Finite Group Databasebeta

← C59×#14543 #28426652

Subgroups — C59×#14543 #28426652

Order 15104.

1490 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C59×#399C211yesmaximal, characteristic
2C2×C59×#388C212yesmaximal
3C2×C59×#387C212yesmaximal, complemented
4C59×#1441C212yesmaximal, complemented
5C59×#1440C211yesmaximal, characteristic
6C59×#1439C212yesmaximal
7C59×#1437C211yesmaximal, characteristic
8C59×#1436C212yesmaximal, complemented
9C59×C4⋊#95C212yesmaximal, complemented
10C22×C4⋊C4×C59C2212yes—
11C22×C4⋊C4×C59C2212yes—
12C22×C4⋊C4×C59C2212yes—
13C22×C4⋊C4×C59C2211yescharacteristic
14C22×C22⋊C4×C59C2211yescharacteristic
15C22×C22⋊C4×C59C2212yes—
16C22×C22⋊C4×C59C2212yes—
17C22×C22⋊C4×C59C2211yescharacteristic
18C22×C22⋊C4×C59C2211yescharacteristic
19C22×C42×C59C2211yescharacteristic
20C22×C42×C59C2212yes—
21C59×#399C418yescomplemented
22C59×#388—28no—
23C59×#387—28no—
24C2×#95×C59C2212yes—
25C2×#95×C59C2212yes—
26C2×#95×C59C2212yes—
27C2×#95×C59C2212yes—
28C2×#95×C59C2211yescharacteristic
29C2×#95×C59C2212yes—
30C2×#95×C59C2212yes—
31C2×#95×C59C2212yes—
32C2×#95×C59C2211yescharacteristic
33C2×#95×C59C2212yes—
34C25×C59C2311yescharacteristic
35C23×C4×C59C2312yes—
36C23×C4×C59C2311yescharacteristic
37C23×C4×C59C2311yescharacteristic
38C23×C4×C59C2312yes—
39C23×C4×C59C2312yes—
40C23×C4×C59C2312yes—
41C23×C4×C59C2312yes—
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—24no—
48C2×C4⋊C4×C59—24no—
49C2×C4⋊C4×C59—41no—
50C2×C4⋊C4×C59—41no—
51C2×C4⋊C4×C59—42no—
52C2×C4⋊C4×C59—42no—
53C2×C4⋊C4×C59C2×C418yes—
54C2×C4⋊C4×C59C2×C414yes—
55C2×C22⋊C4×C59—24no—
56C2×C22⋊C4×C59—24no—
57C2×C22⋊C4×C59—24no—
58C2×C22⋊C4×C59—24no—
59C2×C22⋊C4×C59—24no—
60C2×C22⋊C4×C59—41no—
61C2×C22⋊C4×C59—41no—
62C2×C22⋊C4×C59—42no—
63C2×C22⋊C4×C59—41no—
64C2×C22⋊C4×C59—41no—
65C2×C22⋊C4×C59—42no—
66C2×C22⋊C4×C59C2×C418yes—
67C2×C22⋊C4×C59C2×C414yes—
68C2×C42×C59—24no—
69C2×C42×C59—24no—
70C2×C42×C59—24no—
71C2×C42×C59—42no—
72C2×C42×C59—41no—
73#95×C59—24no—
74#95×C59—24no—
75#95×C59—24no—
76#95×C59—24no—
77#95×C59—41no—
78#95×C59—42no—
79#95×C59—42no—
80#95×C59—42no—
81#95×C59C2×C414yes—
82#95×C59D418yes—
83C24×C59—22no—
84C24×C59—22no—
85C24×C59—22no—
86C24×C59—21no—
87C24×C59—21no—
88C24×C59—22no—
89C24×C59—22no—
90C24×C59—22no—
91C24×C59C22×C412yes—
92C24×C59C2411yescharacteristic
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—22no—
102C22×C4×C59—22no—
103C22×C4×C59—22no—
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—21no—
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—21no—
120C22×C4×C59—21no—
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×C59C22×C412yes—
137C22×C4×C59C22×C414yes—
138C22×C4×C59C22×C412yes—
139C22×C4×C59C22×C414yes—
140C22×C4×C59C2×D414yes—
141C22×C4×C59C2×D414yes—
142C22×C4×C59C2×D414yes—
143C22×C4×C59#4114yes—
144C22×C4×C59#4114yes—
145C4⋊C4×C59—216no—
146C4⋊C4×C59—44no—
147C4⋊C4×C59—48no—
148C4⋊C4×C59—48no—
149C22⋊C4×C59—216no—
150C22⋊C4×C59—44no—
151C22⋊C4×C59—44no—
152C22⋊C4×C59—48no—
153C22⋊C4×C59—44no—
154C42×C59—48no—
155C42×C59—44no—
156C23×C59—24no—
157C23×C59—22no—
158C23×C59—22no—
159C23×C59—22no—
160C23×C59—24no—
161C23×C59—42no—
162C23×C59—42no—
163C23×C59—42no—
164C23×C59—42no—
165C23×C59—42no—
166C23×C59—42no—
167C23×C59—41no—
168C23×C59—42no—
169C23×C59—42no—
170C23×C59—42no—
171C23×C59—42no—
172C23×C59—42no—
173C23×C59—41no—
174C23×C59—41no—
175C23×C59—42no—
176C23×C59—41no—
177C23×C59C23×C411yescharacteristic
178C23×C59C22×D412yes—
179C23×C59C2×#4112yes—
180C23×C59C2×#4112yes—
181C23×C59H(5,𝔽2)11yescharacteristic
182C23×C59H(5,𝔽2)11yescharacteristic
183C23×C59H(5,𝔽2)12yes—
184C23×C592−1+412yes—
185C23×C592−1+412yes—
186C2×C4×C59—24no—
187C2×C4×C59—24no—
188C2×C4×C59—24no—
189C2×C4×C59—24no—
190C2×C4×C59—24no—
191C2×C4×C59—24no—
192C2×C4×C59—24no—
193C2×C4×C59—24no—
194C2×C4×C59—24no—
195C2×C4×C59—22no—
196C2×C4×C59—22no—
197C2×C4×C59—24no—
198C2×C4×C59—24no—
199C2×C4×C59—24no—
200C2×C4×C59—24no—
201C2×C4×C59—24no—
202C2×C4×C59—24no—
203C2×C4×C59—24no—
204C2×C4×C59—24no—
205C2×C4×C59—24no—
206C2×C4×C59—24no—
207C2×C4×C59—24no—
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—41no—
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—41no—
224C2×C4×C59—41no—
225C2×C4×C59—42no—
226C2×C4×C59—42no—
227C2×C4×C59—42no—
228C2×C4×C59—42no—
229C2×C4×C59—41no—
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×C59C4×D418yes—
238#14543C5911yesmaximal, characteristic, direct product factor, Sylow
239C22×C59—44no—
240C22×C59—42no—
241C22×C59—44no—
242C22×C59—42no—
243C22×C59—42no—
244C22×C59—82no—
245C22×C59—82no—
246C22×C59—82no—
247C22×C59—82no—
248C22×C59C2×C4×D412yes—
249C22×C59C4×#4111yescharacteristic
250C22×C59#51811yescharacteristic
251C22×C59#51911yescharacteristic
252C22×C59#52012yes—
253C22×C59#53612yes—
254C22×C59#53712yes—
255C22×C59#53912yes—
256C22×C59#54112yes—
257C22×C59#54212yes—
258C22×C59#54212yes—
259C22×C59D4211yescharacteristic
260C22×C59#54612yes—
261C22×C59#54712yes—
262C22×C59#55012yes—
263C22×C59#55112yes—
264C22×C59#55212yes—
265C22×C59#55911yescharacteristic
266C22×C59#56011yescharacteristic
267C22×C59#56212yes—
268C22×C59#56311yescharacteristic
269C4×C59—28no—
270C4×C59—44no—
271C4×C59—42no—
272C4×C59—42no—
273C4×C59—44no—
274C4×C59—44no—
275C4×C59—44no—
276C4×C59—82no—
277C2×#399C2×C5911yescharacteristic
278C2×#388C2×C5912yes—
279C2×#387C2×C5912yescomplemented
280#1441C2×C5912yescomplemented
281#1440C2×C5911yescharacteristic
282#1439C2×C5912yes—
283#1437C2×C5911yescharacteristic
284#1436C2×C5912yescomplemented
285C4⋊#95C2×C5912yescomplemented
286C2×C59—82no—
287C2×C59#232312yes—
288C2×C59#233211yescharacteristic
289C2×C59#235912yes—
290C2×C59#236611yescharacteristic
291C2×C59#237611yescharacteristic
292C2×C59#267212yes—
293C2×C59#270512yes—
294C2×C59#272112yes—
295C2×C59#275412yes—
296C22×C4⋊C4C22×C5912yes—
297C22×C4⋊C4C22×C5912yes—
298C22×C4⋊C4C22×C5912yes—
299C22×C4⋊C4C22×C5911yescharacteristic
300C22×C22⋊C4C22×C5912yes—
301C22×C22⋊C4C22×C5911yescharacteristic
302C22×C22⋊C4C22×C5912yes—
303C22×C22⋊C4C22×C5911yescharacteristic
304C22×C22⋊C4C22×C5911yescharacteristic
305C22×C42C22×C5912yes—
306C22×C42C22×C5911yescharacteristic
307#399C4×C5918yescomplemented
308#388—28no—
309#387—28no—
310C2×#95C22×C5912yes—
311C2×#95C22×C5912yes—
312C2×#95C22×C5912yes—
313C2×#95C22×C5912yes—
314C2×#95C22×C5911yescharacteristic
315C2×#95C22×C5912yes—
316C2×#95C22×C5912yes—
317C2×#95C22×C5912yes—
318C2×#95C22×C5911yescharacteristic
319C2×#95C22×C5912yes—
320C59#1454311yescharacteristic, direct product factor, Sylow
321C25C23×C5911yescharacteristic
322C23×C4C23×C5912yes—
323C23×C4C23×C5912yes—
324C23×C4C23×C5911yescharacteristic
325C23×C4C23×C5911yescharacteristic
326C23×C4C23×C5912yes—
327C23×C4C23×C5912yes—
328C23×C4C23×C5912yes—
329C23×C4C23×C5912yes—
330C2×C4⋊C4—24no—
331C2×C4⋊C4—24no—
332C2×C4⋊C4—24no—
333C2×C4⋊C4—24no—
334C2×C4⋊C4—24no—
335C2×C4⋊C4—24no—
336C2×C4⋊C4—41no—
337C2×C4⋊C4—41no—
338C2×C4⋊C4—42no—
339C2×C4⋊C4—42no—
340C2×C4⋊C4C2×C4×C5918yes—
341C2×C4⋊C4C2×C4×C5914yes—
342C2×C22⋊C4—24no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—24no—
345C2×C22⋊C4—24no—
346C2×C22⋊C4—24no—
347C2×C22⋊C4—41no—
348C2×C22⋊C4—41no—
349C2×C22⋊C4—42no—
350C2×C22⋊C4—41no—
351C2×C22⋊C4—41no—
352C2×C22⋊C4—42no—
353C2×C22⋊C4C2×C4×C5918yes—
354C2×C22⋊C4C2×C4×C5914yes—
355C2×C42—24no—
356C2×C42—24no—
357C2×C42—24no—
358C2×C42—42no—
359C2×C42—41no—
360#95—24no—
361#95—24no—
362#95—24no—
363#95—24no—
364#95—41no—
365#95—42no—
366#95—42no—
367#95—42no—
368#95C2×C4×C5914yes—
369#95D4×C5918yes—
370C24—22no—
371C24—22no—
372C24—22no—
373C24—21no—
374C24—21no—
375C24—22no—
376C24—22no—
377C24—22no—
378C24C22×C4×C5912yes—
379C24C24×C5911yescharacteristic
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×C4—22no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—21no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—21no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—21no—
407C22×C4—21no—
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×C4C22×C4×C5912yes—
424C22×C4C22×C4×C5914yes—
425C22×C4C22×C4×C5912yes—
426C22×C4C22×C4×C5914yes—
427C22×C4C2×D4×C5914yes—
428C22×C4C2×D4×C5914yes—
429C22×C4C2×D4×C5914yes—
430C22×C4#41×C5914yes—
431C22×C4#41×C5914yes—
432C4⋊C4—216no—
433C4⋊C4—44no—
434C4⋊C4—48no—
435C4⋊C4—48no—
436C22⋊C4—216no—
437C22⋊C4—44no—
438C22⋊C4—44no—
439C22⋊C4—48no—
440C22⋊C4—44no—
441C42—48no—
442C42—44no—
443C23—24no—
444C23—22no—
445C23—22no—
446C23—22no—
447C23—24no—
448C23—42no—
449C23—42no—
450C23—42no—
451C23—42no—
452C23—42no—
453C23—42no—
454C23—41no—
455C23—42no—
456C23—42no—
457C23—42no—
458C23—42no—
459C23—42no—
460C23—41no—
461C23—41no—
462C23—42no—
463C23—41no—
464C23C23×C4×C5911yescharacteristic
465C23C22×D4×C5912yes—
466C23C2×#41×C5912yes—
467C23C2×#41×C5912yes—
468C23H(5,𝔽2)×C5911yescharacteristic
469C23H(5,𝔽2)×C5911yescharacteristic
470C23H(5,𝔽2)×C5912yes—
471C232−1+4×C5912yes—
472C232−1+4×C5912yes—
473C2×C4—24no—
474C2×C4—24no—
475C2×C4—24no—
476C2×C4—24no—
477C2×C4—24no—
478C2×C4—24no—
479C2×C4—24no—
480C2×C4—24no—
481C2×C4—24no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—24no—
485C2×C4—24no—
486C2×C4—24no—
487C2×C4—24no—
488C2×C4—24no—
489C2×C4—24no—
490C2×C4—24no—
491C2×C4—24no—
492C2×C4—24no—
493C2×C4—24no—
494C2×C4—24no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—41no—
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—41no—
511C2×C4—41no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—41no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4C4×D4×C5918yes—
525C22—44no—
526C22—42no—
527C22—44no—
528C22—42no—
529C22—42no—
530C22—82no—
531C22—82no—
532C22—82no—
533C22—82no—
534C22C2×C4×D4×C5912yes—
535C22C4×#41×C5911yescharacteristic
536C22C59×#51811yescharacteristic
537C22C59×#51911yescharacteristic
538C22C59×#52012yes—
539C22C59×#53612yes—
540C22C59×#53712yes—
541C22C59×#53912yes—
542C22C59×#54112yes—
543C22C59×#54212yes—
544C22C59×#54212yes—
545C22D42×C5911yescharacteristic
546C22C59×#54612yes—
547C22C59×#54712yes—
548C22C59×#55012yes—
549C22C59×#55112yes—
550C22C59×#55212yes—
551C22C59×#55911yescharacteristic
552C22C59×#56011yescharacteristic
553C22C59×#56212yes—
554C22C59×#56311yescharacteristic
555C4—28no—
556C4—44no—
557C4—42no—
558C4—42no—
559C4—44no—
560C4—44no—
561C4—44no—
562C4—82no—
563C2—82no—
564C2C59×#232312yes—
565C2C59×#233211yescharacteristic
566C2C59×#235912yes—
567C2C59×#236611yescharacteristic
568C2C59×#237611yescharacteristic
569C2C59×#267212yes—
570C2C59×#270512yes—
571C2C59×#272112yes—
572C2C59×#275412yes—
subgroupG/H
center, socleC24×C59C24
commutatorC23C23×C4×C59
Frattini, cosocleC24C24×C59
prime radicalC25×C59C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C59 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C59×#387C2semidirect
4. C59×#1441C2semidirect
8. C59×#1436C2semidirect
9. C59×C4⋊#95C2semidirect
21. C59×#399C4semidirect
238. #14543C59direct (N × H)
279. C2×#387C2×C59semidirect
280. #1441C2×C59semidirect
284. #1436C2×C59semidirect
285. C4⋊#95C2×C59semidirect
307. #399C4×C59semidirect
320. C59#14543direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C59×#3992
C2×C59×#3882
C2×C59×#3872
C59×#14412
C59×#14402
C59×#14392
C59×#14372
C59×#14362
C59×C4⋊#952
#1454359