Finite Group Databasebeta

← C59×#13888 #28425997

Subgroups — C59×#13888 #28425997

Order 15104.

1602 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C59×#382C211yesmaximal, characteristic, complemented
2C2×C4×C22⋊C4×C59C211yesmaximal, characteristic
3C2×C4×C22⋊C4×C59C211yesmaximal, characteristic
4C59×#1440C212yesmaximal
5C59×#1439C212yesmaximal
6C59×#1436C212yesmaximal, complemented
7C59×#1434C211yesmaximal, characteristic, complemented
8C59×#1434C211yesmaximal, characteristic, complemented
9C59×#1434C212yesmaximal, complemented
10C59×#1434C211yesmaximal, characteristic, complemented
11C59×C22⋊#95C211yesmaximal, characteristic
12C24×C4×C59C2211yescharacteristic
13C22×C4⋊C4×C59C2212yes—
14C22×C22⋊C4×C59C2212yes—
15C22×C22⋊C4×C59C2211yescharacteristic
16C22×C22⋊C4×C59C2211yescharacteristic
17C22×C22⋊C4×C59C2212yes—
18C22×C42×C59C2212yes—
19C22×C42×C59C2211yescharacteristic
20C22×C42×C59C2211yescharacteristic
21C59×#382—24no—
22C4×C22⋊C4×C59—24no—
23C4×C22⋊C4×C59C418yescomplemented
24C2×#95×C59C2211yescharacteristic
25C2×#95×C59C2211yescharacteristic
26C2×#95×C59C2212yes—
27C2×#95×C59C2211yescharacteristic
28C2×#95×C59C2212yes—
29C2×#95×C59C2212yes—
30C2×#95×C59C2212yes—
31C2×#95×C59C2212yes—
32C2×#95×C59C2212yes—
33C2×#95×C59C2212yes—
34C2×#95×C59C2212yes—
35C2×#95×C59C2211yescharacteristic
36C2×#95×C59C2211yescharacteristic
37C2×#95×C59C2211yescharacteristic
38C25×C59C2311yescharacteristic
39C23×C4×C59—22no—
40C23×C4×C59—24no—
41C23×C4×C59—22no—
42C23×C4×C59—42no—
43C23×C4×C59C2×C414yes—
44C23×C4×C59C2312yes—
45C23×C4×C59C2312yes—
46C23×C4×C59C2311yescharacteristic
47C23×C4×C59C2311yescharacteristic
48C23×C4×C59C2311yescharacteristic
49C23×C4×C59C2312yes—
50C23×C4×C59C2312yes—
51C23×C4×C59C2311yescharacteristic
52C23×C4×C59C2311yescharacteristic
53C23×C4×C59C2311yescharacteristic
54C2×C4⋊C4×C59—24no—
55C2×C4⋊C4×C59—24no—
56C2×C4⋊C4×C59—42no—
57C2×C22⋊C4×C59—24no—
58C2×C22⋊C4×C59—24no—
59C2×C22⋊C4×C59—24no—
60C2×C22⋊C4×C59—24no—
61C2×C22⋊C4×C59—22no—
62C2×C22⋊C4×C59—22no—
63C2×C22⋊C4×C59—24no—
64C2×C22⋊C4×C59—42no—
65C2×C22⋊C4×C59—42no—
66C2×C22⋊C4×C59C2×C414yes—
67C2×C22⋊C4×C59C2×C414yes—
68C2×C42×C59—22no—
69C2×C42×C59—22no—
70C2×C42×C59—24no—
71C2×C42×C59—24no—
72C2×C42×C59—42no—
73C2×C42×C59—42no—
74C2×C42×C59C2×C414yes—
75C2×C42×C59C2×C414yes—
76#95×C59—22no—
77#95×C59—24no—
78#95×C59—22no—
79#95×C59—24no—
80#95×C59—24no—
81#95×C59—24no—
82#95×C59—24no—
83#95×C59—22no—
84#95×C59—42no—
85#95×C59—42no—
86#95×C59—42no—
87#95×C59C2×C414yes—
88#95×C59C2×C414yes—
89#95×C59D414yes—
90C24×C59—21no—
91C24×C59—21no—
92C24×C59—21no—
93C24×C59—22no—
94C24×C59—22no—
95C24×C59—21no—
96C24×C59—21no—
97C24×C59—22no—
98C24×C59—21no—
99C24×C59C22×C412yes—
100C24×C59#4114yes—
101C24×C59C2411yescharacteristic
102C22×C4×C59—21no—
103C22×C4×C59—21no—
104C22×C4×C59—21no—
105C22×C4×C59—22no—
106C22×C4×C59—21no—
107C22×C4×C59—22no—
108C22×C4×C59—22no—
109C22×C4×C59—21no—
110C22×C4×C59—21no—
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—21no—
122C22×C4×C59—21no—
123C22×C4×C59—22no—
124C22×C4×C59—22no—
125C22×C4×C59—22no—
126C22×C4×C59—22no—
127C22×C4×C59—21no—
128C22×C4×C59—22no—
129C22×C4×C59—22no—
130C22×C4×C59—22no—
131C22×C4×C59—22no—
132C22×C4×C59—22no—
133C22×C4×C59—21no—
134C22×C4×C59—22no—
135C22×C4×C59—28no—
136C22×C4×C59—28no—
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—22no—
145C22×C4×C59—22no—
146C22×C4×C59—22no—
147C22×C4×C59—22no—
148C22×C4×C59—22no—
149C22×C4×C59—22no—
150C22×C4×C59—22no—
151C22×C4×C59—44no—
152C22×C4×C59—48no—
153C22×C4×C59—48no—
154C22×C4×C59C22×C412yes—
155C22×C4×C59C22×C412yes—
156C22×C4×C59C22×C412yes—
157C22×C4×C59C22×C412yes—
158C22×C4×C59C22×C412yes—
159C22×C4×C59C22×C412yes—
160C22×C4×C59C2×D414yes—
161C22×C4×C59C2×D412yes—
162C22×C4×C59#4114yes—
163C22×C4×C59#4112yes—
164C22×C4×C59#4114yes—
165C22×C4×C59#4112yes—
166C22×C4×C59#4112yes—
167C4⋊C4×C59—48no—
168C22⋊C4×C59—216no—
169C22⋊C4×C59—28no—
170C22⋊C4×C59—28no—
171C22⋊C4×C59—48no—
172C42×C59—28no—
173C42×C59—44no—
174C42×C59—48no—
175C23×C59—22no—
176C23×C59—22no—
177C23×C59—22no—
178C23×C59—22no—
179C23×C59—22no—
180C23×C59—22no—
181C23×C59—24no—
182C23×C59—24no—
183C23×C59—24no—
184C23×C59—24no—
185C23×C59—24no—
186C23×C59—24no—
187C23×C59—42no—
188C23×C59—41no—
189C23×C59—41no—
190C23×C59—42no—
191C23×C59—42no—
192C23×C59—41no—
193C23×C59—41no—
194C23×C59—42no—
195C23×C59—42no—
196C23×C59—42no—
197C23×C59#11714yes—
198C23×C59C23×C411yescharacteristic
199C23×C59C22×D411yescharacteristic
200C23×C59C2×#4112yes—
201C23×C59C2×#4112yes—
202C23×C59C2×#4111yescharacteristic
203C23×C59C2×#4111yescharacteristic
204C23×C59C2×#4111yescharacteristic
205C23×C59C2×#4112yes—
206C23×C59H(5,𝔽2)12yes—
207C23×C59H(5,𝔽2)11yescharacteristic
208C23×C592−1+411yescharacteristic
209C2×C4×C59—22no—
210C2×C4×C59—22no—
211C2×C4×C59—22no—
212C2×C4×C59—22no—
213C2×C4×C59—22no—
214C2×C4×C59—22no—
215C2×C4×C59—24no—
216C2×C4×C59—22no—
217C2×C4×C59—24no—
218C2×C4×C59—22no—
219C2×C4×C59—24no—
220C2×C4×C59—24no—
221C2×C4×C59—22no—
222C2×C4×C59—22no—
223C2×C4×C59—22no—
224C2×C4×C59—22no—
225C2×C4×C59—22no—
226C2×C4×C59—22no—
227C2×C4×C59—22no—
228C2×C4×C59—22no—
229C2×C4×C59—22no—
230C2×C4×C59—22no—
231C2×C4×C59—22no—
232C2×C4×C59—24no—
233C2×C4×C59—24no—
234C2×C4×C59—24no—
235C2×C4×C59—24no—
236C2×C4×C59—24no—
237C2×C4×C59—24no—
238C2×C4×C59—416no—
239C2×C4×C59—42no—
240C2×C4×C59—42no—
241C2×C4×C59—42no—
242C2×C4×C59—42no—
243C2×C4×C59—42no—
244C2×C4×C59—42no—
245C2×C4×C59—42no—
246C2×C4×C59—42no—
247C2×C4×C59—42no—
248C2×C4×C59—42no—
249C2×C4×C59—42no—
250C2×C4×C59—42no—
251C2×C4×C59—42no—
252C2×C4×C59—42no—
253C2×C4×C59—42no—
254C2×C4×C59—42no—
255C2×C4×C59—42no—
256C2×C4×C59—42no—
257C2×C4×C59—42no—
258C2×C4×C59—42no—
259C2×C4×C59—42no—
260C2×C4×C59—42no—
261C2×C4×C59—42no—
262C2×C4×C59—42no—
263C2×C4×C59—42no—
264C2×C4×C59—42no—
265C2×C4×C59—42no—
266C2×C4×C59—42no—
267C2×C4×C59#11714yes—
268C2×C4×C59#11714yes—
269C2×C4×C59C4×D414yes—
270#13888C5911yesmaximal, characteristic, direct product factor, Sylow
271C22×C59—24no—
272C22×C59—24no—
273C22×C59—24no—
274C22×C59—42no—
275C22×C59—42no—
276C22×C59—42no—
277C22×C59—42no—
278C22×C59—44no—
279C22×C59—44no—
280C22×C59—44no—
281C22×C59—44no—
282C22×C59C2×#11711yescharacteristic
283C22×C59C2×#11711yescharacteristic
284C22×C59C2×#11711yescharacteristic
285C22×C59C2×C4×D411yescharacteristic
286C22×C59C4×#4111yescharacteristic
287C22×C59#51811yescharacteristic
288C22×C59#52011yescharacteristic
289C22×C59#52512yes—
290C22×C59#52912yes—
291C22×C59#52912yes—
292C22×C59#52912yes—
293C22×C59#53812yes—
294C22×C59#53912yes—
295C22×C59#54612yes—
296C22×C59#54611yescharacteristic
297C22×C59#54811yescharacteristic
298C22×C59#55112yes—
299C22×C59#55212yes—
300C22×C59#55211yescharacteristic
301C22×C59#55311yescharacteristic
302C22×C59#55312yes—
303C22×C59#55512yes—
304C22×C59#55912yes—
305C4×C59—24no—
306C4×C59—24no—
307C4×C59—24no—
308C4×C59—42no—
309C4×C59—42no—
310C4×C59—44no—
311C4×C59—44no—
312C4×C59—42no—
313C4×C59—82no—
314C4×C59—82no—
315C2×#382C2×C5911yescharacteristic, complemented
316C2×C4×C22⋊C4C2×C5911yescharacteristic
317C2×C4×C22⋊C4C2×C5911yescharacteristic
318#1440C2×C5912yes—
319#1439C2×C5912yes—
320#1436C2×C5912yescomplemented
321#1434C2×C5911yescharacteristic, complemented
322#1434C2×C5911yescharacteristic, complemented
323#1434C2×C5912yescomplemented
324#1434C2×C5911yescharacteristic, complemented
325C22⋊#95C2×C5911yescharacteristic
326C2×C59—44no—
327C2×C59#228311yescharacteristic
328C2×C59#229011yescharacteristic
329C2×C59#231811yescharacteristic
330C2×C59#234211yescharacteristic
331C2×C59#234611yescharacteristic
332C2×C59#235211yescharacteristic
333C2×C59#235711yescharacteristic
334C2×C59#245912yes—
335C2×C59#246012yes—
336C2×C59#251712yes—
337C2×C59#251812yes—
338C24×C4C22×C5911yescharacteristic
339C22×C4⋊C4C22×C5912yes—
340C22×C22⋊C4C22×C5912yes—
341C22×C22⋊C4C22×C5911yescharacteristic
342C22×C22⋊C4C22×C5911yescharacteristic
343C22×C22⋊C4C22×C5912yes—
344C22×C42C22×C5912yes—
345C22×C42C22×C5911yescharacteristic
346C22×C42C22×C5911yescharacteristic
347#382—24no—
348C4×C22⋊C4—24no—
349C4×C22⋊C4C4×C5918yescomplemented
350C2×#95C22×C5911yescharacteristic
351C2×#95C22×C5912yes—
352C2×#95C22×C5911yescharacteristic
353C2×#95C22×C5912yes—
354C2×#95C22×C5912yes—
355C2×#95C22×C5911yescharacteristic
356C2×#95C22×C5912yes—
357C2×#95C22×C5912yes—
358C2×#95C22×C5912yes—
359C2×#95C22×C5912yes—
360C2×#95C22×C5912yes—
361C2×#95C22×C5911yescharacteristic
362C2×#95C22×C5911yescharacteristic
363C2×#95C22×C5911yescharacteristic
364C59#1388811yescharacteristic, direct product factor, Sylow
365C25C23×C5911yescharacteristic
366C23×C4—22no—
367C23×C4—24no—
368C23×C4—22no—
369C23×C4—42no—
370C23×C4C2×C4×C5914yes—
371C23×C4C23×C5912yes—
372C23×C4C23×C5912yes—
373C23×C4C23×C5911yescharacteristic
374C23×C4C23×C5911yescharacteristic
375C23×C4C23×C5911yescharacteristic
376C23×C4C23×C5912yes—
377C23×C4C23×C5912yes—
378C23×C4C23×C5911yescharacteristic
379C23×C4C23×C5911yescharacteristic
380C23×C4C23×C5911yescharacteristic
381C2×C4⋊C4—24no—
382C2×C4⋊C4—24no—
383C2×C4⋊C4—42no—
384C2×C22⋊C4—24no—
385C2×C22⋊C4—24no—
386C2×C22⋊C4—24no—
387C2×C22⋊C4—24no—
388C2×C22⋊C4—22no—
389C2×C22⋊C4—22no—
390C2×C22⋊C4—24no—
391C2×C22⋊C4—42no—
392C2×C22⋊C4—42no—
393C2×C22⋊C4C2×C4×C5914yes—
394C2×C22⋊C4C2×C4×C5914yes—
395C2×C42—22no—
396C2×C42—22no—
397C2×C42—24no—
398C2×C42—24no—
399C2×C42—42no—
400C2×C42—42no—
401C2×C42C2×C4×C5914yes—
402C2×C42C2×C4×C5914yes—
403#95—22no—
404#95—24no—
405#95—22no—
406#95—24no—
407#95—24no—
408#95—24no—
409#95—24no—
410#95—22no—
411#95—42no—
412#95—42no—
413#95—42no—
414#95C2×C4×C5914yes—
415#95C2×C4×C5914yes—
416#95D4×C5914yes—
417C24—21no—
418C24—21no—
419C24—21no—
420C24—22no—
421C24—22no—
422C24—21no—
423C24—21no—
424C24—22no—
425C24—21no—
426C24C22×C4×C5912yes—
427C24#41×C5914yes—
428C24C24×C5911yescharacteristic
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—22no—
433C22×C4—21no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—21no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—21no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—21no—
461C22×C4—22no—
462C22×C4—28no—
463C22×C4—28no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—44no—
479C22×C4—48no—
480C22×C4—48no—
481C22×C4C22×C4×C5912yes—
482C22×C4C22×C4×C5912yes—
483C22×C4C22×C4×C5912yes—
484C22×C4C22×C4×C5912yes—
485C22×C4C22×C4×C5912yes—
486C22×C4C22×C4×C5912yes—
487C22×C4C2×D4×C5914yes—
488C22×C4C2×D4×C5912yes—
489C22×C4#41×C5914yes—
490C22×C4#41×C5912yes—
491C22×C4#41×C5914yes—
492C22×C4#41×C5912yes—
493C22×C4#41×C5912yes—
494C4⋊C4—48no—
495C22⋊C4—216no—
496C22⋊C4—28no—
497C22⋊C4—28no—
498C22⋊C4—48no—
499C42—28no—
500C42—44no—
501C42—48no—
502C23—22no—
503C23—22no—
504C23—22no—
505C23—22no—
506C23—22no—
507C23—22no—
508C23—24no—
509C23—24no—
510C23—24no—
511C23—24no—
512C23—24no—
513C23—24no—
514C23—42no—
515C23—41no—
516C23—41no—
517C23—42no—
518C23—41no—
519C23—42no—
520C23—41no—
521C23—42no—
522C23—42no—
523C23—42no—
524C23#117×C5914yes—
525C23C23×C4×C5911yescharacteristic
526C23C22×D4×C5911yescharacteristic
527C23C2×#41×C5912yes—
528C23C2×#41×C5912yes—
529C23C2×#41×C5911yescharacteristic
530C23C2×#41×C5911yescharacteristic
531C23C2×#41×C5911yescharacteristic
532C23C2×#41×C5912yes—
533C23H(5,𝔽2)×C5912yes—
534C23H(5,𝔽2)×C5911yescharacteristic
535C232−1+4×C5911yescharacteristic
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—24no—
543C2×C4—22no—
544C2×C4—24no—
545C2×C4—22no—
546C2×C4—24no—
547C2×C4—24no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—24no—
560C2×C4—24no—
561C2×C4—24no—
562C2×C4—24no—
563C2×C4—24no—
564C2×C4—24no—
565C2×C4—416no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—42no—
580C2×C4—42no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4—42no—
594C2×C4#117×C5914yes—
595C2×C4#117×C5914yes—
596C2×C4C4×D4×C5914yes—
597C22—24no—
598C22—24no—
599C22—24no—
600C22—44no—
601C22—44no—
602C22—42no—
603C22—42no—
604C22—42no—
605C22—42no—
606C22—44no—
607C22—44no—
608C22C2×#117×C5911yescharacteristic
609C22C2×#117×C5911yescharacteristic
610C22C2×#117×C5911yescharacteristic
611C22C2×C4×D4×C5911yescharacteristic
612C22C4×#41×C5911yescharacteristic
613C22C59×#51811yescharacteristic
614C22C59×#52011yescharacteristic
615C22C59×#52512yes—
616C22C59×#52912yes—
617C22C59×#52912yes—
618C22C59×#52912yes—
619C22C59×#53812yes—
620C22C59×#53912yes—
621C22C59×#54612yes—
622C22C59×#54611yescharacteristic
623C22C59×#54811yescharacteristic
624C22C59×#55112yes—
625C22C59×#55211yescharacteristic
626C22C59×#55212yes—
627C22C59×#55311yescharacteristic
628C22C59×#55312yes—
629C22C59×#55512yes—
630C22C59×#55912yes—
631C4—24no—
632C4—24no—
633C4—24no—
634C4—42no—
635C4—42no—
636C4—42no—
637C4—44no—
638C4—44no—
639C4—82no—
640C4—82no—
641C2—44no—
642C2C59×#228311yescharacteristic
643C2C59×#229011yescharacteristic
644C2C59×#231811yescharacteristic
645C2C59×#234211yescharacteristic
646C2C59×#234611yescharacteristic
647C2C59×#235211yescharacteristic
648C2C59×#235711yescharacteristic
649C2C59×#245912yes—
650C2C59×#246012yes—
651C2C59×#251712yes—
652C2C59×#251812yes—
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
1. C2×C59×#382C2semidirect
6. C59×#1436C2semidirect
7. C59×#1434C2semidirect
8. C59×#1434C2semidirect
9. C59×#1434C2semidirect
10. C59×#1434C2semidirect
23. C4×C22⋊C4×C59C4semidirect
270. #13888C59direct (N × H)
315. C2×#382C2×C59semidirect
320. #1436C2×C59semidirect
321. #1434C2×C59semidirect
322. #1434C2×C59semidirect
323. #1434C2×C59semidirect
324. #1434C2×C59semidirect
349. C4×C22⋊C4C4×C59semidirect
364. C59#13888direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C59×#3822
C2×C4×C22⋊C4×C592
C59×#14402
C59×#14392
C59×#14362
C59×#14342
C59×C22⋊#952
#1388859