Finite Group Databasebeta

← C59×#16517 #28428626

Subgroups — C59×#16517 #28428626

Order 15104.

1234 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C59×#398C212yesmaximal
2C2×C59×#398C211yesmaximal, characteristic
3C2×C59×#389C211yesmaximal, characteristic
4C2×C59×#387C211yesmaximal, characteristic
5C2×C59×#382C211yesmaximal, characteristic
6C59×#1445C211yesmaximal, characteristic
7C59×#1443C212yesmaximal
8C59×#1442C212yesmaximal
9C59×#1442C211yesmaximal, characteristic
10C59×#1441C211yesmaximal, characteristic
11C59×#1441C212yesmaximal
12C22×C4⋊C4×C59C2211yescharacteristic
13C22×C4⋊C4×C59C2212yes—
14C22×C4⋊C4×C59C2211yescharacteristic
15C22×C4⋊C4×C59C2211yescharacteristic
16C22×C4⋊C4×C59C2212yes—
17C22×C4⋊C4×C59C2212yes—
18C22×C4⋊C4×C59C2211yescharacteristic
19C22×C42×C59C2211yescharacteristic
20C59×#398—28no—
21C59×#398—24no—
22C59×#389—24no—
23C59×#387—24no—
24C59×#382—24no—
25C2×#95×C59C2211yescharacteristic
26C2×#95×C59C2212yes—
27C2×#95×C59C2211yescharacteristic
28C2×#95×C59C2211yescharacteristic
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
40C23×C4×C59C2311yescharacteristic
41C23×C4×C59C2311yescharacteristic
42C23×C4×C59C2312yes—
43C23×C4×C59C2312yes—
44C23×C4×C59C2311yescharacteristic
45C23×C4×C59C2311yescharacteristic
46C23×C4×C59C2312yes—
47C23×C4×C59C2311yescharacteristic
48C23×C4×C59C2312yes—
49C23×C4×C59C2311yescharacteristic
50C23×C4×C59C2311yescharacteristic
51C2×C4⋊C4×C59—22no—
52C2×C4⋊C4×C59—22no—
53C2×C4⋊C4×C59—24no—
54C2×C4⋊C4×C59—22no—
55C2×C4⋊C4×C59—24no—
56C2×C4⋊C4×C59—22no—
57C2×C4⋊C4×C59—24no—
58C2×C4⋊C4×C59—22no—
59C2×C4⋊C4×C59—24no—
60C2×C4⋊C4×C59—24no—
61C2×C4⋊C4×C59—24no—
62C2×C4⋊C4×C59—24no—
63C2×C4⋊C4×C59—22no—
64C2×C4⋊C4×C59—22no—
65C2×C4⋊C4×C59—22no—
66C2×C4⋊C4×C59—24no—
67C2×C4⋊C4×C59—22no—
68C2×C4⋊C4×C59—42no—
69C2×C4⋊C4×C59—42no—
70C2×C4⋊C4×C59D414yes—
71C2×C42×C59—22no—
72C2×C42×C59—22no—
73C2×C42×C59D414yes—
74#95×C59—24no—
75#95×C59—22no—
76#95×C59—22no—
77#95×C59—22no—
78#95×C59—22no—
79#95×C59—22no—
80#95×C59—24no—
81#95×C59—24no—
82#95×C59—24no—
83#95×C59—24no—
84#95×C59—24no—
85#95×C59—24no—
86#95×C59—24no—
87#95×C59—42no—
88#95×C59D414yes—
89C24×C59C2411yescharacteristic
90C22×C4×C59—21no—
91C22×C4×C59—21no—
92C22×C4×C59—22no—
93C22×C4×C59—21no—
94C22×C4×C59—22no—
95C22×C4×C59—21no—
96C22×C4×C59—21no—
97C22×C4×C59—21no—
98C22×C4×C59—22no—
99C22×C4×C59—21no—
100C22×C4×C59—22no—
101C22×C4×C59—22no—
102C22×C4×C59—21no—
103C22×C4×C59—22no—
104C22×C4×C59—21no—
105C22×C4×C59—21no—
106C22×C4×C59—21no—
107C22×C4×C59—22no—
108C22×C4×C59—21no—
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—22no—
121C22×C4×C59—22no—
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—22no—
131C22×C4×C59—22no—
132C22×C4×C59—22no—
133C22×C4×C59—22no—
134C22×C4×C59—22no—
135C22×C4×C59—21no—
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—21no—
145C22×C4×C59—22no—
146C22×C4×C59C2×D412yes—
147C22×C4×C59C2×D412yes—
148C22×C4×C59C2×D414yes—
149C22×C4×C59C2×D412yes—
150C22×C4×C59C2×D412yes—
151C22×C4×C59C2×D412yes—
152C22×C4×C59C2×D412yes—
153C22×C4×C59C2×D412yes—
154C22×C4×C59#4114yes—
155C22×C4×C59#4112yes—
156C22×C4×C59#4112yes—
157C4⋊C4×C59—28no—
158C4⋊C4×C59—28no—
159C4⋊C4×C59—48no—
160C4⋊C4×C59—48no—
161C4⋊C4×C59—44no—
162C4⋊C4×C59—48no—
163C4⋊C4×C59—44no—
164C42×C59—28no—
165C23×C59C22×D411yescharacteristic
166C23×C59C22×D411yescharacteristic
167C23×C59C22×D411yescharacteristic
168C23×C59C2×#4111yescharacteristic
169C23×C59C2×#4111yescharacteristic
170C23×C59C2×#4112yes—
171C23×C59H(5,𝔽2)11yescharacteristic
172C23×C592−1+412yes—
173C23×C592−1+412yes—
174C23×C592−1+412yes—
175C23×C592−1+411yescharacteristic
176C2×C4×C59—22no—
177C2×C4×C59—22no—
178C2×C4×C59—22no—
179C2×C4×C59—22no—
180C2×C4×C59—22no—
181C2×C4×C59—24no—
182C2×C4×C59—22no—
183C2×C4×C59—22no—
184C2×C4×C59—24no—
185C2×C4×C59—22no—
186C2×C4×C59—22no—
187C2×C4×C59—22no—
188C2×C4×C59—22no—
189C2×C4×C59—24no—
190C2×C4×C59—22no—
191C2×C4×C59—22no—
192C2×C4×C59—24no—
193C2×C4×C59—24no—
194C2×C4×C59—22no—
195C2×C4×C59—24no—
196C2×C4×C59—22no—
197C2×C4×C59—24no—
198C2×C4×C59—24no—
199C2×C4×C59—24no—
200C2×C4×C59—41no—
201C2×C4×C59—42no—
202C2×C4×C59—41no—
203C2×C4×C59—41no—
204C2×C4×C59—42no—
205C2×C4×C59—42no—
206C2×C4×C59—42no—
207C2×C4×C59—41no—
208C2×C4×C59—42no—
209C2×C4×C59—42no—
210C2×C4×C59—42no—
211C2×C4×C59—41no—
212C2×C4×C59—42no—
213C2×C4×C59—42no—
214C2×C4×C59—42no—
215C2×C4×C59—41no—
216C2×C4×C59—42no—
217C2×C4×C59—41no—
218C2×C4×C59—42no—
219C2×C4×C59—42no—
220C2×C4×C59—41no—
221C2×C4×C59—41no—
222C2×C4×C59—41no—
223C2×C4×C59—41no—
224C2×C4×C59—42no—
225C2×C4×C59—42no—
226C2×C4×C59—41no—
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#12114yes—
242C2×C4×C59#12114yes—
243#16517C5911yesmaximal, characteristic, direct product factor, Sylow
244C22×C59C2×#12111yescharacteristic
245C22×C59C2×#12111yescharacteristic
246C22×C59#52511yescharacteristic
247C22×C59#53611yescharacteristic
248C22×C59#53611yescharacteristic
249C22×C59#53611yescharacteristic
250C22×C59#53612yes—
251C22×C59#53612yes—
252C22×C59#53711yescharacteristic
253C22×C59#54112yes—
254C22×C59#54112yes—
255C22×C59#54112yes—
256C22×C59#54212yes—
257C22×C59D4211yescharacteristic
258C22×C59#54712yes—
259C22×C59#54711yescharacteristic
260C22×C59#54811yescharacteristic
261C22×C59#54812yes—
262C22×C59#55212yes—
263C22×C59#55212yes—
264C22×C59#55311yescharacteristic
265C22×C59#56312yes—
266C22×C59#56412yes—
267C4×C59—24no—
268C4×C59—24no—
269C4×C59—42no—
270C4×C59—42no—
271C4×C59—42no—
272C4×C59—44no—
273C4×C59—44no—
274C4×C59—81no—
275C4×C59—81no—
276C4×C59—82no—
277C4×C59—82no—
278C2×#398C2×C5911yescharacteristic
279C2×#398C2×C5912yes—
280C2×#389C2×C5911yescharacteristic
281C2×#387C2×C5911yescharacteristic
282C2×#382C2×C5911yescharacteristic
283#1445C2×C5911yescharacteristic
284#1443C2×C5912yes—
285#1442C2×C5911yescharacteristic
286#1442C2×C5912yes—
287#1441C2×C5911yescharacteristic
288#1441C2×C5912yes—
289C2×C59#241311yescharacteristic
290C2×C59#241611yescharacteristic
291C2×C59#253611yescharacteristic
292C2×C59#262111yescharacteristic
293C2×C59#262111yescharacteristic
294C2×C59#263711yescharacteristic
295C2×C59#267412yes—
296C2×C59#271912yes—
297C2×C59#271912yes—
298C2×C59#276612yes—
299C2×C59#282211yescharacteristic
300C22×C4⋊C4C22×C5911yescharacteristic
301C22×C4⋊C4C22×C5912yes—
302C22×C4⋊C4C22×C5911yescharacteristic
303C22×C4⋊C4C22×C5911yescharacteristic
304C22×C4⋊C4C22×C5912yes—
305C22×C4⋊C4C22×C5912yes—
306C22×C4⋊C4C22×C5911yescharacteristic
307C22×C42C22×C5911yescharacteristic
308#398—28no—
309#398—24no—
310#389—24no—
311#387—24no—
312#382—24no—
313C2×#95C22×C5912yes—
314C2×#95C22×C5912yes—
315C2×#95C22×C5912yes—
316C2×#95C22×C5912yes—
317C2×#95C22×C5912yes—
318C2×#95C22×C5911yescharacteristic
319C2×#95C22×C5912yes—
320C2×#95C22×C5911yescharacteristic
321C2×#95C22×C5911yescharacteristic
322C2×#95C22×C5912yes—
323C2×#95C22×C5912yes—
324C2×#95C22×C5911yescharacteristic
325C2×#95C22×C5911yescharacteristic
326C2×#95C22×C5912yes—
327C2×#95C22×C5911yescharacteristic
328C59#1651711yescharacteristic, direct product factor, Sylow
329C23×C4C23×C5912yes—
330C23×C4C23×C5911yescharacteristic
331C23×C4C23×C5912yes—
332C23×C4C23×C5911yescharacteristic
333C23×C4C23×C5911yescharacteristic
334C23×C4C23×C5912yes—
335C23×C4C23×C5911yescharacteristic
336C23×C4C23×C5911yescharacteristic
337C23×C4C23×C5912yes—
338C23×C4C23×C5911yescharacteristic
339C23×C4C23×C5911yescharacteristic
340C2×C4⋊C4—22no—
341C2×C4⋊C4—22no—
342C2×C4⋊C4—24no—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—24no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—24no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—24no—
349C2×C4⋊C4—24no—
350C2×C4⋊C4—24no—
351C2×C4⋊C4—24no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—24no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—42no—
358C2×C4⋊C4—42no—
359C2×C4⋊C4D4×C5914yes—
360C2×C42—22no—
361C2×C42—22no—
362C2×C42D4×C5914yes—
363#95—24no—
364#95—22no—
365#95—22no—
366#95—22no—
367#95—22no—
368#95—22no—
369#95—24no—
370#95—24no—
371#95—24no—
372#95—24no—
373#95—24no—
374#95—24no—
375#95—24no—
376#95—42no—
377#95D4×C5914yes—
378C24C24×C5911yescharacteristic
379C22×C4—21no—
380C22×C4—21no—
381C22×C4—22no—
382C22×C4—21no—
383C22×C4—22no—
384C22×C4—21no—
385C22×C4—21no—
386C22×C4—21no—
387C22×C4—22no—
388C22×C4—21no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—21no—
392C22×C4—22no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—22no—
397C22×C4—21no—
398C22×C4—22no—
399C22×C4—21no—
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—21no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—22no—
415C22×C4—22no—
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—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—21no—
434C22×C4—22no—
435C22×C4C2×D4×C5912yes—
436C22×C4C2×D4×C5912yes—
437C22×C4C2×D4×C5914yes—
438C22×C4C2×D4×C5912yes—
439C22×C4C2×D4×C5912yes—
440C22×C4C2×D4×C5912yes—
441C22×C4C2×D4×C5912yes—
442C22×C4C2×D4×C5912yes—
443C22×C4#41×C5914yes—
444C22×C4#41×C5912yes—
445C22×C4#41×C5912yes—
446C4⋊C4—28no—
447C4⋊C4—28no—
448C4⋊C4—48no—
449C4⋊C4—48no—
450C4⋊C4—44no—
451C4⋊C4—48no—
452C4⋊C4—44no—
453C42—28no—
454C23C22×D4×C5911yescharacteristic
455C23C22×D4×C5911yescharacteristic
456C23C22×D4×C5911yescharacteristic
457C23C2×#41×C5911yescharacteristic
458C23C2×#41×C5911yescharacteristic
459C23C2×#41×C5912yes—
460C23H(5,𝔽2)×C5911yescharacteristic
461C232−1+4×C5912yes—
462C232−1+4×C5912yes—
463C232−1+4×C5912yes—
464C232−1+4×C5911yescharacteristic
465C2×C4—22no—
466C2×C4—22no—
467C2×C4—22no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—24no—
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—24no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—22no—
478C2×C4—24no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—24no—
482C2×C4—24no—
483C2×C4—22no—
484C2×C4—24no—
485C2×C4—22no—
486C2×C4—24no—
487C2×C4—24no—
488C2×C4—24no—
489C2×C4—42no—
490C2×C4—41no—
491C2×C4—42no—
492C2×C4—41no—
493C2×C4—41no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—41no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—41no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—41no—
505C2×C4—42no—
506C2×C4—41no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—41no—
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—42no—
529C2×C4—42no—
530C2×C4#121×C5914yes—
531C2×C4#121×C5914yes—
532C22C2×#121×C5911yescharacteristic
533C22C2×#121×C5911yescharacteristic
534C22C59×#52511yescharacteristic
535C22C59×#53611yescharacteristic
536C22C59×#53611yescharacteristic
537C22C59×#53611yescharacteristic
538C22C59×#53612yes—
539C22C59×#53612yes—
540C22C59×#53711yescharacteristic
541C22C59×#54112yes—
542C22C59×#54112yes—
543C22C59×#54112yes—
544C22C59×#54212yes—
545C22D42×C5911yescharacteristic
546C22C59×#54712yes—
547C22C59×#54711yescharacteristic
548C22C59×#54812yes—
549C22C59×#54811yescharacteristic
550C22C59×#55212yes—
551C22C59×#55212yes—
552C22C59×#55311yescharacteristic
553C22C59×#56312yes—
554C22C59×#56412yes—
555C4—24no—
556C4—24no—
557C4—44no—
558C4—42no—
559C4—42no—
560C4—42no—
561C4—44no—
562C4—81no—
563C4—81no—
564C4—82no—
565C4—82no—
566C2C59×#241311yescharacteristic
567C2C59×#241611yescharacteristic
568C2C59×#253611yescharacteristic
569C2C59×#262111yescharacteristic
570C2C59×#262111yescharacteristic
571C2C59×#263711yescharacteristic
572C2C59×#267412yes—
573C2C59×#271912yes—
574C2C59×#271912yes—
575C2C59×#276612yes—
576C2C59×#282211yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C59C24
commutator, Frattini, cosocleC24C24×C59
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C59 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
243. #16517C59direct (N × H)
328. C59#16517direct (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×#3892
C2×C59×#3872
C2×C59×#3822
C59×#14452
C59×#14432
C59×#14422
C59×#14412
#1651759