Finite Group Databasebeta

← C59×#16481 #28428590

Subgroups — C59×#16481 #28428590

Order 15104.

1462 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C59×#393C211yesmaximal, characteristic
2C2×C59×#385C211yesmaximal, characteristic
3C59×#1446C212yesmaximal, complemented
4C59×#1443C212yesmaximal, complemented
5C59×#1442C212yesmaximal, complemented
6C59×#1441C212yesmaximal, complemented
7C59×#1440C212yesmaximal
8C59×#1439C211yesmaximal, characteristic
9C59×C22⋊#95C212yesmaximal
10C23×Q8×C59C2211yescharacteristic
11C24×C4×C59C2211yescharacteristic
12C22×C4⋊C4×C59C2212yes—
13C22×C4⋊C4×C59C2211yescharacteristic
14C22×C22⋊C4×C59C2212yes—
15C22×C22⋊C4×C59C2211yescharacteristic
16C22×C22⋊C4×C59C2212yes—
17C22×C22⋊C4×C59C2211yescharacteristic
18C59×#393—24no—
19C59×#385—24no—
20C2×#95×C59C2212yes—
21C2×#95×C59C2212yes—
22C2×#95×C59C2211yescharacteristic
23C2×#95×C59C2212yes—
24C2×#95×C59C2212yes—
25C2×#95×C59C2212yes—
26C2×#95×C59C2212yes—
27C2×#95×C59C2212yes—
28C2×#95×C59C2211yescharacteristic
29C2×#95×C59C2212yes—
30C2×#95×C59C2212yes—
31C2×#95×C59C2212yes—
32C2×#95×C59C2212yes—
33C25×C59C2311yescharacteristic
34C22×Q8×C59—22no—
35C22×Q8×C59—24no—
36C22×Q8×C59—42no—
37C22×Q8×C59—41no—
38C22×Q8×C59—41no—
39C23×C4×C59—22no—
40C23×C4×C59—24no—
41C23×C4×C59—41no—
42C23×C4×C59—41no—
43C23×C4×C59—42no—
44C23×C4×C59C2312yes—
45C23×C4×C59C2312yes—
46C23×C4×C59C2312yes—
47C23×C4×C59C2311yescharacteristic
48C23×C4×C59C2311yescharacteristic
49C23×C4×C59C2312yes—
50C23×C4×C59C2312yes—
51C23×C4×C59C2312yes—
52C2×C4⋊C4×C59—24no—
53C2×C4⋊C4×C59—24no—
54C2×C4⋊C4×C59—42no—
55C2×C4⋊C4×C59—41no—
56C2×C4⋊C4×C59—42no—
57C2×C22⋊C4×C59—22no—
58C2×C22⋊C4×C59—22no—
59C2×C22⋊C4×C59—24no—
60C2×C22⋊C4×C59—24no—
61C2×C22⋊C4×C59—24no—
62C2×C22⋊C4×C59—41no—
63C2×C22⋊C4×C59—41no—
64C2×C22⋊C4×C59—42no—
65C2×C22⋊C4×C59—42no—
66C2×C22⋊C4×C59—42no—
67C2×C22⋊C4×C59D414yes—
68C2×C22⋊C4×C59Q814yescomplemented
69#95×C59—24no—
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—41no—
77#95×C59—42no—
78#95×C59—42no—
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
94C2×Q8×C59—48no—
95C2×Q8×C59—44no—
96C2×Q8×C59—44no—
97C2×Q8×C59—48no—
98C2×Q8×C59—44no—
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—22no—
108C22×C4×C59—22no—
109C22×C4×C59—22no—
110C22×C4×C59—21no—
111C22×C4×C59—22no—
112C22×C4×C59—22no—
113C22×C4×C59—22no—
114C22×C4×C59—22no—
115C22×C4×C59—22no—
116C22×C4×C59—22no—
117C22×C4×C59—22no—
118C22×C4×C59—22no—
119C22×C4×C59—21no—
120C22×C4×C59—21no—
121C22×C4×C59—21no—
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—22no—
142C22×C4×C59—22no—
143C22×C4×C59—22no—
144C22×C4×C59—22no—
145C22×C4×C59—22no—
146C22×C4×C59—44no—
147C22×C4×C59—48no—
148C22×C4×C59—48no—
149C22×C4×C59—44no—
150C22×C4×C59—44no—
151C22×C4×C59C2×D412yes—
152C22×C4×C59C2×D412yes—
153C22×C4×C59C2×Q814yes—
154C22×C4×C59#4114yes—
155C22×C4×C59#4114yes—
156C4⋊C4×C59—48no—
157C4⋊C4×C59—44no—
158C22⋊C4×C59—28no—
159C22⋊C4×C59—44no—
160C22⋊C4×C59—48no—
161C22⋊C4×C59—48no—
162C23×C59—24no—
163C23×C59—22no—
164C23×C59—22no—
165C23×C59—24no—
166C23×C59—22no—
167C23×C59—22no—
168C23×C59—22no—
169C23×C59—22no—
170C23×C59—24no—
171C23×C59—24no—
172C23×C59—24no—
173C23×C59—24no—
174C23×C59—42no—
175C23×C59—42no—
176C23×C59—42no—
177C23×C59—42no—
178C23×C59—41no—
179C23×C59—41no—
180C23×C59—42no—
181C23×C59—41no—
182C23×C59—41no—
183C23×C59—42no—
184C23×C59C22⋊Q814yes—
185C23×C59C22×D411yescharacteristic
186C23×C59C22×Q811yescharacteristic
187C23×C59C2×#4111yescharacteristic
188C23×C59C2×#4112yes—
189C23×C59C2×#4112yes—
190C23×C59H(5,𝔽2)11yescharacteristic
191C23×C59H(5,𝔽2)11yescharacteristic
192C23×C59H(5,𝔽2)12yes—
193C23×C59H(5,𝔽2)12yes—
194C23×C592−1+411yescharacteristic
195C23×C592−1+411yescharacteristic
196Q8×C59—416no—
197C2×C4×C59—24no—
198C2×C4×C59—22no—
199C2×C4×C59—22no—
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—24no—
207C2×C4×C59—24no—
208C2×C4×C59—24no—
209C2×C4×C59—24no—
210C2×C4×C59—416no—
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—42no—
220C2×C4×C59—42no—
221C2×C4×C59—42no—
222C2×C4×C59—42no—
223C2×C4×C59—41no—
224C2×C4×C59—41no—
225C2×C4×C59—41no—
226C2×C4×C59—42no—
227C2×C4×C59—41no—
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—
246C2×C4×C59—42no—
247C2×C4×C59—42no—
248C2×C4×C59—42no—
249C2×C4×C59—42no—
250#16481C5911yesmaximal, characteristic, direct product factor, Sylow
251C22×C59—24no—
252C22×C59—28no—
253C22×C59—42no—
254C22×C59—44no—
255C22×C59—42no—
256C22×C59—42no—
257C22×C59—44no—
258C22×C59—42no—
259C22×C59—42no—
260C22×C59—42no—
261C22×C59—44no—
262C22×C59C2×C22⋊Q811yescharacteristic
263C22×C59#52912yes—
264C22×C59#53411yescharacteristic
265C22×C59#53611yescharacteristic
266C22×C59#53812yes—
267C22×C59#53812yes—
268C22×C59#53812yes—
269C22×C59#53911yescharacteristic
270C22×C59#53911yescharacteristic
271C22×C59#54212yes—
272C22×C59#54212yes—
273C22×C59#54411yescharacteristic
274C22×C59#54411yescharacteristic
275C22×C59#54612yes—
276C22×C59#54612yes—
277C22×C59#55111yescharacteristic
278C22×C59#55111yescharacteristic
279C22×C59#55412yes—
280C22×C59#55412yes—
281C22×C59#55612yes—
282C22×C59#56011yescharacteristic
283C22×C59H(3,𝔽4)11yescharacteristic
284C22×C59#56212yes—
285C4×C59—42no—
286C4×C59—44no—
287C4×C59—42no—
288C4×C59—44no—
289C4×C59—44no—
290C4×C59—82no—
291C4×C59—82no—
292C4×C59—82no—
293C2×#393C2×C5911yescharacteristic
294C2×#385C2×C5911yescharacteristic
295#1446C2×C5912yescomplemented
296#1443C2×C5912yescomplemented
297#1442C2×C5912yescomplemented
298#1441C2×C5912yescomplemented
299#1440C2×C5912yes—
300#1439C2×C5911yescharacteristic
301C22⋊#95C2×C5912yes—
302C2×C59—44no—
303C2×C59#245012yes—
304C2×C59#252311yescharacteristic
305C2×C59#262711yescharacteristic
306C2×C59#265312yes—
307C2×C59#268411yescharacteristic
308C2×C59#269711yescharacteristic
309C2×C59#270012yes—
310C2×C59#274211yescharacteristic
311C2×C59#276311yescharacteristic
312C2×C59#278812yes—
313C2×C59#282411yescharacteristic
314C23×Q8C22×C5911yescharacteristic
315C24×C4C22×C5911yescharacteristic
316C22×C4⋊C4C22×C5912yes—
317C22×C4⋊C4C22×C5911yescharacteristic
318C22×C22⋊C4C22×C5912yes—
319C22×C22⋊C4C22×C5911yescharacteristic
320C22×C22⋊C4C22×C5912yes—
321C22×C22⋊C4C22×C5911yescharacteristic
322#393—24no—
323#385—24no—
324C2×#95C22×C5912yes—
325C2×#95C22×C5911yescharacteristic
326C2×#95C22×C5912yes—
327C2×#95C22×C5912yes—
328C2×#95C22×C5912yes—
329C2×#95C22×C5912yes—
330C2×#95C22×C5912yes—
331C2×#95C22×C5912yes—
332C2×#95C22×C5911yescharacteristic
333C2×#95C22×C5912yes—
334C2×#95C22×C5912yes—
335C2×#95C22×C5912yes—
336C2×#95C22×C5912yes—
337C59#1648111yescharacteristic, direct product factor, Sylow
338C25C23×C5911yescharacteristic
339C22×Q8—22no—
340C22×Q8—24no—
341C22×Q8—42no—
342C22×Q8—41no—
343C22×Q8—41no—
344C23×C4—22no—
345C23×C4—24no—
346C23×C4—41no—
347C23×C4—41no—
348C23×C4—42no—
349C23×C4C23×C5912yes—
350C23×C4C23×C5912yes—
351C23×C4C23×C5912yes—
352C23×C4C23×C5911yescharacteristic
353C23×C4C23×C5911yescharacteristic
354C23×C4C23×C5912yes—
355C23×C4C23×C5912yes—
356C23×C4C23×C5912yes—
357C2×C4⋊C4—24no—
358C2×C4⋊C4—24no—
359C2×C4⋊C4—42no—
360C2×C4⋊C4—41no—
361C2×C4⋊C4—42no—
362C2×C22⋊C4—22no—
363C2×C22⋊C4—22no—
364C2×C22⋊C4—24no—
365C2×C22⋊C4—24no—
366C2×C22⋊C4—24no—
367C2×C22⋊C4—41no—
368C2×C22⋊C4—41no—
369C2×C22⋊C4—42no—
370C2×C22⋊C4—42no—
371C2×C22⋊C4—42no—
372C2×C22⋊C4D4×C5914yes—
373C2×C22⋊C4Q8×C5914yescomplemented
374#95—24no—
375#95—24no—
376#95—22no—
377#95—24no—
378#95—24no—
379#95—42no—
380#95—42no—
381#95—41no—
382#95—42no—
383#95—42no—
384#95—42no—
385#95—42no—
386#95—42no—
387C24—22no—
388C24—22no—
389C24—22no—
390C24—21no—
391C24—21no—
392C24—22no—
393C24—21no—
394C24—21no—
395C24C2×D4×C5912yes—
396C24C2×Q8×C5912yes—
397C24#41×C5912yes—
398C24C24×C5911yescharacteristic
399C2×Q8—48no—
400C2×Q8—44no—
401C2×Q8—44no—
402C2×Q8—48no—
403C2×Q8—44no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
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—21no—
425C22×C4—21no—
426C22×C4—21no—
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—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—44no—
452C22×C4—48no—
453C22×C4—48no—
454C22×C4—44no—
455C22×C4—44no—
456C22×C4C2×D4×C5912yes—
457C22×C4C2×D4×C5912yes—
458C22×C4C2×Q8×C5914yes—
459C22×C4#41×C5914yes—
460C22×C4#41×C5914yes—
461C4⋊C4—48no—
462C4⋊C4—44no—
463C22⋊C4—28no—
464C22⋊C4—44no—
465C22⋊C4—48no—
466C22⋊C4—48no—
467C23—24no—
468C23—22no—
469C23—22no—
470C23—24no—
471C23—22no—
472C23—22no—
473C23—22no—
474C23—22no—
475C23—24no—
476C23—24no—
477C23—24no—
478C23—24no—
479C23—42no—
480C23—42no—
481C23—42no—
482C23—42no—
483C23—41no—
484C23—41no—
485C23—42no—
486C23—41no—
487C23—41no—
488C23—42no—
489C23C22⋊Q8×C5914yes—
490C23C22×D4×C5911yescharacteristic
491C23C22×Q8×C5911yescharacteristic
492C23C2×#41×C5911yescharacteristic
493C23C2×#41×C5912yes—
494C23C2×#41×C5912yes—
495C23H(5,𝔽2)×C5911yescharacteristic
496C23H(5,𝔽2)×C5911yescharacteristic
497C23H(5,𝔽2)×C5912yes—
498C23H(5,𝔽2)×C5912yes—
499C232−1+4×C5911yescharacteristic
500C232−1+4×C5911yescharacteristic
501Q8—416no—
502C2×C4—24no—
503C2×C4—22no—
504C2×C4—22no—
505C2×C4—24no—
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—24no—
515C2×C4—416no—
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—42no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—42no—
532C2×C4—41no—
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—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—42no—
555C22—24no—
556C22—28no—
557C22—42no—
558C22—42no—
559C22—42no—
560C22—44no—
561C22—42no—
562C22—44no—
563C22—42no—
564C22—42no—
565C22—44no—
566C22C2×C22⋊Q8×C5911yescharacteristic
567C22C59×#52912yes—
568C22C59×#53411yescharacteristic
569C22C59×#53611yescharacteristic
570C22C59×#53812yes—
571C22C59×#53812yes—
572C22C59×#53812yes—
573C22C59×#53911yescharacteristic
574C22C59×#53911yescharacteristic
575C22C59×#54212yes—
576C22C59×#54212yes—
577C22C59×#54411yescharacteristic
578C22C59×#54411yescharacteristic
579C22C59×#54612yes—
580C22C59×#54612yes—
581C22C59×#55111yescharacteristic
582C22C59×#55111yescharacteristic
583C22C59×#55412yes—
584C22C59×#55412yes—
585C22C59×#55612yes—
586C22C59×#56011yescharacteristic
587C22C59×H(3,𝔽4)11yescharacteristic
588C22C59×#56212yes—
589C4—44no—
590C4—42no—
591C4—42no—
592C4—44no—
593C4—44no—
594C4—82no—
595C4—82no—
596C4—82no—
597C2—44no—
598C2C59×#245012yes—
599C2C59×#252311yescharacteristic
600C2C59×#262711yescharacteristic
601C2C59×#265312yes—
602C2C59×#268411yescharacteristic
603C2C59×#269711yescharacteristic
604C2C59×#270012yes—
605C2C59×#274211yescharacteristic
606C2C59×#276311yescharacteristic
607C2C59×#278812yes—
608C2C59×#282411yescharacteristic
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×#1446C2semidirect
4. C59×#1443C2semidirect
5. C59×#1442C2semidirect
6. C59×#1441C2semidirect
68. C2×C22⋊C4×C59Q8semidirect
250. #16481C59direct (N × H)
295. #1446C2×C59semidirect
296. #1443C2×C59semidirect
297. #1442C2×C59semidirect
298. #1441C2×C59semidirect
337. C59#16481direct (N × H)
373. C2×C22⋊C4Q8×C59semidirect

Maximal subgroups

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

subgroupindex
C2×C59×#3932
C2×C59×#3852
C59×#14462
C59×#14432
C59×#14422
C59×#14412
C59×#14402
C59×#14392
C59×C22⋊#952
#1648159