Finite Group Databasebeta

← C59×#16473 #28428582

Subgroups — C59×#16473 #28428582

Order 15104.

1398 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C59×#399C211yesmaximal, characteristic
2C2×C59×#385C211yesmaximal, characteristic
3C59×#1442C212yesmaximal, complemented
4C59×#1442C212yesmaximal, complemented
5C59×#1441C212yesmaximal, complemented
6C59×#1441C212yesmaximal, complemented
7C59×#1440C212yesmaximal
8C59×#1439C211yesmaximal, characteristic
9C59×C22⋊#95C212yesmaximal
10C24×C4×C59C2211yescharacteristic
11C22×C4⋊C4×C59C2212yes—
12C22×C4⋊C4×C59C2212yes—
13C22×C4⋊C4×C59C2211yescharacteristic
14C22×C4⋊C4×C59C2211yescharacteristic
15C22×C22⋊C4×C59C2212yes—
16C22×C22⋊C4×C59C2211yescharacteristic
17C22×C22⋊C4×C59C2212yes—
18C22×C22⋊C4×C59C2211yescharacteristic
19C59×#399—24no—
20C59×#385—24no—
21C2×#95×C59C2212yes—
22C2×#95×C59C2211yescharacteristic
23C2×#95×C59C2212yes—
24C2×#95×C59C2212yes—
25C2×#95×C59C2212yes—
26C2×#95×C59C2212yes—
27C2×#95×C59C2212yes—
28C2×#95×C59C2212yes—
29C2×#95×C59C2211yescharacteristic
30C2×#95×C59C2212yes—
31C2×#95×C59C2212yes—
32C2×#95×C59C2212yes—
33C25×C59C2311yescharacteristic
34C23×C4×C59—22no—
35C23×C4×C59—24no—
36C23×C4×C59—41no—
37C23×C4×C59—41no—
38C23×C4×C59—42no—
39C23×C4×C59C2312yes—
40C23×C4×C59C2312yes—
41C23×C4×C59C2312yes—
42C23×C4×C59C2311yescharacteristic
43C23×C4×C59C2311yescharacteristic
44C23×C4×C59C2312yes—
45C23×C4×C59C2312yes—
46C23×C4×C59C2312yes—
47C2×C4⋊C4×C59—24no—
48C2×C4⋊C4×C59—24no—
49C2×C4⋊C4×C59—22no—
50C2×C4⋊C4×C59—24no—
51C2×C4⋊C4×C59—24no—
52C2×C4⋊C4×C59—42no—
53C2×C4⋊C4×C59—42no—
54C2×C4⋊C4×C59—41no—
55C2×C4⋊C4×C59—41no—
56C2×C4⋊C4×C59—41no—
57C2×C4⋊C4×C59—42no—
58C2×C22⋊C4×C59—22no—
59C2×C22⋊C4×C59—22no—
60C2×C22⋊C4×C59—24no—
61C2×C22⋊C4×C59—24no—
62C2×C22⋊C4×C59—24no—
63C2×C22⋊C4×C59—41no—
64C2×C22⋊C4×C59—41no—
65C2×C22⋊C4×C59—42no—
66C2×C22⋊C4×C59—42no—
67C2×C22⋊C4×C59—42no—
68C2×C22⋊C4×C59D414yes—
69C2×C22⋊C4×C59Q814yes—
70#95×C59—24no—
71#95×C59—22no—
72#95×C59—24no—
73#95×C59—24no—
74#95×C59—42no—
75#95×C59—42no—
76#95×C59—42no—
77#95×C59—42no—
78#95×C59—41no—
79#95×C59—42no—
80#95×C59—42no—
81#95×C59—42no—
82C24×C59—22no—
83C24×C59—22no—
84C24×C59—22no—
85C24×C59—21no—
86C24×C59—21no—
87C24×C59—22no—
88C24×C59—21no—
89C24×C59—21no—
90C24×C59C2×D412yes—
91C24×C59C2×Q812yes—
92C24×C59#4112yes—
93C24×C59C2411yescharacteristic
94C22×C4×C59—22no—
95C22×C4×C59—22no—
96C22×C4×C59—22no—
97C22×C4×C59—22no—
98C22×C4×C59—22no—
99C22×C4×C59—22no—
100C22×C4×C59—22no—
101C22×C4×C59—22no—
102C22×C4×C59—22no—
103C22×C4×C59—22no—
104C22×C4×C59—22no—
105C22×C4×C59—22no—
106C22×C4×C59—21no—
107C22×C4×C59—22no—
108C22×C4×C59—22no—
109C22×C4×C59—22no—
110C22×C4×C59—22no—
111C22×C4×C59—22no—
112C22×C4×C59—21no—
113C22×C4×C59—21no—
114C22×C4×C59—21no—
115C22×C4×C59—22no—
116C22×C4×C59—22no—
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—22no—
129C22×C4×C59—22no—
130C22×C4×C59—22no—
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—22no—
139C22×C4×C59—22no—
140C22×C4×C59—22no—
141C22×C4×C59—44no—
142C22×C4×C59—48no—
143C22×C4×C59—48no—
144C22×C4×C59—44no—
145C22×C4×C59—44no—
146C22×C4×C59C2×D412yes—
147C22×C4×C59C2×D412yes—
148C22×C4×C59C2×Q814yes—
149C22×C4×C59#4114yes—
150C22×C4×C59#4114yes—
151C4⋊C4×C59—48no—
152C4⋊C4×C59—48no—
153C4⋊C4×C59—44no—
154C4⋊C4×C59—44no—
155C22⋊C4×C59—28no—
156C22⋊C4×C59—44no—
157C22⋊C4×C59—48no—
158C22⋊C4×C59—48no—
159C23×C59—24no—
160C23×C59—22no—
161C23×C59—22no—
162C23×C59—24no—
163C23×C59—22no—
164C23×C59—22no—
165C23×C59—22no—
166C23×C59—22no—
167C23×C59—24no—
168C23×C59—24no—
169C23×C59—24no—
170C23×C59—24no—
171C23×C59—42no—
172C23×C59—42no—
173C23×C59—42no—
174C23×C59—42no—
175C23×C59—41no—
176C23×C59—42no—
177C23×C59—41no—
178C23×C59—41no—
179C23×C59—41no—
180C23×C59—42no—
181C23×C59C22⋊Q814yes—
182C23×C59C22×D411yescharacteristic
183C23×C59C22×Q811yescharacteristic
184C23×C59C2×#4111yescharacteristic
185C23×C59C2×#4112yes—
186C23×C59C2×#4112yes—
187C23×C59H(5,𝔽2)11yescharacteristic
188C23×C59H(5,𝔽2)11yescharacteristic
189C23×C59H(5,𝔽2)12yes—
190C23×C59H(5,𝔽2)12yes—
191C23×C592−1+411yescharacteristic
192C23×C592−1+411yescharacteristic
193C2×C4×C59—24no—
194C2×C4×C59—22no—
195C2×C4×C59—22no—
196C2×C4×C59—24no—
197C2×C4×C59—24no—
198C2×C4×C59—24no—
199C2×C4×C59—24no—
200C2×C4×C59—24no—
201C2×C4×C59—24no—
202C2×C4×C59—24no—
203C2×C4×C59—24no—
204C2×C4×C59—24no—
205C2×C4×C59—24no—
206C2×C4×C59—416no—
207C2×C4×C59—42no—
208C2×C4×C59—42no—
209C2×C4×C59—42no—
210C2×C4×C59—42no—
211C2×C4×C59—42no—
212C2×C4×C59—42no—
213C2×C4×C59—42no—
214C2×C4×C59—42no—
215C2×C4×C59—42no—
216C2×C4×C59—42no—
217C2×C4×C59—42no—
218C2×C4×C59—42no—
219C2×C4×C59—41no—
220C2×C4×C59—41no—
221C2×C4×C59—41no—
222C2×C4×C59—41no—
223C2×C4×C59—42no—
224C2×C4×C59—42no—
225C2×C4×C59—42no—
226C2×C4×C59—42no—
227C2×C4×C59—42no—
228C2×C4×C59—42no—
229C2×C4×C59—42no—
230C2×C4×C59—42no—
231C2×C4×C59—42no—
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—42no—
245C2×C4×C59—42no—
246#16473C5911yesmaximal, characteristic, direct product factor, Sylow
247C22×C59—24no—
248C22×C59—28no—
249C22×C59—42no—
250C22×C59—44no—
251C22×C59—44no—
252C22×C59—42no—
253C22×C59—42no—
254C22×C59—42no—
255C22×C59—44no—
256C22×C59—42no—
257C22×C59—42no—
258C22×C59C2×C22⋊Q811yescharacteristic
259C22×C59#52912yes—
260C22×C59#53411yescharacteristic
261C22×C59#53611yescharacteristic
262C22×C59#53812yes—
263C22×C59#53812yes—
264C22×C59#53911yescharacteristic
265C22×C59#53911yescharacteristic
266C22×C59#53912yes—
267C22×C59#54012yes—
268C22×C59#54212yes—
269C22×C59#54411yescharacteristic
270C22×C59#54411yescharacteristic
271C22×C59#54612yes—
272C22×C59#54612yes—
273C22×C59#55111yescharacteristic
274C22×C59#55212yes—
275C22×C59#55412yes—
276C22×C59#55412yes—
277C22×C59#55911yescharacteristic
278C22×C59#56011yescharacteristic
279C22×C59#56011yescharacteristic
280C22×C59#56212yes—
281C4×C59—44no—
282C4×C59—42no—
283C4×C59—44no—
284C4×C59—44no—
285C4×C59—42no—
286C4×C59—82no—
287C4×C59—82no—
288C4×C59—82no—
289C2×#399C2×C5911yescharacteristic
290C2×#385C2×C5911yescharacteristic
291#1442C2×C5912yescomplemented
292#1442C2×C5912yescomplemented
293#1441C2×C5912yescomplemented
294#1441C2×C5912yescomplemented
295#1440C2×C5912yes—
296#1439C2×C5911yescharacteristic
297C22⋊#95C2×C5912yes—
298C2×C59—44no—
299C2×C59#245012yes—
300C2×C59#251711yescharacteristic
301C2×C59#262711yescharacteristic
302C2×C59#264912yes—
303C2×C59#268712yes—
304C2×C59#269711yescharacteristic
305C2×C59#270911yescharacteristic
306C2×C59#274211yescharacteristic
307C2×C59#276812yes—
308C2×C59#280711yescharacteristic
309C2×C59#282611yescharacteristic
310C24×C4C22×C5911yescharacteristic
311C22×C4⋊C4C22×C5912yes—
312C22×C4⋊C4C22×C5912yes—
313C22×C4⋊C4C22×C5911yescharacteristic
314C22×C4⋊C4C22×C5911yescharacteristic
315C22×C22⋊C4C22×C5912yes—
316C22×C22⋊C4C22×C5911yescharacteristic
317C22×C22⋊C4C22×C5912yes—
318C22×C22⋊C4C22×C5911yescharacteristic
319#399—24no—
320#385—24no—
321C2×#95C22×C5911yescharacteristic
322C2×#95C22×C5912yes—
323C2×#95C22×C5912yes—
324C2×#95C22×C5912yes—
325C2×#95C22×C5912yes—
326C2×#95C22×C5912yes—
327C2×#95C22×C5912yes—
328C2×#95C22×C5912yes—
329C2×#95C22×C5911yescharacteristic
330C2×#95C22×C5912yes—
331C2×#95C22×C5912yes—
332C2×#95C22×C5912yes—
333C59#1647311yescharacteristic, direct product factor, Sylow
334C25C23×C5911yescharacteristic
335C23×C4—22no—
336C23×C4—24no—
337C23×C4—41no—
338C23×C4—41no—
339C23×C4—42no—
340C23×C4C23×C5912yes—
341C23×C4C23×C5912yes—
342C23×C4C23×C5912yes—
343C23×C4C23×C5911yescharacteristic
344C23×C4C23×C5911yescharacteristic
345C23×C4C23×C5912yes—
346C23×C4C23×C5912yes—
347C23×C4C23×C5912yes—
348C2×C4⋊C4—24no—
349C2×C4⋊C4—24no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—24no—
352C2×C4⋊C4—24no—
353C2×C4⋊C4—42no—
354C2×C4⋊C4—42no—
355C2×C4⋊C4—41no—
356C2×C4⋊C4—41no—
357C2×C4⋊C4—41no—
358C2×C4⋊C4—42no—
359C2×C22⋊C4—22no—
360C2×C22⋊C4—22no—
361C2×C22⋊C4—24no—
362C2×C22⋊C4—24no—
363C2×C22⋊C4—24no—
364C2×C22⋊C4—41no—
365C2×C22⋊C4—41no—
366C2×C22⋊C4—42no—
367C2×C22⋊C4—42no—
368C2×C22⋊C4—42no—
369C2×C22⋊C4D4×C5914yes—
370C2×C22⋊C4Q8×C5914yes—
371#95—24no—
372#95—22no—
373#95—24no—
374#95—24no—
375#95—42no—
376#95—42no—
377#95—42no—
378#95—42no—
379#95—41no—
380#95—42no—
381#95—42no—
382#95—42no—
383C24—22no—
384C24—22no—
385C24—22no—
386C24—21no—
387C24—21no—
388C24—22no—
389C24—21no—
390C24—21no—
391C24C2×D4×C5912yes—
392C24C2×Q8×C5912yes—
393C24#41×C5912yes—
394C24C24×C5911yescharacteristic
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—21no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—44no—
443C22×C4—48no—
444C22×C4—48no—
445C22×C4—44no—
446C22×C4—44no—
447C22×C4C2×D4×C5912yes—
448C22×C4C2×D4×C5912yes—
449C22×C4C2×Q8×C5914yes—
450C22×C4#41×C5914yes—
451C22×C4#41×C5914yes—
452C4⋊C4—48no—
453C4⋊C4—48no—
454C4⋊C4—44no—
455C4⋊C4—44no—
456C22⋊C4—28no—
457C22⋊C4—44no—
458C22⋊C4—48no—
459C22⋊C4—48no—
460C23—24no—
461C23—22no—
462C23—22no—
463C23—24no—
464C23—22no—
465C23—22no—
466C23—22no—
467C23—22no—
468C23—24no—
469C23—24no—
470C23—24no—
471C23—24no—
472C23—42no—
473C23—42no—
474C23—42no—
475C23—42no—
476C23—41no—
477C23—42no—
478C23—41no—
479C23—41no—
480C23—41no—
481C23—42no—
482C23C22⋊Q8×C5914yes—
483C23C22×D4×C5911yescharacteristic
484C23C22×Q8×C5911yescharacteristic
485C23C2×#41×C5911yescharacteristic
486C23C2×#41×C5912yes—
487C23C2×#41×C5912yes—
488C23H(5,𝔽2)×C5911yescharacteristic
489C23H(5,𝔽2)×C5911yescharacteristic
490C23H(5,𝔽2)×C5912yes—
491C23H(5,𝔽2)×C5912yes—
492C232−1+4×C5911yescharacteristic
493C232−1+4×C5911yescharacteristic
494C2×C4—24no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—24no—
498C2×C4—24no—
499C2×C4—24no—
500C2×C4—24no—
501C2×C4—24no—
502C2×C4—24no—
503C2×C4—24no—
504C2×C4—24no—
505C2×C4—24no—
506C2×C4—24no—
507C2×C4—416no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—42no—
547C22—24no—
548C22—28no—
549C22—42no—
550C22—44no—
551C22—42no—
552C22—42no—
553C22—42no—
554C22—44no—
555C22—44no—
556C22—42no—
557C22—42no—
558C22C2×C22⋊Q8×C5911yescharacteristic
559C22C59×#52912yes—
560C22C59×#53411yescharacteristic
561C22C59×#53611yescharacteristic
562C22C59×#53812yes—
563C22C59×#53812yes—
564C22C59×#53911yescharacteristic
565C22C59×#53912yes—
566C22C59×#53911yescharacteristic
567C22C59×#54012yes—
568C22C59×#54212yes—
569C22C59×#54411yescharacteristic
570C22C59×#54411yescharacteristic
571C22C59×#54612yes—
572C22C59×#54612yes—
573C22C59×#55111yescharacteristic
574C22C59×#55212yes—
575C22C59×#55412yes—
576C22C59×#55412yes—
577C22C59×#55911yescharacteristic
578C22C59×#56011yescharacteristic
579C22C59×#56011yescharacteristic
580C22C59×#56212yes—
581C4—44no—
582C4—44no—
583C4—42no—
584C4—44no—
585C4—42no—
586C4—82no—
587C4—82no—
588C4—82no—
589C2—44no—
590C2C59×#245012yes—
591C2C59×#251711yescharacteristic
592C2C59×#262711yescharacteristic
593C2C59×#264912yes—
594C2C59×#268712yes—
595C2C59×#269711yescharacteristic
596C2C59×#270911yescharacteristic
597C2C59×#274211yescharacteristic
598C2C59×#276812yes—
599C2C59×#280711yescharacteristic
600C2C59×#282611yescharacteristic
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. C59×#1442C2semidirect
4. C59×#1442C2semidirect
5. C59×#1441C2semidirect
6. C59×#1441C2semidirect
246. #16473C59direct (N × H)
291. #1442C2×C59semidirect
292. #1442C2×C59semidirect
293. #1441C2×C59semidirect
294. #1441C2×C59semidirect
333. C59#16473direct (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×#3852
C59×#14422
C59×#14412
C59×#14402
C59×#14392
C59×C22⋊#952
#1647359