Finite Group Databasebeta

← C59×#16563 #28428672

Subgroups — C59×#16563 #28428672

Order 15104.

1238 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C59×#398C211yesmaximal, characteristic
2C2×C59×#387C212yesmaximal
3C2×C59×#384C211yesmaximal, characteristic
4C59×#1441C212yesmaximal
5C59×#1441C212yesmaximal
6C59×#1441C211yesmaximal, characteristic
7C59×#1441C212yesmaximal
8C59×#1441C212yesmaximal
9C59×#1441C212yesmaximal
10C22×C4⋊C4×C59C2212yes—
11C22×C4⋊C4×C59C2212yes—
12C22×C4⋊C4×C59C2212yes—
13C22×C4⋊C4×C59C2212yes—
14C22×C4⋊C4×C59C2211yescharacteristic
15C22×C4⋊C4×C59C2211yescharacteristic
16C22×C4⋊C4×C59C2211yescharacteristic
17C22×C4⋊C4×C59C2211yescharacteristic
18C22×C42×C59C2211yescharacteristic
19C59×#398—24no—
20C59×#387—28no—
21C59×#384—24no—
22C2×#95×C59C2212yes—
23C2×#95×C59C2212yes—
24C2×#95×C59C2212yes—
25C2×#95×C59C2212yes—
26C2×#95×C59C2212yes—
27C2×#95×C59C2211yescharacteristic
28C2×#95×C59C2212yes—
29C2×#95×C59C2212yes—
30C2×#95×C59C2212yes—
31C2×#95×C59C2212yes—
32C2×#95×C59C2212yes—
33C2×#95×C59C2211yescharacteristic
34C23×C4×C59C2312yes—
35C23×C4×C59C2312yes—
36C23×C4×C59C2312yes—
37C23×C4×C59C2311yescharacteristic
38C23×C4×C59C2311yescharacteristic
39C23×C4×C59C2312yes—
40C23×C4×C59C2312yes—
41C23×C4×C59C2311yescharacteristic
42C23×C4×C59C2312yes—
43C2×C4⋊C4×C59—24no—
44C2×C4⋊C4×C59—24no—
45C2×C4⋊C4×C59—24no—
46C2×C4⋊C4×C59—24no—
47C2×C4⋊C4×C59—22no—
48C2×C4⋊C4×C59—24no—
49C2×C4⋊C4×C59—22no—
50C2×C4⋊C4×C59—24no—
51C2×C4⋊C4×C59—24no—
52C2×C4⋊C4×C59—24no—
53C2×C4⋊C4×C59—24no—
54C2×C4⋊C4×C59—41no—
55C2×C4⋊C4×C59—41no—
56C2×C4⋊C4×C59—42no—
57C2×C4⋊C4×C59—42no—
58C2×C4⋊C4×C59—41no—
59C2×C4⋊C4×C59—41no—
60C2×C4⋊C4×C59—41no—
61C2×C4⋊C4×C59—41no—
62C2×C4⋊C4×C59—41no—
63C2×C4⋊C4×C59—42no—
64C2×C4⋊C4×C59D414yes—
65C2×C4⋊C4×C59Q818yes—
66C2×C42×C59—22no—
67C2×C42×C59—22no—
68C2×C42×C59D414yes—
69#95×C59—24no—
70#95×C59—24no—
71#95×C59—24no—
72#95×C59—24no—
73#95×C59—22no—
74#95×C59—24no—
75#95×C59—41no—
76#95×C59—42no—
77#95×C59—42no—
78#95×C59—42no—
79#95×C59—42no—
80#95×C59—42no—
81C24×C59C2411yescharacteristic
82C22×C4×C59—22no—
83C22×C4×C59—22no—
84C22×C4×C59—21no—
85C22×C4×C59—21no—
86C22×C4×C59—22no—
87C22×C4×C59—21no—
88C22×C4×C59—21no—
89C22×C4×C59—22no—
90C22×C4×C59—22no—
91C22×C4×C59—22no—
92C22×C4×C59—22no—
93C22×C4×C59—22no—
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—21no—
102C22×C4×C59—22no—
103C22×C4×C59—21no—
104C22×C4×C59—21no—
105C22×C4×C59—21no—
106C22×C4×C59—22no—
107C22×C4×C59—22no—
108C22×C4×C59—22no—
109C22×C4×C59—22no—
110C22×C4×C59—22no—
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—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×C59C2×D412yes—
132C22×C4×C59C2×D412yes—
133C22×C4×C59C2×D412yes—
134C22×C4×C59C2×D412yes—
135C22×C4×C59C2×D414yes—
136C22×C4×C59C2×Q814yes—
137C22×C4×C59C2×Q814yes—
138C22×C4×C59C2×Q814yes—
139C22×C4×C59#4112yes—
140C22×C4×C59#4114yes—
141C4⋊C4×C59—216no—
142C4⋊C4×C59—44no—
143C4⋊C4×C59—48no—
144C4⋊C4×C59—48no—
145C4⋊C4×C59—44no—
146C4⋊C4×C59—44no—
147C4⋊C4×C59—44no—
148C4⋊C4×C59—48no—
149C42×C59—28no—
150C23×C59C22×D411yescharacteristic
151C23×C59C22×D411yescharacteristic
152C23×C59C22×Q812yes—
153C23×C59C2×#4111yescharacteristic
154C23×C59C2×#4112yes—
155C23×C59H(5,𝔽2)11yescharacteristic
156C23×C59H(5,𝔽2)11yescharacteristic
157C23×C59H(5,𝔽2)12yes—
158C23×C592−1+411yescharacteristic
159C23×C592−1+411yescharacteristic
160C23×C592−1+412yes—
161C2×C4×C59—24no—
162C2×C4×C59—22no—
163C2×C4×C59—22no—
164C2×C4×C59—22no—
165C2×C4×C59—22no—
166C2×C4×C59—24no—
167C2×C4×C59—22no—
168C2×C4×C59—22no—
169C2×C4×C59—24no—
170C2×C4×C59—24no—
171C2×C4×C59—24no—
172C2×C4×C59—24no—
173C2×C4×C59—24no—
174C2×C4×C59—24no—
175C2×C4×C59—22no—
176C2×C4×C59—22no—
177C2×C4×C59—24no—
178C2×C4×C59—24no—
179C2×C4×C59—24no—
180C2×C4×C59—24no—
181C2×C4×C59—24no—
182C2×C4×C59—24no—
183C2×C4×C59—42no—
184C2×C4×C59—42no—
185C2×C4×C59—42no—
186C2×C4×C59—42no—
187C2×C4×C59—42no—
188C2×C4×C59—42no—
189C2×C4×C59—42no—
190C2×C4×C59—42no—
191C2×C4×C59—42no—
192C2×C4×C59—42no—
193C2×C4×C59—41no—
194C2×C4×C59—41no—
195C2×C4×C59—41no—
196C2×C4×C59—41no—
197C2×C4×C59—42no—
198C2×C4×C59—42no—
199C2×C4×C59—42no—
200C2×C4×C59—42no—
201C2×C4×C59—42no—
202C2×C4×C59—42no—
203C2×C4×C59—42no—
204C2×C4×C59—42no—
205C2×C4×C59—42no—
206C2×C4×C59—42no—
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#12114yes—
219C2×C4×C59C22⋊Q818yes—
220#16563C5911yesmaximal, characteristic, direct product factor, Sylow
221C22×C59C2×#12111yescharacteristic
222C22×C59C2×C22⋊Q812yes—
223C22×C59#53411yescharacteristic
224C22×C59#53611yescharacteristic
225C22×C59#53711yescharacteristic
226C22×C59#53712yes—
227C22×C59#53711yescharacteristic
228C22×C59#53911yescharacteristic
229C22×C59#53911yescharacteristic
230C22×C59#54012yes—
231C22×C59#54112yes—
232C22×C59#54412yes—
233C22×C59#54412yes—
234C22×C59#54612yes—
235C22×C59D4×Q812yes—
236C22×C59#55212yes—
237C22×C59#55412yes—
238C22×C59#55712yes—
239C22×C59Q8211yescharacteristic
240C22×C59#55911yescharacteristic
241C22×C59#56011yescharacteristic
242C22×C59#56312yes—
243C22×C59#56311yescharacteristic
244C4×C59—24no—
245C4×C59—28no—
246C4×C59—44no—
247C4×C59—44no—
248C4×C59—42no—
249C4×C59—42no—
250C4×C59—82no—
251C4×C59—82no—
252C4×C59—82no—
253C2×#398C2×C5911yescharacteristic
254C2×#387C2×C5912yes—
255C2×#384C2×C5911yescharacteristic
256#1441C2×C5912yes—
257#1441C2×C5912yes—
258#1441C2×C5912yes—
259#1441C2×C5912yes—
260#1441C2×C5912yes—
261#1441C2×C5911yescharacteristic
262C2×C59#241712yes—
263C2×C59#258211yescharacteristic
264C2×C59#261811yescharacteristic
265C2×C59#262912yes—
266C2×C59#270911yescharacteristic
267C2×C59#271312yes—
268C2×C59#273411yescharacteristic
269C2×C59#279112yes—
270C2×C59#279211yescharacteristic
271C2×C59#279411yescharacteristic
272C2×C59#282311yescharacteristic
273C22×C4⋊C4C22×C5912yes—
274C22×C4⋊C4C22×C5912yes—
275C22×C4⋊C4C22×C5912yes—
276C22×C4⋊C4C22×C5912yes—
277C22×C4⋊C4C22×C5911yescharacteristic
278C22×C4⋊C4C22×C5911yescharacteristic
279C22×C4⋊C4C22×C5911yescharacteristic
280C22×C4⋊C4C22×C5911yescharacteristic
281C22×C42C22×C5911yescharacteristic
282#398—24no—
283#387—28no—
284#384—24no—
285C2×#95C22×C5912yes—
286C2×#95C22×C5911yescharacteristic
287C2×#95C22×C5912yes—
288C2×#95C22×C5912yes—
289C2×#95C22×C5912yes—
290C2×#95C22×C5912yes—
291C2×#95C22×C5912yes—
292C2×#95C22×C5912yes—
293C2×#95C22×C5912yes—
294C2×#95C22×C5912yes—
295C2×#95C22×C5912yes—
296C2×#95C22×C5911yescharacteristic
297C59#1656311yescharacteristic, direct product factor, Sylow
298C23×C4C23×C5912yes—
299C23×C4C23×C5912yes—
300C23×C4C23×C5912yes—
301C23×C4C23×C5911yescharacteristic
302C23×C4C23×C5911yescharacteristic
303C23×C4C23×C5912yes—
304C23×C4C23×C5912yes—
305C23×C4C23×C5911yescharacteristic
306C23×C4C23×C5912yes—
307C2×C4⋊C4—24no—
308C2×C4⋊C4—24no—
309C2×C4⋊C4—24no—
310C2×C4⋊C4—24no—
311C2×C4⋊C4—22no—
312C2×C4⋊C4—24no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4—24no—
315C2×C4⋊C4—24no—
316C2×C4⋊C4—24no—
317C2×C4⋊C4—24no—
318C2×C4⋊C4—41no—
319C2×C4⋊C4—41no—
320C2×C4⋊C4—42no—
321C2×C4⋊C4—42no—
322C2×C4⋊C4—41no—
323C2×C4⋊C4—41no—
324C2×C4⋊C4—41no—
325C2×C4⋊C4—41no—
326C2×C4⋊C4—41no—
327C2×C4⋊C4—42no—
328C2×C4⋊C4D4×C5914yes—
329C2×C4⋊C4Q8×C5918yes—
330C2×C42—22no—
331C2×C42—22no—
332C2×C42D4×C5914yes—
333#95—24no—
334#95—24no—
335#95—24no—
336#95—24no—
337#95—22no—
338#95—24no—
339#95—41no—
340#95—42no—
341#95—42no—
342#95—42no—
343#95—42no—
344#95—42no—
345C24C24×C5911yescharacteristic
346C22×C4—22no—
347C22×C4—22no—
348C22×C4—21no—
349C22×C4—21no—
350C22×C4—22no—
351C22×C4—21no—
352C22×C4—21no—
353C22×C4—22no—
354C22×C4—22no—
355C22×C4—22no—
356C22×C4—22no—
357C22×C4—22no—
358C22×C4—22no—
359C22×C4—22no—
360C22×C4—22no—
361C22×C4—22no—
362C22×C4—22no—
363C22×C4—22no—
364C22×C4—22no—
365C22×C4—21no—
366C22×C4—22no—
367C22×C4—21no—
368C22×C4—21no—
369C22×C4—21no—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4C2×D4×C5912yes—
396C22×C4C2×D4×C5912yes—
397C22×C4C2×D4×C5912yes—
398C22×C4C2×D4×C5912yes—
399C22×C4C2×D4×C5914yes—
400C22×C4C2×Q8×C5914yes—
401C22×C4C2×Q8×C5914yes—
402C22×C4C2×Q8×C5914yes—
403C22×C4#41×C5912yes—
404C22×C4#41×C5914yes—
405C4⋊C4—216no—
406C4⋊C4—44no—
407C4⋊C4—48no—
408C4⋊C4—48no—
409C4⋊C4—44no—
410C4⋊C4—44no—
411C4⋊C4—44no—
412C4⋊C4—48no—
413C42—28no—
414C23C22×D4×C5911yescharacteristic
415C23C22×D4×C5911yescharacteristic
416C23C22×Q8×C5912yes—
417C23C2×#41×C5911yescharacteristic
418C23C2×#41×C5912yes—
419C23H(5,𝔽2)×C5911yescharacteristic
420C23H(5,𝔽2)×C5911yescharacteristic
421C23H(5,𝔽2)×C5912yes—
422C232−1+4×C5911yescharacteristic
423C232−1+4×C5911yescharacteristic
424C232−1+4×C5912yes—
425C2×C4—24no—
426C2×C4—22no—
427C2×C4—22no—
428C2×C4—22no—
429C2×C4—22no—
430C2×C4—24no—
431C2×C4—22no—
432C2×C4—22no—
433C2×C4—24no—
434C2×C4—24no—
435C2×C4—24no—
436C2×C4—24no—
437C2×C4—24no—
438C2×C4—24no—
439C2×C4—22no—
440C2×C4—22no—
441C2×C4—24no—
442C2×C4—24no—
443C2×C4—24no—
444C2×C4—24no—
445C2×C4—24no—
446C2×C4—24no—
447C2×C4—42no—
448C2×C4—42no—
449C2×C4—42no—
450C2×C4—42no—
451C2×C4—42no—
452C2×C4—42no—
453C2×C4—42no—
454C2×C4—42no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—42no—
462C2×C4—42no—
463C2×C4—42no—
464C2×C4—42no—
465C2×C4—42no—
466C2×C4—42no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—42no—
470C2×C4—42no—
471C2×C4—42no—
472C2×C4—42no—
473C2×C4—42no—
474C2×C4—42no—
475C2×C4—42no—
476C2×C4—42no—
477C2×C4—42no—
478C2×C4—42no—
479C2×C4—42no—
480C2×C4—42no—
481C2×C4—42no—
482C2×C4#121×C5914yes—
483C2×C4C22⋊Q8×C5918yes—
484C22C2×#121×C5911yescharacteristic
485C22C2×C22⋊Q8×C5912yes—
486C22C59×#53411yescharacteristic
487C22C59×#53611yescharacteristic
488C22C59×#53711yescharacteristic
489C22C59×#53712yes—
490C22C59×#53711yescharacteristic
491C22C59×#53911yescharacteristic
492C22C59×#53911yescharacteristic
493C22C59×#54012yes—
494C22C59×#54112yes—
495C22C59×#54412yes—
496C22C59×#54412yes—
497C22C59×#54612yes—
498C22D4×Q8×C5912yes—
499C22C59×#55212yes—
500C22C59×#55412yes—
501C22C59×#55712yes—
502C22Q82×C5911yescharacteristic
503C22C59×#55911yescharacteristic
504C22C59×#56011yescharacteristic
505C22C59×#56312yes—
506C22C59×#56311yescharacteristic
507C4—24no—
508C4—28no—
509C4—44no—
510C4—44no—
511C4—42no—
512C4—42no—
513C4—82no—
514C4—82no—
515C4—82no—
516C2C59×#241712yes—
517C2C59×#258211yescharacteristic
518C2C59×#261811yescharacteristic
519C2C59×#262912yes—
520C2C59×#270911yescharacteristic
521C2C59×#271312yes—
522C2C59×#273411yescharacteristic
523C2C59×#279112yes—
524C2C59×#279211yescharacteristic
525C2C59×#279411yescharacteristic
526C2C59×#282311yescharacteristic
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
220. #16563C59direct (N × H)
297. C59#16563direct (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×#3872
C2×C59×#3842
C59×#14412
#1656359