yescharacteristic
297C22×C59#53612yes—
298C22×C59#53612yes—
299C22×C59#53711yescharacteristic
300C22×C59#53912yes—
301C22×C59#54112yes—
302C22×C59#54212yes—
303C22×C59#54212yes—
304C22×C59#54611yescharacteristic
305C22×C59#54612yes—
306C22×C59#54612yes—
307C22×C59#54611yescharacteristic
308C22×C59#54811yescharacteristic
309C22×C59#54811yescharacteristic
310C22×C59#55212yes—
311C22×C59#55612yes—
312C22×C59#56212yes—
313C22×C59#56312yes—
314C4×C59—24no—
315C4×C59—42no—
316C4×C59—44no—
317C4×C59—44no—
318C4×C59—44no—
319C4×C59—42no—
320C4×C59—42no—
321C4×C59—81no—
322C4×C59—81no—
323C4×C59—82no—
324C2×#398C2×C5911yescharacteristic, complemented
325C2×#397C2×C5911yescharacteristic
326C2×#395C2×C5911yescharacteristic, complemented
327C2×#393C2×C5911yescharacteristic
328C2×#391C2×C5911yescharacteristic, complemented
329C2×#388C2×C5911yescharacteristic
330#1445C2×C5912yescomplemented
331#1445C2×C5912yescomplemented
332#1439C2×C5912yes—
333#1439C2×C5912yes—
334#1434C2×C5911yescharacteristic, complemented
335C2×C59—82no—
336C2×C59#253911yescharacteristic
337C2×C59#254011yescharacteristic
338C2×C59#259911yescharacteristic
339C2×C59#263711yescharacteristic
340C2×C59#263811yescharacteristic
341C2×C59#265811yescharacteristic
342C2×C59#268712yes—
343C2×C59#269012yes—
344C2×C59#270012yes—
345C2×C59#271612yes—
346C2×C59#281411yescharacteristic
347C23×Q8C22×C5911yescharacteristic
348C22×C4⋊C4C22×C5911yescharacteristic
349C22×C4⋊C4C22×C5911yescharacteristic
350C22×C4⋊C4C22×C5912yes—
351C22×C4⋊C4C22×C5912yes—
352C22×C22⋊C4C22×C5911yescharacteristic
353C22×C22⋊C4C22×C5911yescharacteristic
354C22×C22⋊C4C22×C5912yes—
355C22×C22⋊C4C22×C5912yes—
356C22×C22⋊C4C22×C5911yescharacteristic
357C22×C42C22×C5911yescharacteristic
358#398—24no—
359#397—24no—
360#395—24no—
361#393—24no—
362#391—24no—
363#388—24no—
364C2×#95C22×C5912yes—
365C2×#95C22×C5912yes—
366C2×#95C22×C5912yes—
367C2×#95C22×C5912yes—
368C2×#95C22×C5912yes—
369C2×#95C22×C5912yes—
370C2×#95C22×C5911yescharacteristic
371C2×#95C22×C5911yescharacteristic
372C2×#95C22×C5912yes—
373C2×#95C22×C5912yes—
374C2×#95C22×C5911yescharacteristic
375C2×#95C22×C5911yescharacteristic
376C59#1681211yescharacteristic, direct product factor, Sylow
377C25C23×C5911yescharacteristic
378C22×Q8—22no—
379C22×Q8—22no—
380C22×Q8—22no—
381C22×Q8—24no—
382C22×Q8—42no—
383C23×C4C23×C5911yescharacteristic
384C23×C4C23×C5912yes—
385C23×C4C23×C5911yescharacteristic
386C23×C4C23×C5912yes—
387C23×C4C23×C5912yes—
388C23×C4C23×C5911yescharacteristic
389C23×C4C23×C5911yescharacteristic
390C23×C4C23×C5911yescharacteristic
391C23×C4C23×C5912yes—
392C23×C4C23×C5911yescharacteristic
393C2×C4⋊C4—22no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4—24no—
396C2×C4⋊C4—22no—
397C2×C4⋊C4—22no—
398C2×C4⋊C4—24no—
399C2×C4⋊C4—22no—
400C2×C4⋊C4—22no—
401C2×C4⋊C4—24no—
402C2×C4⋊C4—24no—
403C2×C4⋊C4—42no—
404C2×C4⋊C4—42no—
405C2×C22⋊C4—22no—
406C2×C22⋊C4—22no—
407C2×C22⋊C4—22no—
408C2×C22⋊C4—24no—
409C2×C22⋊C4—22no—
410C2×C22⋊C4—22no—
411C2×C22⋊C4—24no—
412C2×C22⋊C4—22no—
413C2×C22⋊C4—24no—
414C2×C22⋊C4—22no—
415C2×C22⋊C4—24no—
416C2×C22⋊C4—42no—
417C2×C22⋊C4—42no—
418C2×C22⋊C4—42no—
419C2×C42—42no—
420C2×C42D4×C5914yes—
421#95—22no—
422#95—22no—
423#95—24no—
424#95—24no—
425#95—24no—
426#95—24no—
427#95—24no—
428#95—24no—
429#95—42no—
430#95—42no—
431#95D4×C5914yes—
432#95D4×C5914yes—
433C24—21no—
434C24—21no—
435C24—21no—
436C24—21no—
437C24—22no—
438C24—22no—
439C24—21no—
440C24—22no—
441C24—21no—
442C24—22no—
443C24#41×C5912yes—
444C24C24×C5911yescharacteristic
445C2×Q8—28no—
446C2×Q8—48no—
447C2×Q8—48no—
448C2×Q8—44no—
449C2×Q8—44no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—21no—
453C22×C4—22no—
454C22×C4—21no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—21no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—21no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—22no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—21no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4C2×D4×C5912yes—
502C22×C4C2×D4×C5912yes—
503C22×C4C2×D4×C5914yes—
504C22×C4C2×D4×C5914yes—
505C22×C4C2×D4×C5912yes—
506C22×C4C2×D4×C5912yes—
507C22×C4C2×D4×C5912yes—
508C22×C4#41×C5912yes—
509C22×C4#41×C5914yes—
510C4⋊C4—48no—
511C4⋊C4—48no—
512C4⋊C4—44no—
513C4⋊C4—44no—
514C22⋊C4—28no—
515C22⋊C4—48no—
516C22⋊C4—48no—
517C22⋊C4—44no—
518C22⋊C4—44no—
519C42—44no—
520C23—22no—
521C23—24no—
522C23—22no—
523C23—22no—
524C23—24no—
525C23—41no—
526C23—41no—
527C23—41no—
528C23—41no—
529C23—41no—
530C23—42no—
531C23—42no—
532C23—41no—
533C23—42no—
534C23—42no—
535C23—42no—
536C23—42no—
537C23—41no—
538C23—42no—
539C23—41no—
540C23—42no—
541C23—42no—
542C23—42no—
543C23C22×D4×C5911yescharacteristic
544C23C22×D4×C5911yescharacteristic
545C23C22×D4×C5911yescharacteristic
546C23C2×#41×C5911yescharacteristic
547C23C2×#41×C5912yes—
548C23C2×#41×C5911yescharacteristic
549C23H(5,𝔽2)×C5912yes—
550C23H(5,𝔽2)×C5911yescharacteristic
551C232−1+4×C5912yes—
552C232−1+4×C5912yes—
553C232−1+4×C5911yescharacteristic
554Q8—416no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—24no—
558C2×C4—24no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—24no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—24no—
567C2×C4—24no—
568C2×C4—22no—
569C2×C4—24no—
570C2×C4—24no—
571C2×C4—24no—
572C2×C4—22no—
573C2×C4—24no—
574C2×C4—24no—
575C2×C4—24no—
576C2×C4—22no—
577C2×C4—41no—
578C2×C4—42no—
579C2×C4—42no—
580C2×C4—41no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—41no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—41no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4—41no—
598C2×C4—42no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—42no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—42no—
606C2×C4—42no—
607C2×C4—42no—
608C2×C4—42no—
609C2×C4—42no—
610C2×C4—42no—
611C2×C4—42no—
612C2×C4—42no—
613C2×C4—42no—
614C2×C4#127×C5914yes—
615C22—42no—
616C22—42no—
617C22—42no—
618C22—44no—
619C22—44no—
620C22—81no—
621C22—81no—
622C22—81no—
623C22—81no—
624C22—82no—
625C22—82no—
626C22C59×#52511yescharacteristic
627C22C59×#52511yescharacteristic
628C22C2×#127×C5911yescharacteristic
629C22C59×#53411yescharacteristic
630C22C59×#53611yescharacteristic
631C22C59×#53611yescharacteristic
632C22C59×#53612yes—
633C22C59×#53612yes—
634C22C59×#53711yescharacteristic
635C22C59×#53912yes—
636C22C59×#54112yes—
637C22C59×#54212yes—
638C22C59×#54212yes—
639C22C59×#54612yes—
640C22C59×#54612yes—
641C22C59×#54611yescharacteristic
642C22C59×#54611yescharacteristic
643C22C59×#54811yescharacteristic
644C22C59×#54811yescharacteristic
645C22C59×#55212yes—
646C22C59×#55612yes—
647C22C59×#56212yes—
648C22C59×#56312yes—
649C4—24no—
650C4—44no—
651C4—42no—
652C4—42no—
653C4—42no—
654C4—44no—
655C4—44no—
656C4—81no—
657C4—82no—
658C4—81no—
659C2—82no—
660C2C59×#253911yescharacteristic
661C2C59×#254011yescharacteristic
662C2C59×#259911yescharacteristic
663C2C59×#263711yescharacteristic
664C2C59×#263811yescharacteristic
665C2C59×#265811yescharacteristic
666C2C59×#268712yes—
667C2C59×#269012yes—
668C2C59×#270012yes—
669C2C59×#271612yes—
670C2C59×#281411yescharacteristic
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
1. C2×C59×#398C2semidirect
3. C2×C59×#395C2semidirect
5. C2×C59×#391C2semidirect
7. C59×#1445C2semidirect
8. C59×#1445C2semidirect
11. C59×#1434C2semidirect
279. #16812C59direct (N × H)
324. C2×#398C2×C59semidirect
326. C2×#395C2×C59semidirect
328. C2×#391C2×C59semidirect
330. #1445C2×C59semidirect
331. #1445C2×C59semidirect
334. #1434C2×C59semidirect
376. C59#16812direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C59×#3982
C2×C59×#3972
C2×C59×#3952
C2×C59×#3932
C2×C59×#3912
C2×C59×#3882
C59×#14452
C59×#14392
C59×#14342
#1681259