Finite Group Databasebeta

← C59×#16339 #28428448

Subgroups — C59×#16339 #28428448

Order 15104.

1490 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C59×#400C212yesmaximal, complemented
2C2×C59×#385C212yesmaximal
3C59×#1444C212yesmaximal, complemented
4C59×#1442C212yesmaximal, complemented
5C59×#1441C212yesmaximal, complemented
6C59×#1439C211yesmaximal, characteristic
7C59×#1439C212yesmaximal
8C59×#1439C211yesmaximal, characteristic
9C59×C22⋊#95C211yesmaximal, characteristic
10C24×C4×C59C2211yescharacteristic
11C22×C4⋊C4×C59C2212yes—
12C22×C4⋊C4×C59C2211yescharacteristic
13C22×C4⋊C4×C59C2212yes—
14C22×C4⋊C4×C59C2212yes—
15C22×C4⋊C4×C59C2211yescharacteristic
16C22×C22⋊C4×C59C2212yes—
17C22×C22⋊C4×C59C2212yes—
18C22×C22⋊C4×C59C2211yescharacteristic
19C22×C22⋊C4×C59C2211yescharacteristic
20C59×#400—28no—
21C59×#385—28no—
22C2×#95×C59C2212yes—
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×C59C2211yescharacteristic
32C2×#95×C59C2212yes—
33C25×C59C2311yescharacteristic
34C23×C4×C59—22no—
35C23×C4×C59—24no—
36C23×C4×C59—42no—
37C23×C4×C59—41no—
38C23×C4×C59—41no—
39C23×C4×C59C2312yes—
40C23×C4×C59C2312yes—
41C23×C4×C59C2312yes—
42C23×C4×C59C2312yes—
43C23×C4×C59C2312yes—
44C23×C4×C59C2311yescharacteristic
45C23×C4×C59C2311yescharacteristic
46C23×C4×C59C2312yes—
47C2×C4⋊C4×C59—24no—
48C2×C4⋊C4×C59—24no—
49C2×C4⋊C4×C59—24no—
50C2×C4⋊C4×C59—24no—
51C2×C4⋊C4×C59—24no—
52C2×C4⋊C4×C59—41no—
53C2×C4⋊C4×C59—42no—
54C2×C4⋊C4×C59—42no—
55C2×C4⋊C4×C59—42no—
56C2×C4⋊C4×C59—42no—
57C2×C4⋊C4×C59—42no—
58C2×C4⋊C4×C59—42no—
59C2×C4⋊C4×C59—41no—
60C2×C22⋊C4×C59—24no—
61C2×C22⋊C4×C59—24no—
62C2×C22⋊C4×C59—24no—
63C2×C22⋊C4×C59—24no—
64C2×C22⋊C4×C59—22no—
65C2×C22⋊C4×C59—24no—
66C2×C22⋊C4×C59—41no—
67C2×C22⋊C4×C59—41no—
68C2×C22⋊C4×C59—42no—
69C2×C22⋊C4×C59—41no—
70C2×C22⋊C4×C59—41no—
71C2×C22⋊C4×C59Q814yes—
72#95×C59—24no—
73#95×C59—24no—
74#95×C59—24no—
75#95×C59—24no—
76#95×C59—24no—
77#95×C59—24no—
78#95×C59—41no—
79#95×C59—41no—
80#95×C59—42no—
81#95×C59—42no—
82#95×C59D418yes—
83C24×C59—22no—
84C24×C59—22no—
85C24×C59—21no—
86C24×C59—21no—
87C24×C59—21no—
88C24×C59—22no—
89C24×C59—21no—
90C24×C59—22no—
91C24×C59C2×Q812yes—
92C24×C59#4112yes—
93C24×C59#4112yes—
94C24×C59C2411yescharacteristic
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—22no—
107C22×C4×C59—21no—
108C22×C4×C59—21no—
109C22×C4×C59—22no—
110C22×C4×C59—22no—
111C22×C4×C59—22no—
112C22×C4×C59—22no—
113C22×C4×C59—22no—
114C22×C4×C59—21no—
115C22×C4×C59—21no—
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×D414yes—
147C22×C4×C59C2×D414yes—
148C22×C4×C59C2×D414yes—
149C22×C4×C59C2×Q812yes—
150C22×C4×C59C2×Q812yes—
151C22×C4×C59#4114yes—
152C4⋊C4×C59—44no—
153C4⋊C4×C59—48no—
154C4⋊C4×C59—48no—
155C4⋊C4×C59—48no—
156C4⋊C4×C59—44no—
157C22⋊C4×C59—216no—
158C22⋊C4×C59—44no—
159C22⋊C4×C59—48no—
160C22⋊C4×C59—44no—
161C23×C59—24no—
162C23×C59—22no—
163C23×C59—22no—
164C23×C59—22no—
165C23×C59—22no—
166C23×C59—24no—
167C23×C59—22no—
168C23×C59—22no—
169C23×C59—24no—
170C23×C59—24no—
171C23×C59—24no—
172C23×C59—24no—
173C23×C59—42no—
174C23×C59—42no—
175C23×C59—42no—
176C23×C59—42no—
177C23×C59—41no—
178C23×C59—42no—
179C23×C59—41no—
180C23×C59—41no—
181C23×C59—41no—
182C23×C59—42no—
183C23×C59#12514yes—
184C23×C59C22×D412yes—
185C23×C59C22×Q811yescharacteristic
186C23×C59C2×#4111yescharacteristic
187C23×C59C2×#4112yes—
188C23×C59C2×#4111yescharacteristic
189C23×C59H(5,𝔽2)11yescharacteristic
190C23×C59H(5,𝔽2)12yes—
191C23×C59H(5,𝔽2)11yescharacteristic
192C23×C59H(5,𝔽2)11yescharacteristic
193C23×C592−1+412yes—
194C23×C592−1+411yescharacteristic
195C2×C4×C59—24no—
196C2×C4×C59—24no—
197C2×C4×C59—24no—
198C2×C4×C59—24no—
199C2×C4×C59—24no—
200C2×C4×C59—24no—
201C2×C4×C59—22no—
202C2×C4×C59—22no—
203C2×C4×C59—24no—
204C2×C4×C59—24no—
205C2×C4×C59—24no—
206C2×C4×C59—24no—
207C2×C4×C59—24no—
208C2×C4×C59—24no—
209C2×C4×C59—24no—
210C2×C4×C59—24no—
211C2×C4×C59—416no—
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—42no—
220C2×C4×C59—42no—
221C2×C4×C59—42no—
222C2×C4×C59—42no—
223C2×C4×C59—42no—
224C2×C4×C59—41no—
225C2×C4×C59—42no—
226C2×C4×C59—42no—
227C2×C4×C59—42no—
228C2×C4×C59—42no—
229C2×C4×C59—41no—
230C2×C4×C59—41no—
231C2×C4×C59—42no—
232C2×C4×C59—41no—
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—
246C2×C4×C59—42no—
247C2×C4×C59—42no—
248#16339C5911yesmaximal, characteristic, direct product factor, Sylow
249C22×C59—24no—
250C22×C59—28no—
251C22×C59—42no—
252C22×C59—44no—
253C22×C59—42no—
254C22×C59—42no—
255C22×C59—44no—
256C22×C59—42no—
257C22×C59—44no—
258C22×C59—42no—
259C22×C59—42no—
260C22×C59#52512yes—
261C22×C59C2×#12511yescharacteristic
262C22×C59#53512yes—
263C22×C59#53712yes—
264C22×C59#53811yescharacteristic
265C22×C59#53812yes—
266C22×C59#53811yescharacteristic
267C22×C59#53912yes—
268C22×C59#53911yescharacteristic
269C22×C59#53912yes—
270C22×C59#53911yescharacteristic
271C22×C59#54311yescharacteristic
272C22×C59#54411yescharacteristic
273C22×C59D4211yescharacteristic
274C22×C59#54612yes—
275C22×C59#54712yes—
276C22×C59D4×Q812yes—
277C22×C59#55212yes—
278C22×C59#55412yes—
279C22×C59#55911yescharacteristic
280C22×C59H(3,𝔽4)11yescharacteristic
281C22×C59#56311yescharacteristic
282C22×C59#56312yes—
283C4×C59—44no—
284C4×C59—44no—
285C4×C59—42no—
286C4×C59—44no—
287C4×C59—44no—
288C4×C59—42no—
289C4×C59—82no—
290C4×C59—82no—
291C2×#400C2×C5912yescomplemented
292C2×#385C2×C5912yes—
293#1444C2×C5912yescomplemented
294#1442C2×C5912yescomplemented
295#1441C2×C5912yescomplemented
296#1439C2×C5911yescharacteristic
297#1439C2×C5912yes—
298#1439C2×C5911yescharacteristic
299C22⋊#95C2×C5911yescharacteristic
300C2×C59—44no—
301C2×C59#245511yescharacteristic
302C2×C59#247312yes—
303C2×C59#263612yes—
304C2×C59#264611yescharacteristic
305C2×C59#267011yescharacteristic
306C2×C59#268311yescharacteristic
307C2×C59#269512yes—
308C2×C59#272012yes—
309C2×C59#277111yescharacteristic
310C2×C59#280411yescharacteristic
311C2×C59#283511yescharacteristic
312C24×C4C22×C5911yescharacteristic
313C22×C4⋊C4C22×C5911yescharacteristic
314C22×C4⋊C4C22×C5912yes—
315C22×C4⋊C4C22×C5912yes—
316C22×C4⋊C4C22×C5912yes—
317C22×C4⋊C4C22×C5911yescharacteristic
318C22×C22⋊C4C22×C5912yes—
319C22×C22⋊C4C22×C5912yes—
320C22×C22⋊C4C22×C5911yescharacteristic
321C22×C22⋊C4C22×C5911yescharacteristic
322#400—28no—
323#385—28no—
324C2×#95C22×C5912yes—
325C2×#95C22×C5912yes—
326C2×#95C22×C5912yes—
327C2×#95C22×C5912yes—
328C2×#95C22×C5912yes—
329C2×#95C22×C5912yes—
330C2×#95C22×C5912yes—
331C2×#95C22×C5911yescharacteristic
332C2×#95C22×C5912yes—
333C2×#95C22×C5911yescharacteristic
334C2×#95C22×C5912yes—
335C59#1633911yescharacteristic, direct product factor, Sylow
336C25C23×C5911yescharacteristic
337C23×C4—22no—
338C23×C4—24no—
339C23×C4—42no—
340C23×C4—41no—
341C23×C4—41no—
342C23×C4C23×C5912yes—
343C23×C4C23×C5912yes—
344C23×C4C23×C5912yes—
345C23×C4C23×C5912yes—
346C23×C4C23×C5912yes—
347C23×C4C23×C5911yescharacteristic
348C23×C4C23×C5911yescharacteristic
349C23×C4C23×C5912yes—
350C2×C4⋊C4—24no—
351C2×C4⋊C4—24no—
352C2×C4⋊C4—24no—
353C2×C4⋊C4—24no—
354C2×C4⋊C4—24no—
355C2×C4⋊C4—41no—
356C2×C4⋊C4—42no—
357C2×C4⋊C4—42no—
358C2×C4⋊C4—42no—
359C2×C4⋊C4—42no—
360C2×C4⋊C4—42no—
361C2×C4⋊C4—42no—
362C2×C4⋊C4—41no—
363C2×C22⋊C4—24no—
364C2×C22⋊C4—24no—
365C2×C22⋊C4—24no—
366C2×C22⋊C4—24no—
367C2×C22⋊C4—22no—
368C2×C22⋊C4—24no—
369C2×C22⋊C4—41no—
370C2×C22⋊C4—41no—
371C2×C22⋊C4—42no—
372C2×C22⋊C4—41no—
373C2×C22⋊C4—41no—
374C2×C22⋊C4Q8×C5914yes—
375#95—24no—
376#95—24no—
377#95—24no—
378#95—24no—
379#95—24no—
380#95—24no—
381#95—41no—
382#95—41no—
383#95—42no—
384#95—42no—
385#95D4×C5918yes—
386C24—22no—
387C24—22no—
388C24—21no—
389C24—21no—
390C24—21no—
391C24—22no—
392C24—21no—
393C24—22no—
394C24C2×Q8×C5912yes—
395C24#41×C5912yes—
396C24#41×C5912yes—
397C24C24×C5911yescharacteristic
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—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—21no—
418C22×C4—21no—
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—22no—
443C22×C4—22no—
444C22×C4—44no—
445C22×C4—48no—
446C22×C4—48no—
447C22×C4—44no—
448C22×C4—44no—
449C22×C4C2×D4×C5914yes—
450C22×C4C2×D4×C5914yes—
451C22×C4C2×D4×C5914yes—
452C22×C4C2×Q8×C5912yes—
453C22×C4C2×Q8×C5912yes—
454C22×C4#41×C5914yes—
455C4⋊C4—44no—
456C4⋊C4—48no—
457C4⋊C4—48no—
458C4⋊C4—48no—
459C4⋊C4—44no—
460C22⋊C4—216no—
461C22⋊C4—44no—
462C22⋊C4—48no—
463C22⋊C4—44no—
464C23—24no—
465C23—22no—
466C23—22no—
467C23—22no—
468C23—22no—
469C23—24no—
470C23—22no—
471C23—22no—
472C23—24no—
473C23—24no—
474C23—24no—
475C23—24no—
476C23—42no—
477C23—42no—
478C23—42no—
479C23—42no—
480C23—41no—
481C23—42no—
482C23—41no—
483C23—41no—
484C23—41no—
485C23—42no—
486C23#125×C5914yes—
487C23C22×D4×C5912yes—
488C23C22×Q8×C5911yescharacteristic
489C23C2×#41×C5911yescharacteristic
490C23C2×#41×C5912yes—
491C23C2×#41×C5911yescharacteristic
492C23H(5,𝔽2)×C5911yescharacteristic
493C23H(5,𝔽2)×C5912yes—
494C23H(5,𝔽2)×C5911yescharacteristic
495C23H(5,𝔽2)×C5911yescharacteristic
496C232−1+4×C5912yes—
497C232−1+4×C5911yescharacteristic
498C2×C4—24no—
499C2×C4—24no—
500C2×C4—24no—
501C2×C4—24no—
502C2×C4—24no—
503C2×C4—24no—
504C2×C4—22no—
505C2×C4—22no—
506C2×C4—24no—
507C2×C4—24no—
508C2×C4—24no—
509C2×C4—24no—
510C2×C4—24no—
511C2×C4—24no—
512C2×C4—24no—
513C2×C4—24no—
514C2×C4—416no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—41no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—41no—
532C2×C4—42no—
533C2×C4—41no—
534C2×C4—42no—
535C2×C4—41no—
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—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—42no—
551C22—24no—
552C22—28no—
553C22—42no—
554C22—42no—
555C22—42no—
556C22—44no—
557C22—42no—
558C22—42no—
559C22—44no—
560C22—42no—
561C22—44no—
562C22C59×#52512yes—
563C22C2×#125×C5911yescharacteristic
564C22C59×#53512yes—
565C22C59×#53712yes—
566C22C59×#53811yescharacteristic
567C22C59×#53812yes—
568C22C59×#53811yescharacteristic
569C22C59×#53912yes—
570C22C59×#53912yes—
571C22C59×#53911yescharacteristic
572C22C59×#53911yescharacteristic
573C22C59×#54311yescharacteristic
574C22C59×#54411yescharacteristic
575C22D42×C5911yescharacteristic
576C22C59×#54612yes—
577C22C59×#54712yes—
578C22D4×Q8×C5912yes—
579C22C59×#55212yes—
580C22C59×#55412yes—
581C22C59×#55911yescharacteristic
582C22C59×H(3,𝔽4)11yescharacteristic
583C22C59×#56311yescharacteristic
584C22C59×#56312yes—
585C4—42no—
586C4—44no—
587C4—44no—
588C4—42no—
589C4—44no—
590C4—44no—
591C4—82no—
592C4—82no—
593C2—44no—
594C2C59×#245511yescharacteristic
595C2C59×#247312yes—
596C2C59×#263612yes—
597C2C59×#264611yescharacteristic
598C2C59×#267011yescharacteristic
599C2C59×#268311yescharacteristic
600C2C59×#269512yes—
601C2C59×#272012yes—
602C2C59×#277111yescharacteristic
603C2C59×#280411yescharacteristic
604C2C59×#283511yescharacteristic
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×#400C2semidirect
3. C59×#1444C2semidirect
4. C59×#1442C2semidirect
5. C59×#1441C2semidirect
248. #16339C59direct (N × H)
291. C2×#400C2×C59semidirect
293. #1444C2×C59semidirect
294. #1442C2×C59semidirect
295. #1441C2×C59semidirect
335. C59#16339direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C59×#4002
C2×C59×#3852
C59×#14442
C59×#14422
C59×#14412
C59×#14392
C59×C22⋊#952
#1633959