Finite Group Databasebeta

← C59×#16902 #28429011

Subgroups — C59×#16902 #28429011

Order 15104.

1306 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C59×#1445C212yesmaximal, complemented
2C59×#1445C212yesmaximal, complemented
3C59×#1443C212yesmaximal, complemented
4C59×#1441C212yesmaximal, complemented
5C59×#1439C212yesmaximal
6C59×#1439C212yesmaximal
7C59×C22⋊#95C211yesmaximal, characteristic
8C59×C22⋊#95C211yesmaximal, characteristic
9C59×C22⋊#95C211yesmaximal, characteristic
10C24×C4×C59C2211yescharacteristic
11C22×C4⋊C4×C59C2212yes—
12C22×C4⋊C4×C59C2212yes—
13C22×C22⋊C4×C59C2212yes—
14C22×C22⋊C4×C59C2212yes—
15C22×C22⋊C4×C59C2211yescharacteristic
16C22×C22⋊C4×C59C2211yescharacteristic
17C2×#95×C59C2212yes—
18C2×#95×C59C2211yescharacteristic
19C2×#95×C59C2212yes—
20C2×#95×C59C2212yes—
21C2×#95×C59C2211yescharacteristic
22C2×#95×C59C2212yes—
23C2×#95×C59C2212yes—
24C2×#95×C59C2211yescharacteristic
25C2×#95×C59C2211yescharacteristic
26C2×#95×C59C2212yes—
27C2×#95×C59C2212yes—
28C2×#95×C59C2212yes—
29C2×#95×C59C2212yes—
30C2×#95×C59C2212yes—
31C25×C59C2311yescharacteristic
32C23×C4×C59—41no—
33C23×C4×C59—41no—
34C23×C4×C59—42no—
35C23×C4×C59—42no—
36C23×C4×C59Q814yes—
37C23×C4×C59C2312yes—
38C23×C4×C59C2312yes—
39C23×C4×C59C2312yes—
40C23×C4×C59C2312yes—
41C23×C4×C59C2311yescharacteristic
42C23×C4×C59C2311yescharacteristic
43C23×C4×C59C2312yes—
44C23×C4×C59C2312yes—
45C2×C4⋊C4×C59—24no—
46C2×C4⋊C4×C59—24no—
47C2×C4⋊C4×C59—24no—
48C2×C4⋊C4×C59—42no—
49C2×C4⋊C4×C59—42no—
50C2×C4⋊C4×C59—42no—
51C2×C22⋊C4×C59—24no—
52C2×C22⋊C4×C59—24no—
53C2×C22⋊C4×C59—22no—
54C2×C22⋊C4×C59—22no—
55C2×C22⋊C4×C59—24no—
56C2×C22⋊C4×C59—24no—
57C2×C22⋊C4×C59—42no—
58C2×C22⋊C4×C59—42no—
59C2×C22⋊C4×C59—41no—
60C2×C22⋊C4×C59—41no—
61C2×C22⋊C4×C59—41no—
62C2×C22⋊C4×C59—41no—
63#95×C59—24no—
64#95×C59—42no—
65#95×C59—42no—
66#95×C59—42no—
67#95×C59—41no—
68#95×C59—41no—
69#95×C59—42no—
70#95×C59—42no—
71#95×C59—41no—
72#95×C59—41no—
73#95×C59—42no—
74#95×C59—42no—
75#95×C59—42no—
76#95×C59—42no—
77C24×C59—22no—
78C24×C59—22no—
79C24×C59—21no—
80C24×C59—21no—
81C24×C59—21no—
82C24×C59—22no—
83C24×C59—22no—
84C24×C59—21no—
85C24×C59C2×Q812yes—
86C24×C59#4112yes—
87C24×C59#4112yes—
88C24×C59C2411yescharacteristic
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—21no—
101C22×C4×C59—21no—
102C22×C4×C59—21no—
103C22×C4×C59—21no—
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—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×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—44no—
138C22×C4×C59—44no—
139C22×C4×C59—44no—
140C22×C4×C59—48no—
141C22×C4×C59—48no—
142C22×C4×C59C2×Q812yes—
143C22×C4×C59C2×Q812yes—
144C22×C4×C59#4114yes—
145C22×C4×C59#4114yes—
146C4⋊C4×C59—48no—
147C4⋊C4×C59—48no—
148C22⋊C4×C59—48no—
149C22⋊C4×C59—48no—
150C22⋊C4×C59—44no—
151C22⋊C4×C59—44no—
152C23×C59—22no—
153C23×C59—22no—
154C23×C59—22no—
155C23×C59—22no—
156C23×C59—22no—
157C23×C59—22no—
158C23×C59—22no—
159C23×C59—22no—
160C23×C59—22no—
161C23×C59—22no—
162C23×C59—24no—
163C23×C59—24no—
164C23×C59—24no—
165C23×C59—24no—
166C23×C59—42no—
167C23×C59—42no—
168C23×C59—42no—
169C23×C59—42no—
170C23×C59—42no—
171C23×C59—42no—
172C23×C59—42no—
173C23×C59—42no—
174C23×C59#12514yes—
175C23×C59C22×Q811yescharacteristic
176C23×C59C2×#4111yescharacteristic
177C23×C59C2×#4111yescharacteristic
178C23×C59C2×#4112yes—
179C23×C59C2×#4112yes—
180C23×C59H(5,𝔽2)11yescharacteristic
181C23×C59H(5,𝔽2)11yescharacteristic
182C23×C59H(5,𝔽2)11yescharacteristic
183C23×C59H(5,𝔽2)12yes—
184C23×C59H(5,𝔽2)12yes—
185C23×C592−1+411yescharacteristic
186C2×C4×C59—24no—
187C2×C4×C59—24no—
188C2×C4×C59—22no—
189C2×C4×C59—22no—
190C2×C4×C59—22no—
191C2×C4×C59—22no—
192C2×C4×C59—22no—
193C2×C4×C59—22no—
194C2×C4×C59—24no—
195C2×C4×C59—24no—
196C2×C4×C59—24no—
197C2×C4×C59—24no—
198C2×C4×C59—416no—
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—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—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—
239#16902C5911yesmaximal, characteristic, direct product factor, Sylow
240C22×C59—24no—
241C22×C59—24no—
242C22×C59—24no—
243C22×C59—42no—
244C22×C59—42no—
245C22×C59—42no—
246C22×C59—42no—
247C22×C59—44no—
248C22×C59—44no—
249C22×C59—44no—
250C22×C59—44no—
251C22×C59C2×#12511yescharacteristic
252C22×C59#53311yescharacteristic
253C22×C59#53311yescharacteristic
254C22×C59#53811yescharacteristic
255C22×C59#53811yescharacteristic
256C22×C59#53812yes—
257C22×C59#53911yescharacteristic
258C22×C59#53911yescharacteristic
259C22×C59#53912yes—
260C22×C59#54012yes—
261C22×C59#54212yes—
262C22×C59#54311yescharacteristic
263C22×C59#54311yescharacteristic
264C22×C59#54311yescharacteristic
265C22×C59#54411yescharacteristic
266C22×C59#55112yes—
267C22×C59#55112yes—
268C22×C59#55112yes—
269C22×C59#55312yes—
270C22×C59#55312yes—
271C22×C59#55912yes—
272C22×C59#56012yes—
273C22×C59#56012yes—
274C4×C59—42no—
275C4×C59—42no—
276C4×C59—44no—
277C4×C59—44no—
278C4×C59—82no—
279C4×C59—82no—
280C4×C59—82no—
281C4×C59—82no—
282#1445C2×C5912yescomplemented
283#1445C2×C5912yescomplemented
284#1443C2×C5912yescomplemented
285#1441C2×C5912yescomplemented
286#1439C2×C5912yes—
287#1439C2×C5912yes—
288C22⋊#95C2×C5911yescharacteristic
289C22⋊#95C2×C5911yescharacteristic
290C22⋊#95C2×C5911yescharacteristic
291C2×C59—44no—
292C2×C59#256911yescharacteristic
293C2×C59#256911yescharacteristic
294C2×C59#260711yescharacteristic
295C2×C59#264611yescharacteristic
296C2×C59#266511yescharacteristic
297C2×C59#266711yescharacteristic
298C2×C59#274612yes—
299C2×C59#274912yes—
300C2×C59#279612yes—
301C2×C59#279712yes—
302C2×C59#284211yescharacteristic
303C24×C4C22×C5911yescharacteristic
304C22×C4⋊C4C22×C5912yes—
305C22×C4⋊C4C22×C5912yes—
306C22×C22⋊C4C22×C5912yes—
307C22×C22⋊C4C22×C5912yes—
308C22×C22⋊C4C22×C5911yescharacteristic
309C22×C22⋊C4C22×C5911yescharacteristic
310C2×#95C22×C5912yes—
311C2×#95C22×C5911yescharacteristic
312C2×#95C22×C5912yes—
313C2×#95C22×C5912yes—
314C2×#95C22×C5911yescharacteristic
315C2×#95C22×C5912yes—
316C2×#95C22×C5911yescharacteristic
317C2×#95C22×C5912yes—
318C2×#95C22×C5911yescharacteristic
319C2×#95C22×C5912yes—
320C2×#95C22×C5912yes—
321C2×#95C22×C5912yes—
322C2×#95C22×C5912yes—
323C2×#95C22×C5912yes—
324C59#1690211yescharacteristic, direct product factor, Sylow
325C25C23×C5911yescharacteristic
326C23×C4—41no—
327C23×C4—41no—
328C23×C4—42no—
329C23×C4—42no—
330C23×C4Q8×C5914yes—
331C23×C4C23×C5912yes—
332C23×C4C23×C5912yes—
333C23×C4C23×C5912yes—
334C23×C4C23×C5912yes—
335C23×C4C23×C5911yescharacteristic
336C23×C4C23×C5911yescharacteristic
337C23×C4C23×C5912yes—
338C23×C4C23×C5912yes—
339C2×C4⋊C4—24no—
340C2×C4⋊C4—24no—
341C2×C4⋊C4—24no—
342C2×C4⋊C4—42no—
343C2×C4⋊C4—42no—
344C2×C4⋊C4—42no—
345C2×C22⋊C4—24no—
346C2×C22⋊C4—24no—
347C2×C22⋊C4—22no—
348C2×C22⋊C4—22no—
349C2×C22⋊C4—24no—
350C2×C22⋊C4—24no—
351C2×C22⋊C4—42no—
352C2×C22⋊C4—42no—
353C2×C22⋊C4—41no—
354C2×C22⋊C4—41no—
355C2×C22⋊C4—41no—
356C2×C22⋊C4—41no—
357#95—24no—
358#95—42no—
359#95—42no—
360#95—42no—
361#95—41no—
362#95—41no—
363#95—42no—
364#95—42no—
365#95—41no—
366#95—41no—
367#95—42no—
368#95—42no—
369#95—42no—
370#95—42no—
371C24—22no—
372C24—22no—
373C24—21no—
374C24—21no—
375C24—21no—
376C24—22no—
377C24—22no—
378C24—21no—
379C24C2×Q8×C5912yes—
380C24#41×C5912yes—
381C24#41×C5912yes—
382C24C24×C5911yescharacteristic
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—21no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—21no—
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—22no—
409C22×C4—22no—
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—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—44no—
432C22×C4—44no—
433C22×C4—44no—
434C22×C4—48no—
435C22×C4—48no—
436C22×C4C2×Q8×C5912yes—
437C22×C4C2×Q8×C5912yes—
438C22×C4#41×C5914yes—
439C22×C4#41×C5914yes—
440C4⋊C4—48no—
441C4⋊C4—48no—
442C22⋊C4—48no—
443C22⋊C4—48no—
444C22⋊C4—44no—
445C22⋊C4—44no—
446C23—22no—
447C23—22no—
448C23—22no—
449C23—22no—
450C23—22no—
451C23—22no—
452C23—22no—
453C23—22no—
454C23—22no—
455C23—22no—
456C23—24no—
457C23—24no—
458C23—24no—
459C23—24no—
460C23—42no—
461C23—42no—
462C23—42no—
463C23—42no—
464C23—42no—
465C23—42no—
466C23—42no—
467C23—42no—
468C23#125×C5914yes—
469C23C22×Q8×C5911yescharacteristic
470C23C2×#41×C5911yescharacteristic
471C23C2×#41×C5911yescharacteristic
472C23C2×#41×C5912yes—
473C23C2×#41×C5912yes—
474C23H(5,𝔽2)×C5911yescharacteristic
475C23H(5,𝔽2)×C5911yescharacteristic
476C23H(5,𝔽2)×C5911yescharacteristic
477C23H(5,𝔽2)×C5912yes—
478C23H(5,𝔽2)×C5912yes—
479C232−1+4×C5911yescharacteristic
480C2×C4—24no—
481C2×C4—24no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—22no—
486C2×C4—22no—
487C2×C4—22no—
488C2×C4—24no—
489C2×C4—24no—
490C2×C4—24no—
491C2×C4—24no—
492C2×C4—416no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—42no—
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—42no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—42no—
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—42no—
531C2×C4—42no—
532C2×C4—42no—
533C22—24no—
534C22—24no—
535C22—24no—
536C22—44no—
537C22—44no—
538C22—44no—
539C22—44no—
540C22—42no—
541C22—42no—
542C22—42no—
543C22—42no—
544C22C2×#125×C5911yescharacteristic
545C22C59×#53311yescharacteristic
546C22C59×#53311yescharacteristic
547C22C59×#53811yescharacteristic
548C22C59×#53812yes—
549C22C59×#53811yescharacteristic
550C22C59×#53911yescharacteristic
551C22C59×#53912yes—
552C22C59×#53911yescharacteristic
553C22C59×#54012yes—
554C22C59×#54212yes—
555C22C59×#54311yescharacteristic
556C22C59×#54311yescharacteristic
557C22C59×#54311yescharacteristic
558C22C59×#54411yescharacteristic
559C22C59×#55112yes—
560C22C59×#55112yes—
561C22C59×#55112yes—
562C22C59×#55312yes—
563C22C59×#55312yes—
564C22C59×#55912yes—
565C22C59×#56012yes—
566C22C59×#56012yes—
567C4—44no—
568C4—44no—
569C4—42no—
570C4—42no—
571C4—82no—
572C4—82no—
573C4—82no—
574C4—82no—
575C2—44no—
576C2C59×#256911yescharacteristic
577C2C59×#256911yescharacteristic
578C2C59×#260711yescharacteristic
579C2C59×#264611yescharacteristic
580C2C59×#266511yescharacteristic
581C2C59×#266711yescharacteristic
582C2C59×#274612yes—
583C2C59×#274912yes—
584C2C59×#279612yes—
585C2C59×#279712yes—
586C2C59×#284211yescharacteristic
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
1. C59×#1445C2semidirect
2. C59×#1445C2semidirect
3. C59×#1443C2semidirect
4. C59×#1441C2semidirect
239. #16902C59direct (N × H)
282. #1445C2×C59semidirect
283. #1445C2×C59semidirect
284. #1443C2×C59semidirect
285. #1441C2×C59semidirect
324. C59#16902direct (N × H)

Maximal subgroups

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

subgroupindex
C59×#14452
C59×#14432
C59×#14412
C59×#14392
C59×C22⋊#952
#1690259