Finite Group Databasebeta

← C59×#16705 #28428814

Subgroups — C59×#16705 #28428814

Order 15104.

1142 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C59×#400C211yesmaximal, characteristic
2C2×C59×#398C211yesmaximal, characteristic
3C2×C59×#387C211yesmaximal, characteristic
4C2×C59×#382C211yesmaximal, characteristic
5C59×#1445C211yesmaximal, characteristic
6C59×#1445C211yesmaximal, characteristic
7C59×#1443C212yesmaximal
8C59×#1442C212yesmaximal
9C59×#1441C212yesmaximal
10C59×#1441C212yesmaximal
11C59×C4⋊#95C211yesmaximal, characteristic
12C22×C4⋊C4×C59C2211yescharacteristic
13C22×C4⋊C4×C59C2211yescharacteristic
14C22×C4⋊C4×C59C2211yescharacteristic
15C22×C4⋊C4×C59C2212yes—
16C22×C4⋊C4×C59C2211yescharacteristic
17C22×C4⋊C4×C59C2212yes—
18C22×C42×C59C2211yescharacteristic
19C59×#400—24no—
20C59×#398—24no—
21C59×#387—24no—
22C59×#382—24no—
23C2×#95×C59C2212yes—
24C2×#95×C59C2212yes—
25C2×#95×C59C2211yescharacteristic
26C2×#95×C59C2211yescharacteristic
27C2×#95×C59C2211yescharacteristic
28C2×#95×C59C2211yescharacteristic
29C2×#95×C59C2211yescharacteristic
30C2×#95×C59C2212yes—
31C2×#95×C59C2211yescharacteristic
32C2×#95×C59C2212yes—
33C2×#95×C59C2212yes—
34C2×#95×C59C2212yes—
35C2×#95×C59C2212yes—
36C2×#95×C59C2212yes—
37C2×#95×C59C2212yes—
38C2×#95×C59C2212yes—
39C23×C4×C59C2311yescharacteristic
40C23×C4×C59C2312yes—
41C23×C4×C59C2312yes—
42C23×C4×C59C2311yescharacteristic
43C23×C4×C59C2312yes—
44C23×C4×C59C2311yescharacteristic
45C23×C4×C59C2311yescharacteristic
46C23×C4×C59C2311yescharacteristic
47C23×C4×C59C2312yes—
48C23×C4×C59C2311yescharacteristic
49C23×C4×C59C2311yescharacteristic
50C2×C4⋊C4×C59—22no—
51C2×C4⋊C4×C59—22no—
52C2×C4⋊C4×C59—22no—
53C2×C4⋊C4×C59—22no—
54C2×C4⋊C4×C59—22no—
55C2×C4⋊C4×C59—24no—
56C2×C4⋊C4×C59—22no—
57C2×C4⋊C4×C59—22no—
58C2×C4⋊C4×C59—24no—
59C2×C4⋊C4×C59—24no—
60C2×C4⋊C4×C59—22no—
61C2×C4⋊C4×C59—22no—
62C2×C4⋊C4×C59—24no—
63C2×C4⋊C4×C59—42no—
64C2×C4⋊C4×C59—42no—
65C2×C4⋊C4×C59—42no—
66C2×C4⋊C4×C59D414yes—
67C2×C42×C59—24no—
68C2×C42×C59D414yes—
69#95×C59—24no—
70#95×C59—24no—
71#95×C59—22no—
72#95×C59—22no—
73#95×C59—22no—
74#95×C59—22no—
75#95×C59—22no—
76#95×C59—24no—
77#95×C59—22no—
78#95×C59—24no—
79#95×C59—24no—
80#95×C59—24no—
81#95×C59—24no—
82#95×C59—42no—
83#95×C59—42no—
84#95×C59—42no—
85C24×C59C2411yescharacteristic
86C22×C4×C59—22no—
87C22×C4×C59—22no—
88C22×C4×C59—21no—
89C22×C4×C59—22no—
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—22no—
98C22×C4×C59—22no—
99C22×C4×C59—21no—
100C22×C4×C59—22no—
101C22×C4×C59—21no—
102C22×C4×C59—21no—
103C22×C4×C59—22no—
104C22×C4×C59—21no—
105C22×C4×C59—21no—
106C22×C4×C59—22no—
107C22×C4×C59—21no—
108C22×C4×C59—22no—
109C22×C4×C59—22no—
110C22×C4×C59—22no—
111C22×C4×C59—21no—
112C22×C4×C59—22no—
113C22×C4×C59—22no—
114C22×C4×C59—22no—
115C22×C4×C59—22no—
116C22×C4×C59—21no—
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—21no—
129C22×C4×C59—21no—
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—21no—
139C22×C4×C59—21no—
140C22×C4×C59—22no—
141C22×C4×C59—22no—
142C22×C4×C59C2×D412yes—
143C22×C4×C59C2×D412yes—
144C22×C4×C59C2×D412yes—
145C22×C4×C59C2×D412yes—
146C22×C4×C59C2×D412yes—
147C22×C4×C59C2×D412yes—
148C22×C4×C59#4114yes—
149C22×C4×C59#4112yes—
150C22×C4×C59#4114yes—
151C4⋊C4×C59—28no—
152C4⋊C4×C59—48no—
153C4⋊C4×C59—48no—
154C4⋊C4×C59—44no—
155C4⋊C4×C59—44no—
156C4⋊C4×C59—44no—
157C42×C59—28no—
158C23×C59C22×D411yescharacteristic
159C23×C59C22×D411yescharacteristic
160C23×C59C2×#4111yescharacteristic
161C23×C59C2×#4112yes—
162C23×C59C2×#4112yes—
163C23×C59H(5,𝔽2)11yescharacteristic
164C23×C59H(5,𝔽2)11yescharacteristic
165C23×C592−1+411yescharacteristic
166C23×C592−1+411yescharacteristic
167C23×C592−1+412yes—
168C23×C592−1+412yes—
169C2×C4×C59—22no—
170C2×C4×C59—22no—
171C2×C4×C59—22no—
172C2×C4×C59—22no—
173C2×C4×C59—24no—
174C2×C4×C59—24no—
175C2×C4×C59—24no—
176C2×C4×C59—24no—
177C2×C4×C59—22no—
178C2×C4×C59—22no—
179C2×C4×C59—22no—
180C2×C4×C59—22no—
181C2×C4×C59—22no—
182C2×C4×C59—22no—
183C2×C4×C59—22no—
184C2×C4×C59—24no—
185C2×C4×C59—24no—
186C2×C4×C59—24no—
187C2×C4×C59—24no—
188C2×C4×C59—41no—
189C2×C4×C59—42no—
190C2×C4×C59—41no—
191C2×C4×C59—41no—
192C2×C4×C59—41no—
193C2×C4×C59—42no—
194C2×C4×C59—41no—
195C2×C4×C59—41no—
196C2×C4×C59—42no—
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—41no—
204C2×C4×C59—41no—
205C2×C4×C59—41no—
206C2×C4×C59—42no—
207C2×C4×C59—42no—
208C2×C4×C59—42no—
209C2×C4×C59—42no—
210C2×C4×C59—41no—
211C2×C4×C59—42no—
212C2×C4×C59—42no—
213C2×C4×C59—42no—
214C2×C4×C59—41no—
215C2×C4×C59—41no—
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—42no—
225C2×C4×C59—42no—
226C2×C4×C59—42no—
227C2×C4×C59—42no—
228C2×C4×C59—42no—
229C2×C4×C59—42no—
230C2×C4×C59—42no—
231C2×C4×C59—42no—
232C2×C4×C59#12114yes—
233C2×C4×C59#12314yes—
234#16705C5911yesmaximal, characteristic, direct product factor, Sylow
235C22×C59C2×#12111yescharacteristic
236C22×C59C2×#12311yescharacteristic
237C22×C59#53211yescharacteristic
238C22×C59#53511yescharacteristic
239C22×C59#53611yescharacteristic
240C22×C59#53611yescharacteristic
241C22×C59#53611yescharacteristic
242C22×C59#53711yescharacteristic
243C22×C59#53711yescharacteristic
244C22×C59#53912yes—
245C22×C59#54112yes—
246C22×C59#54112yes—
247C22×C59#54211yescharacteristic
248C22×C59#54211yescharacteristic
249C22×C59#54212yes—
250C22×C59#54712yes—
251C22×C59#54812yes—
252C22×C59#55112yes—
253C22×C59#55212yes—
254C22×C59#55212yes—
255C22×C59#55612yes—
256C22×C59#56312yes—
257C22×C59#56412yes—
258C4×C59—24no—
259C4×C59—24no—
260C4×C59—42no—
261C4×C59—42no—
262C4×C59—44no—
263C4×C59—42no—
264C4×C59—82no—
265C4×C59—81no—
266C4×C59—82no—
267C4×C59—81no—
268C4×C59—82no—
269C2×#400C2×C5911yescharacteristic
270C2×#398C2×C5911yescharacteristic
271C2×#387C2×C5911yescharacteristic
272C2×#382C2×C5911yescharacteristic
273#1445C2×C5911yescharacteristic
274#1445C2×C5911yescharacteristic
275#1443C2×C5912yes—
276#1442C2×C5912yes—
277#1441C2×C5912yes—
278#1441C2×C5912yes—
279C4⋊#95C2×C5911yescharacteristic
280C2×C59#248611yescharacteristic
281C2×C59#249811yescharacteristic
282C2×C59#254511yescharacteristic
283C2×C59#262011yescharacteristic
284C2×C59#262511yescharacteristic
285C2×C59#266411yescharacteristic
286C2×C59#271912yes—
287C2×C59#272312yes—
288C2×C59#276212yes—
289C2×C59#276712yes—
290C2×C59#282211yescharacteristic
291C22×C4⋊C4C22×C5911yescharacteristic
292C22×C4⋊C4C22×C5911yescharacteristic
293C22×C4⋊C4C22×C5911yescharacteristic
294C22×C4⋊C4C22×C5912yes—
295C22×C4⋊C4C22×C5911yescharacteristic
296C22×C4⋊C4C22×C5912yes—
297C22×C42C22×C5911yescharacteristic
298#400—24no—
299#398—24no—
300#387—24no—
301#382—24no—
302C2×#95C22×C5911yescharacteristic
303C2×#95C22×C5912yes—
304C2×#95C22×C5911yescharacteristic
305C2×#95C22×C5912yes—
306C2×#95C22×C5912yes—
307C2×#95C22×C5912yes—
308C2×#95C22×C5911yescharacteristic
309C2×#95C22×C5912yes—
310C2×#95C22×C5912yes—
311C2×#95C22×C5911yescharacteristic
312C2×#95C22×C5912yes—
313C2×#95C22×C5911yescharacteristic
314C2×#95C22×C5911yescharacteristic
315C2×#95C22×C5912yes—
316C2×#95C22×C5912yes—
317C2×#95C22×C5912yes—
318C59#1670511yescharacteristic, direct product factor, Sylow
319C23×C4C23×C5912yes—
320C23×C4C23×C5912yes—
321C23×C4C23×C5912yes—
322C23×C4C23×C5911yescharacteristic
323C23×C4C23×C5911yescharacteristic
324C23×C4C23×C5911yescharacteristic
325C23×C4C23×C5911yescharacteristic
326C23×C4C23×C5911yescharacteristic
327C23×C4C23×C5912yes—
328C23×C4C23×C5911yescharacteristic
329C23×C4C23×C5911yescharacteristic
330C2×C4⋊C4—22no—
331C2×C4⋊C4—22no—
332C2×C4⋊C4—22no—
333C2×C4⋊C4—22no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—24no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—24no—
339C2×C4⋊C4—24no—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—22no—
342C2×C4⋊C4—24no—
343C2×C4⋊C4—42no—
344C2×C4⋊C4—42no—
345C2×C4⋊C4—42no—
346C2×C4⋊C4D4×C5914yes—
347C2×C42—24no—
348C2×C42D4×C5914yes—
349#95—24no—
350#95—24no—
351#95—22no—
352#95—22no—
353#95—22no—
354#95—22no—
355#95—22no—
356#95—24no—
357#95—22no—
358#95—24no—
359#95—24no—
360#95—24no—
361#95—24no—
362#95—42no—
363#95—42no—
364#95—42no—
365C24C24×C5911yescharacteristic
366C22×C4—22no—
367C22×C4—22no—
368C22×C4—21no—
369C22×C4—22no—
370C22×C4—21no—
371C22×C4—21no—
372C22×C4—22no—
373C22×C4—21no—
374C22×C4—22no—
375C22×C4—21no—
376C22×C4—21no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—21no—
380C22×C4—22no—
381C22×C4—21no—
382C22×C4—21no—
383C22×C4—22no—
384C22×C4—21no—
385C22×C4—21no—
386C22×C4—22no—
387C22×C4—21no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—21no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—21no—
397C22×C4—22no—
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—21no—
409C22×C4—21no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4C2×D4×C5912yes—
423C22×C4C2×D4×C5912yes—
424C22×C4C2×D4×C5912yes—
425C22×C4C2×D4×C5912yes—
426C22×C4C2×D4×C5912yes—
427C22×C4C2×D4×C5912yes—
428C22×C4#41×C5914yes—
429C22×C4#41×C5912yes—
430C22×C4#41×C5914yes—
431C4⋊C4—28no—
432C4⋊C4—48no—
433C4⋊C4—48no—
434C4⋊C4—44no—
435C4⋊C4—44no—
436C4⋊C4—44no—
437C42—28no—
438C23C22×D4×C5911yescharacteristic
439C23C22×D4×C5911yescharacteristic
440C23C2×#41×C5911yescharacteristic
441C23C2×#41×C5912yes—
442C23C2×#41×C5912yes—
443C23H(5,𝔽2)×C5911yescharacteristic
444C23H(5,𝔽2)×C5911yescharacteristic
445C232−1+4×C5911yescharacteristic
446C232−1+4×C5911yescharacteristic
447C232−1+4×C5912yes—
448C232−1+4×C5912yes—
449C2×C4—22no—
450C2×C4—22no—
451C2×C4—22no—
452C2×C4—22no—
453C2×C4—24no—
454C2×C4—24no—
455C2×C4—24no—
456C2×C4—24no—
457C2×C4—22no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—24no—
465C2×C4—24no—
466C2×C4—24no—
467C2×C4—24no—
468C2×C4—41no—
469C2×C4—42no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—42no—
474C2×C4—41no—
475C2×C4—41no—
476C2×C4—42no—
477C2×C4—42no—
478C2×C4—42no—
479C2×C4—42no—
480C2×C4—42no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—41no—
484C2×C4—41no—
485C2×C4—42no—
486C2×C4—41no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—41no—
492C2×C4—41no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—41no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4#121×C5914yes—
513C2×C4#123×C5914yes—
514C22C2×#121×C5911yescharacteristic
515C22C2×#123×C5911yescharacteristic
516C22C59×#53211yescharacteristic
517C22C59×#53511yescharacteristic
518C22C59×#53611yescharacteristic
519C22C59×#53611yescharacteristic
520C22C59×#53611yescharacteristic
521C22C59×#53711yescharacteristic
522C22C59×#53711yescharacteristic
523C22C59×#53912yes—
524C22C59×#54112yes—
525C22C59×#54112yes—
526C22C59×#54211yescharacteristic
527C22C59×#54211yescharacteristic
528C22C59×#54212yes—
529C22C59×#54712yes—
530C22C59×#54812yes—
531C22C59×#55112yes—
532C22C59×#55212yes—
533C22C59×#55212yes—
534C22C59×#55612yes—
535C22C59×#56312yes—
536C22C59×#56412yes—
537C4—24no—
538C4—24no—
539C4—42no—
540C4—42no—
541C4—42no—
542C4—44no—
543C4—81no—
544C4—82no—
545C4—82no—
546C4—81no—
547C4—82no—
548C2C59×#248611yescharacteristic
549C2C59×#249811yescharacteristic
550C2C59×#254511yescharacteristic
551C2C59×#262011yescharacteristic
552C2C59×#262511yescharacteristic
553C2C59×#266411yescharacteristic
554C2C59×#271912yes—
555C2C59×#272312yes—
556C2C59×#276212yes—
557C2C59×#276712yes—
558C2C59×#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
234. #16705C59direct (N × H)
318. C59#16705direct (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×#3982
C2×C59×#3872
C2×C59×#3822
C59×#14452
C59×#14432
C59×#14422
C59×#14412
C59×C4⋊#952
#1670559