Finite Group Databasebeta

← C59×#16892 #28429001

Subgroups — C59×#16892 #28429001

Order 15104.

1406 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C59×#385C211yesmaximal, characteristic
2C2×C59×#380C211yesmaximal, characteristic
3C59×#1445C212yesmaximal, complemented
4C59×#1444C211yesmaximal, characteristic, complemented
5C59×#1442C212yesmaximal, complemented
6C59×#1442C211yesmaximal, characteristic, complemented
7C59×#1441C211yesmaximal, characteristic, complemented
8C59×#1441C211yesmaximal, characteristic, complemented
9C59×#1440C212yesmaximal
10C59×#1439C212yesmaximal
11C59×C22⋊#95C211yesmaximal, characteristic
12C24×C4×C59C2211yescharacteristic
13C22×C4⋊C4×C59C2211yescharacteristic
14C22×C4⋊C4×C59C2211yescharacteristic
15C22×C4⋊C4×C59C2211yescharacteristic
16C22×C4⋊C4×C59C2211yescharacteristic
17C22×C4⋊C4×C59C2212yes—
18C22×C22⋊C4×C59C2212yes—
19C22×C22⋊C4×C59C2211yescharacteristic
20C22×C22⋊C4×C59C2212yes—
21C22×C22⋊C4×C59C2211yescharacteristic
22C59×#385—24no—
23C59×#380—24no—
24C2×#95×C59C2212yes—
25C2×#95×C59C2211yescharacteristic
26C2×#95×C59C2211yescharacteristic
27C2×#95×C59C2211yescharacteristic
28C2×#95×C59C2211yescharacteristic
29C2×#95×C59C2212yes—
30C2×#95×C59C2212yes—
31C2×#95×C59C2212yes—
32C2×#95×C59C2212yes—
33C2×#95×C59C2212yes—
34C2×#95×C59C2212yes—
35C2×#95×C59C2212yes—
36C2×#95×C59C2212yes—
37C25×C59C2311yescharacteristic
38C23×C4×C59—22no—
39C23×C4×C59—22no—
40C23×C4×C59—42no—
41C23×C4×C59—42no—
42C23×C4×C59D414yes—
43C23×C4×C59C2312yes—
44C23×C4×C59C2312yes—
45C23×C4×C59C2311yescharacteristic
46C23×C4×C59C2312yes—
47C23×C4×C59C2311yescharacteristic
48C23×C4×C59C2311yescharacteristic
49C23×C4×C59C2311yescharacteristic
50C23×C4×C59C2311yescharacteristic
51C23×C4×C59C2312yes—
52C23×C4×C59C2311yescharacteristic
53C2×C4⋊C4×C59—22no—
54C2×C4⋊C4×C59—22no—
55C2×C4⋊C4×C59—22no—
56C2×C4⋊C4×C59—22no—
57C2×C4⋊C4×C59—24no—
58C2×C4⋊C4×C59—22no—
59C2×C4⋊C4×C59—22no—
60C2×C4⋊C4×C59—42no—
61C2×C4⋊C4×C59—42no—
62C2×C4⋊C4×C59—42no—
63C2×C4⋊C4×C59—42no—
64C2×C4⋊C4×C59—42no—
65C2×C22⋊C4×C59—22no—
66C2×C22⋊C4×C59—22no—
67C2×C22⋊C4×C59—24no—
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×C59Q814yes—
76#95×C59—24no—
77#95×C59—22no—
78#95×C59—22no—
79#95×C59—22no—
80#95×C59—24no—
81#95×C59—22no—
82#95×C59—42no—
83#95×C59—42no—
84#95×C59—42no—
85#95×C59—42no—
86#95×C59—42no—
87#95×C59—42no—
88#95×C59—42no—
89C24×C59—22no—
90C24×C59—21no—
91C24×C59—21no—
92C24×C59—21no—
93C24×C59—21no—
94C24×C59—22no—
95C24×C59—22no—
96C24×C59—22no—
97C24×C59C2×D412yes—
98C24×C59C2×Q812yes—
99C24×C59#4112yes—
100C24×C59C2411yescharacteristic
101C22×C4×C59—22no—
102C22×C4×C59—22no—
103C22×C4×C59—21no—
104C22×C4×C59—21no—
105C22×C4×C59—22no—
106C22×C4×C59—22no—
107C22×C4×C59—21no—
108C22×C4×C59—21no—
109C22×C4×C59—22no—
110C22×C4×C59—21no—
111C22×C4×C59—21no—
112C22×C4×C59—21no—
113C22×C4×C59—21no—
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—28no—
124C22×C4×C59—21no—
125C22×C4×C59—22no—
126C22×C4×C59—22no—
127C22×C4×C59—21no—
128C22×C4×C59—22no—
129C22×C4×C59—22no—
130C22×C4×C59—22no—
131C22×C4×C59—22no—
132C22×C4×C59—21no—
133C22×C4×C59—21no—
134C22×C4×C59—22no—
135C22×C4×C59—22no—
136C22×C4×C59—21no—
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—22no—
147C22×C4×C59—22no—
148C22×C4×C59—22no—
149C22×C4×C59—22no—
150C22×C4×C59—22no—
151C22×C4×C59—21no—
152C22×C4×C59—22no—
153C22×C4×C59—22no—
154C22×C4×C59—22no—
155C22×C4×C59—44no—
156C22×C4×C59—44no—
157C22×C4×C59—48no—
158C22×C4×C59—48no—
159C22×C4×C59C2×D412yes—
160C22×C4×C59C2×D412yes—
161C22×C4×C59C2×Q812yes—
162C22×C4×C59C2×Q812yes—
163C22×C4×C59#4114yes—
164C22×C4×C59#4112yes—
165C22×C4×C59#4112yes—
166C4⋊C4×C59—44no—
167C4⋊C4×C59—44no—
168C4⋊C4×C59—44no—
169C4⋊C4×C59—48no—
170C4⋊C4×C59—44no—
171C22⋊C4×C59—28no—
172C22⋊C4×C59—48no—
173C22⋊C4×C59—44no—
174C22⋊C4×C59—48no—
175C23×C59—22no—
176C23×C59—22no—
177C23×C59—22no—
178C23×C59—22no—
179C23×C59—22no—
180C23×C59—22no—
181C23×C59—24no—
182C23×C59—24no—
183C23×C59—24no—
184C23×C59—22no—
185C23×C59—22no—
186C23×C59—24no—
187C23×C59—22no—
188C23×C59—22no—
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×C59C22⋊Q814yes—
198C23×C59C22×D411yescharacteristic
199C23×C59C22×Q811yescharacteristic
200C23×C59C2×#4111yescharacteristic
201C23×C59C2×#4111yescharacteristic
202C23×C59C2×#4111yescharacteristic
203C23×C59C2×#4112yes—
204C23×C59H(5,𝔽2)12yes—
205C23×C59H(5,𝔽2)12yes—
206C23×C59H(5,𝔽2)11yescharacteristic
207C23×C59H(5,𝔽2)11yescharacteristic
208C23×C592−1+412yes—
209C2×C4×C59—22no—
210C2×C4×C59—22no—
211C2×C4×C59—24no—
212C2×C4×C59—24no—
213C2×C4×C59—22no—
214C2×C4×C59—22no—
215C2×C4×C59—22no—
216C2×C4×C59—22no—
217C2×C4×C59—22no—
218C2×C4×C59—24no—
219C2×C4×C59—24no—
220C2×C4×C59—24no—
221C2×C4×C59—24no—
222C2×C4×C59—22no—
223C2×C4×C59—22no—
224C2×C4×C59—416no—
225C2×C4×C59—41no—
226C2×C4×C59—41no—
227C2×C4×C59—41no—
228C2×C4×C59—41no—
229C2×C4×C59—42no—
230C2×C4×C59—42no—
231C2×C4×C59—42no—
232C2×C4×C59—42no—
233C2×C4×C59—42no—
234C2×C4×C59—41no—
235C2×C4×C59—41no—
236C2×C4×C59—42no—
237C2×C4×C59—42no—
238C2×C4×C59—41no—
239C2×C4×C59—41no—
240C2×C4×C59—42no—
241C2×C4×C59—41no—
242C2×C4×C59—41no—
243C2×C4×C59—42no—
244C2×C4×C59—41no—
245C2×C4×C59—42no—
246C2×C4×C59—42no—
247C2×C4×C59—42no—
248C2×C4×C59—41no—
249C2×C4×C59—42no—
250C2×C4×C59—42no—
251C2×C4×C59—42no—
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—42no—
268C2×C4×C59—42no—
269C2×C4×C59#12314yes—
270#16892C5911yesmaximal, characteristic, direct product factor, Sylow
271C22×C59—24no—
272C22×C59—24no—
273C22×C59—24no—
274C22×C59—42no—
275C22×C59—42no—
276C22×C59—42no—
277C22×C59—44no—
278C22×C59—42no—
279C22×C59—44no—
280C22×C59—44no—
281C22×C59—44no—
282C22×C59C2×C22⋊Q811yescharacteristic
283C22×C59C2×#12311yescharacteristic
284C22×C59#53211yescharacteristic
285C22×C59#53411yescharacteristic
286C22×C59#53411yescharacteristic
287C22×C59#53511yescharacteristic
288C22×C59#53611yescharacteristic
289C22×C59#53812yes—
290C22×C59#53812yes—
291C22×C59#53812yes—
292C22×C59#53912yes—
293C22×C59#54012yes—
294C22×C59#54412yes—
295C22×C59#55112yes—
296C22×C59#55212yes—
297C22×C59#55311yescharacteristic
298C22×C59#55311yescharacteristic
299C22×C59#55412yes—
300C22×C59#55411yescharacteristic
301C22×C59#55411yescharacteristic
302C22×C59#55612yes—
303C22×C59#56212yes—
304C22×C59#56212yes—
305C4×C59—24no—
306C4×C59—42no—
307C4×C59—42no—
308C4×C59—42no—
309C4×C59—44no—
310C4×C59—82no—
311C4×C59—81no—
312C4×C59—81no—
313C4×C59—82no—
314C4×C59—82no—
315C2×#385C2×C5911yescharacteristic
316C2×#380C2×C5911yescharacteristic
317#1445C2×C5912yescomplemented
318#1444C2×C5911yescharacteristic, complemented
319#1442C2×C5911yescharacteristic, complemented
320#1442C2×C5912yescomplemented
321#1441C2×C5911yescharacteristic, complemented
322#1441C2×C5911yescharacteristic, complemented
323#1440C2×C5912yes—
324#1439C2×C5912yes—
325C22⋊#95C2×C5911yescharacteristic
326C2×C59—44no—
327C2×C59#248711yescharacteristic
328C2×C59#249911yescharacteristic
329C2×C59#256411yescharacteristic
330C2×C59#262211yescharacteristic
331C2×C59#262711yescharacteristic
332C2×C59#266111yescharacteristic
333C2×C59#275012yes—
334C2×C59#276812yes—
335C2×C59#278612yes—
336C2×C59#278812yes—
337C2×C59#281611yescharacteristic
338C24×C4C22×C5911yescharacteristic
339C22×C4⋊C4C22×C5911yescharacteristic
340C22×C4⋊C4C22×C5912yes—
341C22×C4⋊C4C22×C5911yescharacteristic
342C22×C4⋊C4C22×C5911yescharacteristic
343C22×C4⋊C4C22×C5911yescharacteristic
344C22×C22⋊C4C22×C5912yes—
345C22×C22⋊C4C22×C5911yescharacteristic
346C22×C22⋊C4C22×C5911yescharacteristic
347C22×C22⋊C4C22×C5912yes—
348#385—24no—
349#380—24no—
350C2×#95C22×C5911yescharacteristic
351C2×#95C22×C5911yescharacteristic
352C2×#95C22×C5912yes—
353C2×#95C22×C5911yescharacteristic
354C2×#95C22×C5912yes—
355C2×#95C22×C5911yescharacteristic
356C2×#95C22×C5912yes—
357C2×#95C22×C5912yes—
358C2×#95C22×C5912yes—
359C2×#95C22×C5912yes—
360C2×#95C22×C5912yes—
361C2×#95C22×C5912yes—
362C2×#95C22×C5912yes—
363C59#1689211yescharacteristic, direct product factor, Sylow
364C25C23×C5911yescharacteristic
365C23×C4—22no—
366C23×C4—22no—
367C23×C4—42no—
368C23×C4—42no—
369C23×C4D4×C5914yes—
370C23×C4C23×C5911yescharacteristic
371C23×C4C23×C5912yes—
372C23×C4C23×C5911yescharacteristic
373C23×C4C23×C5912yes—
374C23×C4C23×C5912yes—
375C23×C4C23×C5911yescharacteristic
376C23×C4C23×C5911yescharacteristic
377C23×C4C23×C5911yescharacteristic
378C23×C4C23×C5912yes—
379C23×C4C23×C5911yescharacteristic
380C2×C4⋊C4—22no—
381C2×C4⋊C4—22no—
382C2×C4⋊C4—22no—
383C2×C4⋊C4—22no—
384C2×C4⋊C4—24no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4—22no—
387C2×C4⋊C4—42no—
388C2×C4⋊C4—42no—
389C2×C4⋊C4—42no—
390C2×C4⋊C4—42no—
391C2×C4⋊C4—42no—
392C2×C22⋊C4—22no—
393C2×C22⋊C4—22no—
394C2×C22⋊C4—24no—
395C2×C22⋊C4—22no—
396C2×C22⋊C4—24no—
397C2×C22⋊C4—24no—
398C2×C22⋊C4—42no—
399C2×C22⋊C4—42no—
400C2×C22⋊C4—42no—
401C2×C22⋊C4—42no—
402C2×C22⋊C4Q8×C5914yes—
403#95—24no—
404#95—22no—
405#95—22no—
406#95—22no—
407#95—24no—
408#95—22no—
409#95—42no—
410#95—42no—
411#95—42no—
412#95—42no—
413#95—42no—
414#95—42no—
415#95—42no—
416C24—22no—
417C24—21no—
418C24—21no—
419C24—21no—
420C24—21no—
421C24—22no—
422C24—22no—
423C24—22no—
424C24C2×D4×C5912yes—
425C24C2×Q8×C5912yes—
426C24#41×C5912yes—
427C24C24×C5911yescharacteristic
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—22no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—28no—
451C22×C4—21no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—21no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—21no—
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—22no—
478C22×C4—21no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—44no—
483C22×C4—44no—
484C22×C4—48no—
485C22×C4—48no—
486C22×C4C2×D4×C5912yes—
487C22×C4C2×D4×C5912yes—
488C22×C4C2×Q8×C5912yes—
489C22×C4C2×Q8×C5912yes—
490C22×C4#41×C5914yes—
491C22×C4#41×C5912yes—
492C22×C4#41×C5912yes—
493C4⋊C4—44no—
494C4⋊C4—44no—
495C4⋊C4—44no—
496C4⋊C4—48no—
497C4⋊C4—44no—
498C22⋊C4—28no—
499C22⋊C4—48no—
500C22⋊C4—44no—
501C22⋊C4—48no—
502C23—22no—
503C23—22no—
504C23—22no—
505C23—22no—
506C23—22no—
507C23—22no—
508C23—24no—
509C23—24no—
510C23—24no—
511C23—22no—
512C23—22no—
513C23—22no—
514C23—22no—
515C23—24no—
516C23—42no—
517C23—42no—
518C23—42no—
519C23—42no—
520C23—42no—
521C23—42no—
522C23—42no—
523C23—42no—
524C23C22⋊Q8×C5914yes—
525C23C22×D4×C5911yescharacteristic
526C23C22×Q8×C5911yescharacteristic
527C23C2×#41×C5911yescharacteristic
528C23C2×#41×C5911yescharacteristic
529C23C2×#41×C5911yescharacteristic
530C23C2×#41×C5912yes—
531C23H(5,𝔽2)×C5912yes—
532C23H(5,𝔽2)×C5912yes—
533C23H(5,𝔽2)×C5911yescharacteristic
534C23H(5,𝔽2)×C5911yescharacteristic
535C232−1+4×C5912yes—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—24no—
539C2×C4—24no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—24no—
546C2×C4—24no—
547C2×C4—24no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—24no—
551C2×C4—416no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—42no—
560C2×C4—42no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—42no—
564C2×C4—42no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—42no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—42no—
571C2×C4—41no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—41no—
576C2×C4—42no—
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—42no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4#123×C5914yes—
597C22—24no—
598C22—24no—
599C22—24no—
600C22—44no—
601C22—42no—
602C22—44no—
603C22—44no—
604C22—44no—
605C22—42no—
606C22—42no—
607C22—42no—
608C22C2×C22⋊Q8×C5911yescharacteristic
609C22C2×#123×C5911yescharacteristic
610C22C59×#53211yescharacteristic
611C22C59×#53411yescharacteristic
612C22C59×#53411yescharacteristic
613C22C59×#53511yescharacteristic
614C22C59×#53611yescharacteristic
615C22C59×#53812yes—
616C22C59×#53812yes—
617C22C59×#53812yes—
618C22C59×#53912yes—
619C22C59×#54012yes—
620C22C59×#54412yes—
621C22C59×#55112yes—
622C22C59×#55212yes—
623C22C59×#55311yescharacteristic
624C22C59×#55311yescharacteristic
625C22C59×#55411yescharacteristic
626C22C59×#55411yescharacteristic
627C22C59×#55412yes—
628C22C59×#55612yes—
629C22C59×#56212yes—
630C22C59×#56212yes—
631C4—24no—
632C4—42no—
633C4—44no—
634C4—42no—
635C4—42no—
636C4—82no—
637C4—82no—
638C4—81no—
639C4—81no—
640C4—82no—
641C2—44no—
642C2C59×#248711yescharacteristic
643C2C59×#249911yescharacteristic
644C2C59×#256411yescharacteristic
645C2C59×#262211yescharacteristic
646C2C59×#262711yescharacteristic
647C2C59×#266111yescharacteristic
648C2C59×#275012yes—
649C2C59×#276812yes—
650C2C59×#278612yes—
651C2C59×#278812yes—
652C2C59×#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. C59×#1445C2semidirect
4. C59×#1444C2semidirect
5. C59×#1442C2semidirect
6. C59×#1442C2semidirect
7. C59×#1441C2semidirect
8. C59×#1441C2semidirect
270. #16892C59direct (N × H)
317. #1445C2×C59semidirect
318. #1444C2×C59semidirect
319. #1442C2×C59semidirect
320. #1442C2×C59semidirect
321. #1441C2×C59semidirect
322. #1441C2×C59semidirect
363. C59#16892direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C59×#3852
C2×C59×#3802
C59×#14452
C59×#14442
C59×#14422
C59×#14412
C59×#14402
C59×#14392
C59×C22⋊#952
#1689259