Finite Group Databasebeta

← C59×#14506 #28426615

Subgroups — C59×#14506 #28426615

Order 15104.

1962 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#123×C59C211yesmaximal, characteristic
2C2×C59×#388C212yesmaximal, complemented
3C59×#1445C212yesmaximal, complemented
4C59×#1439C212yesmaximal, complemented
5C59×#1438C211yesmaximal, characteristic
6C59×#1438C211yesmaximal, characteristic
7C59×#1437C212yesmaximal, complemented
8C59×C4⋊#95C212yesmaximal, complemented
9C59×C22⋊#95C212yesmaximal, complemented
10C23×D4×C59C2211yescharacteristic
11C24×C4×C59C2211yescharacteristic
12C2×#123×C59—28no—
13C2×#123×C59C418yescomplemented
14C22×C4⋊C4×C59C2212yes—
15C22×C4⋊C4×C59C2212yes—
16C22×C22⋊C4×C59C2212yes—
17C22×C22⋊C4×C59C2212yes—
18C22×C22⋊C4×C59C2211yescharacteristic
19C22×C22⋊C4×C59C2212yes—
20C22×C22⋊C4×C59C2212yes—
21C22×C22⋊C4×C59C2211yescharacteristic
22C22×C22⋊C4×C59C2211yescharacteristic
23C22×C42×C59C2212yes—
24C59×#388—28no—
25C2×#95×C59C2212yes—
26C2×#95×C59C2212yes—
27C2×#95×C59C2212yes—
28C2×#95×C59C2212yes—
29C2×#95×C59C2212yes—
30C2×#95×C59C2212yes—
31C2×#95×C59C2211yescharacteristic
32C2×#95×C59C2212yes—
33C2×#95×C59C2211yescharacteristic
34C25×C59C2311yescharacteristic
35C25×C59C2311yescharacteristic
36C22×D4×C59—24no—
37C22×D4×C59—42no—
38C22×D4×C59—41no—
39C22×D4×C59—41no—
40C22×D4×C59C2×C414yes—
41C23×C4×C59—24no—
42C23×C4×C59—42no—
43C23×C4×C59—41no—
44C23×C4×C59—41no—
45C23×C4×C59C2×C414yes—
46C23×C4×C59C2312yes—
47C23×C4×C59C2312yes—
48C23×C4×C59C2312yes—
49C23×C4×C59C2311yescharacteristic
50C23×C4×C59C2312yes—
51C23×C4×C59C2312yes—
52C23×C4×C59C2312yes—
53#123×C59—232no—
54C2×C4⋊C4×C59—24no—
55C2×C4⋊C4×C59—24no—
56C2×C4⋊C4×C59—24no—
57C2×C4⋊C4×C59—24no—
58C2×C4⋊C4×C59—42no—
59C2×C4⋊C4×C59C2×C418yes—
60C2×C22⋊C4×C59—24no—
61C2×C22⋊C4×C59—24no—
62C2×C22⋊C4×C59—24no—
63C2×C22⋊C4×C59—24no—
64C2×C22⋊C4×C59—24no—
65C2×C22⋊C4×C59—24no—
66C2×C22⋊C4×C59—24no—
67C2×C22⋊C4×C59—24no—
68C2×C22⋊C4×C59—41no—
69C2×C22⋊C4×C59—42no—
70C2×C22⋊C4×C59—42no—
71C2×C22⋊C4×C59—42no—
72C2×C22⋊C4×C59—42no—
73C2×C22⋊C4×C59—41no—
74C2×C22⋊C4×C59—42no—
75C2×C22⋊C4×C59C2×C418yes—
76C2×C22⋊C4×C59C2×C414yes—
77C2×C22⋊C4×C59D418yes—
78C2×C42×C59—24no—
79C2×C42×C59—24no—
80C2×C42×C59—42no—
81#95×C59—24no—
82#95×C59—24no—
83#95×C59—41no—
84#95×C59—42no—
85#95×C59—42no—
86#95×C59—42no—
87#95×C59—42no—
88#95×C59—42no—
89#95×C59—41no—
90C24×C59—22no—
91C24×C59—22no—
92C24×C59—22no—
93C24×C59—22no—
94C24×C59—21no—
95C24×C59—21no—
96C24×C59—22no—
97C24×C59—22no—
98C24×C59—22no—
99C24×C59—22no—
100C24×C59—22no—
101C24×C59—22no—
102C24×C59—21no—
103C24×C59—21no—
104C24×C59—22no—
105C24×C59C22×C412yes—
106C24×C59C22×C412yes—
107C24×C59C2×D414yes—
108C24×C59C2411yescharacteristic
109C2×D4×C59—28no—
110C2×D4×C59—44no—
111C2×D4×C59—44no—
112C2×D4×C59—48no—
113C2×D4×C59—48no—
114C22×C4×C59—22no—
115C22×C4×C59—22no—
116C22×C4×C59—22no—
117C22×C4×C59—22no—
118C22×C4×C59—28no—
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—21no—
136C22×C4×C59—21no—
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—22no—
152C22×C4×C59—22no—
153C22×C4×C59—22no—
154C22×C4×C59—22no—
155C22×C4×C59—44no—
156C22×C4×C59—44no—
157C22×C4×C59—48no—
158C22×C4×C59—48no—
159C22×C4×C59C22×C414yes—
160C22×C4×C59C22×C412yes—
161C22×C4×C59C22×C414yes—
162C22×C4×C59C2×D414yes—
163C22×C4×C59C2×D414yes—
164C22×C4×C59#4114yes—
165C22×C4×C59#4114yes—
166C4⋊C4×C59—216no—
167C4⋊C4×C59—48no—
168C22⋊C4×C59—216no—
169C22⋊C4×C59—44no—
170C22⋊C4×C59—48no—
171C22⋊C4×C59—48no—
172C22⋊C4×C59—48no—
173C22⋊C4×C59—44no—
174C22⋊C4×C59C22⋊C4116yescomplemented
175C42×C59—48no—
176C23×C59—24no—
177C23×C59—22no—
178C23×C59—22no—
179C23×C59—24no—
180C23×C59—24no—
181C23×C59—24no—
182C23×C59—24no—
183C23×C59—24no—
184C23×C59—24no—
185C23×C59—24no—
186C23×C59—22no—
187C23×C59—24no—
188C23×C59—22no—
189C23×C59—22no—
190C23×C59—24no—
191C23×C59—42no—
192C23×C59—42no—
193C23×C59—42no—
194C23×C59—42no—
195C23×C59—41no—
196C23×C59—42no—
197C23×C59—41no—
198C23×C59—41no—
199C23×C59—42no—
200C23×C59—41no—
201C23×C59—42no—
202C23×C59—42no—
203C23×C59—42no—
204C23×C59—42no—
205C23×C59—42no—
206C23×C59—42no—
207C23×C59—42no—
208C23×C59—42no—
209C23×C59—42no—
210C23×C59—42no—
211C23×C59—41no—
212C23×C59—42no—
213C23×C59—41no—
214C23×C59—41no—
215C23×C59—42no—
216C23×C59—41no—
217C23×C59C2×C22⋊C414yes—
218C23×C59C23×C411yescharacteristic
219C23×C59C22×D412yes—
220C23×C59C2×#4112yes—
221C23×C59C2×#4112yes—
222C23×C59H(5,𝔽2)12yes—
223C23×C59H(5,𝔽2)11yescharacteristic
224C23×C59H(5,𝔽2)11yescharacteristic
225C23×C59H(5,𝔽2)12yes—
226C23×C592−1+412yes—
227D4×C59—416no—
228C2×C4×C59—24no—
229C2×C4×C59—24no—
230C2×C4×C59—24no—
231C2×C4×C59—24no—
232C2×C4×C59—24no—
233C2×C4×C59—24no—
234C2×C4×C59—24no—
235C2×C4×C59—22no—
236C2×C4×C59—24no—
237C2×C4×C59—24no—
238C2×C4×C59—22no—
239C2×C4×C59—22no—
240C2×C4×C59—24no—
241C2×C4×C59—24no—
242C2×C4×C59—24no—
243C2×C4×C59—24no—
244C2×C4×C59—24no—
245C2×C4×C59—24no—
246C2×C4×C59—416no—
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—42no—
268C2×C4×C59—42no—
269C2×C4×C59—42no—
270C2×C4×C59—42no—
271C2×C4×C59—42no—
272C2×C4×C59—42no—
273C2×C4×C59—42no—
274C2×C4×C59—42no—
275C2×C4×C59C2×C22⋊C418yes—
276#14506C5911yesmaximal, characteristic, direct product factor, Sylow
277C22×C59—24no—
278C22×C59—28no—
279C22×C59—44no—
280C22×C59—42no—
281C22×C59—42no—
282C22×C59—44no—
283C22×C59—44no—
284C22×C59—44no—
285C22×C59—44no—
286C22×C59—42no—
287C22×C59—44no—
288C22×C59—44no—
289C22×C59—42no—
290C22×C59—42no—
291C22×C59—82no—
292C22×C59—82no—
293C22×C59—82no—
294C22×C59—82no—
295C22×C59C22×C22⋊C411yescharacteristic
296C22×C59C4×#4112yes—
297C22×C59#51811yescharacteristic
298C22×C59#51811yescharacteristic
299C22×C59#52012yes—
300C22×C59#53512yes—
301C22×C59#53512yes—
302C22×C59#53812yes—
303C22×C59#53912yes—
304C22×C59#54012yes—
305C22×C59#54212yes—
306C22×C59#54612yes—
307C22×C59#54612yes—
308C22×C59#54712yes—
309C22×C59#54712yes—
310C22×C59#55111yescharacteristic
311C22×C59#55312yes—
312C22×C59#55911yescharacteristic
313C22×C59#56011yescharacteristic
314C22×C59#56212yes—
315C22×C59#56311yescharacteristic
316C4×C59—28no—
317C4×C59—44no—
318C4×C59—42no—
319C4×C59—44no—
320C4×C59—44no—
321C4×C59—82no—
322C4×C59—82no—
323C22×#123C2×C5911yescharacteristic
324C2×#388C2×C5912yescomplemented
325#1445C2×C5912yescomplemented
326#1439C2×C5912yescomplemented
327#1438C2×C5911yescharacteristic
328#1438C2×C5911yescharacteristic
329#1437C2×C5912yescomplemented
330C4⋊#95C2×C5912yescomplemented
331C22⋊#95C2×C5912yescomplemented
332C2×C59—44no—
333C2×C59—82no—
334C2×C59#230911yescharacteristic
335C2×C59#233512yes—
336C2×C59#233912yes—
337C2×C59#237411yescharacteristic
338C2×C59#237611yescharacteristic
339C2×C59#270312yes—
340C2×C59#270612yes—
341C2×C59#271012yes—
342C2×C59#271812yes—
343C23×D4C22×C5911yescharacteristic
344C24×C4C22×C5911yescharacteristic
345C2×#123—28no—
346C2×#123C4×C5918yescomplemented
347C22×C4⋊C4C22×C5912yes—
348C22×C4⋊C4C22×C5912yes—
349C22×C22⋊C4C22×C5912yes—
350C22×C22⋊C4C22×C5912yes—
351C22×C22⋊C4C22×C5911yescharacteristic
352C22×C22⋊C4C22×C5912yes—
353C22×C22⋊C4C22×C5912yes—
354C22×C22⋊C4C22×C5911yescharacteristic
355C22×C22⋊C4C22×C5911yescharacteristic
356C22×C42C22×C5912yes—
357#388—28no—
358C2×#95C22×C5912yes—
359C2×#95C22×C5912yes—
360C2×#95C22×C5912yes—
361C2×#95C22×C5912yes—
362C2×#95C22×C5912yes—
363C2×#95C22×C5912yes—
364C2×#95C22×C5911yescharacteristic
365C2×#95C22×C5912yes—
366C2×#95C22×C5911yescharacteristic
367C59#1450611yescharacteristic, direct product factor, Sylow
368C25C23×C5911yescharacteristic
369C25C23×C5911yescharacteristic
370C22×D4—24no—
371C22×D4—42no—
372C22×D4—41no—
373C22×D4—41no—
374C22×D4C2×C4×C5914yes—
375C23×C4—24no—
376C23×C4—42no—
377C23×C4—41no—
378C23×C4—41no—
379C23×C4C2×C4×C5914yes—
380C23×C4C23×C5912yes—
381C23×C4C23×C5912yes—
382C23×C4C23×C5912yes—
383C23×C4C23×C5911yescharacteristic
384C23×C4C23×C5912yes—
385C23×C4C23×C5912yes—
386C23×C4C23×C5912yes—
387#123—232no—
388C2×C4⋊C4—24no—
389C2×C4⋊C4—24no—
390C2×C4⋊C4—24no—
391C2×C4⋊C4—24no—
392C2×C4⋊C4—42no—
393C2×C4⋊C4C2×C4×C5918yes—
394C2×C22⋊C4—24no—
395C2×C22⋊C4—24no—
396C2×C22⋊C4—24no—
397C2×C22⋊C4—24no—
398C2×C22⋊C4—24no—
399C2×C22⋊C4—24no—
400C2×C22⋊C4—24no—
401C2×C22⋊C4—24no—
402C2×C22⋊C4—41no—
403C2×C22⋊C4—42no—
404C2×C22⋊C4—42no—
405C2×C22⋊C4—42no—
406C2×C22⋊C4—42no—
407C2×C22⋊C4—41no—
408C2×C22⋊C4—42no—
409C2×C22⋊C4C2×C4×C5918yes—
410C2×C22⋊C4C2×C4×C5914yes—
411C2×C22⋊C4D4×C5918yes—
412C2×C42—24no—
413C2×C42—24no—
414C2×C42—42no—
415#95—24no—
416#95—24no—
417#95—41no—
418#95—42no—
419#95—42no—
420#95—42no—
421#95—42no—
422#95—42no—
423#95—41no—
424C24—22no—
425C24—22no—
426C24—22no—
427C24—22no—
428C24—21no—
429C24—21no—
430C24—22no—
431C24—22no—
432C24—22no—
433C24—22no—
434C24—22no—
435C24—22no—
436C24—21no—
437C24—21no—
438C24—22no—
439C24C22×C4×C5912yes—
440C24C22×C4×C5912yes—
441C24C2×D4×C5914yes—
442C24C24×C5911yescharacteristic
443C2×D4—28no—
444C2×D4—44no—
445C2×D4—44no—
446C2×D4—48no—
447C2×D4—48no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—28no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—44no—
490C22×C4—44no—
491C22×C4—48no—
492C22×C4—48no—
493C22×C4C22×C4×C5914yes—
494C22×C4C22×C4×C5912yes—
495C22×C4C22×C4×C5914yes—
496C22×C4C2×D4×C5914yes—
497C22×C4C2×D4×C5914yes—
498C22×C4#41×C5914yes—
499C22×C4#41×C5914yes—
500C4⋊C4—216no—
501C4⋊C4—48no—
502C22⋊C4—216no—
503C22⋊C4—44no—
504C22⋊C4—48no—
505C22⋊C4—48no—
506C22⋊C4—48no—
507C22⋊C4—44no—
508C22⋊C4C22⋊C4×C59116yescomplemented
509C42—48no—
510C23—24no—
511C23—22no—
512C23—22no—
513C23—24no—
514C23—24no—
515C23—24no—
516C23—24no—
517C23—24no—
518C23—24no—
519C23—24no—
520C23—22no—
521C23—24no—
522C23—22no—
523C23—22no—
524C23—24no—
525C23—42no—
526C23—42no—
527C23—42no—
528C23—42no—
529C23—41no—
530C23—42no—
531C23—41no—
532C23—41no—
533C23—42no—
534C23—41no—
535C23—42no—
536C23—42no—
537C23—42no—
538C23—42no—
539C23—42no—
540C23—42no—
541C23—42no—
542C23—42no—
543C23—42no—
544C23—42no—
545C23—41no—
546C23—42no—
547C23—41no—
548C23—41no—
549C23—42no—
550C23—41no—
551C23C2×C22⋊C4×C5914yes—
552C23C23×C4×C5911yescharacteristic
553C23C22×D4×C5912yes—
554C23C2×#41×C5912yes—
555C23C2×#41×C5912yes—
556C23H(5,𝔽2)×C5912yes—
557C23H(5,𝔽2)×C5911yescharacteristic
558C23H(5,𝔽2)×C5911yescharacteristic
559C23H(5,𝔽2)×C5912yes—
560C232−1+4×C5912yes—
561D4—416no—
562C2×C4—24no—
563C2×C4—24no—
564C2×C4—24no—
565C2×C4—24no—
566C2×C4—24no—
567C2×C4—24no—
568C2×C4—24no—
569C2×C4—22no—
570C2×C4—24no—
571C2×C4—24no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—24no—
575C2×C4—24no—
576C2×C4—24no—
577C2×C4—24no—
578C2×C4—24no—
579C2×C4—24no—
580C2×C4—416no—
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—42no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—42no—
600C2×C4—42no—
601C2×C4—42no—
602C2×C4—42no—
603C2×C4—42no—
604C2×C4—42no—
605C2×C4—42no—
606C2×C4—42no—
607C2×C4—42no—
608C2×C4—42no—
609C2×C4C2×C22⋊C4×C5918yes—
610C22—24no—
611C22—28no—
612C22—44no—
613C22—42no—
614C22—42no—
615C22—44no—
616C22—44no—
617C22—44no—
618C22—44no—
619C22—42no—
620C22—44no—
621C22—44no—
622C22—42no—
623C22—42no—
624C22—82no—
625C22—82no—
626C22—82no—
627C22—82no—
628C22C22×C22⋊C4×C5911yescharacteristic
629C22C4×#41×C5912yes—
630C22C59×#51811yescharacteristic
631C22C59×#51811yescharacteristic
632C22C59×#52012yes—
633C22C59×#53512yes—
634C22C59×#53512yes—
635C22C59×#53812yes—
636C22C59×#53912yes—
637C22C59×#54012yes—
638C22C59×#54212yes—
639C22C59×#54612yes—
640C22C59×#54612yes—
641C22C59×#54712yes—
642C22C59×#54712yes—
643C22C59×#55111yescharacteristic
644C22C59×#55312yes—
645C22C59×#55911yescharacteristic
646C22C59×#56011yescharacteristic
647C22C59×#56212yes—
648C22C59×#56311yescharacteristic
649C4—28no—
650C4—44no—
651C4—42no—
652C4—44no—
653C4—44no—
654C4—82no—
655C4—82no—
656C2—44no—
657C2—82no—
658C2C59×#230911yescharacteristic
659C2C59×#233512yes—
660C2C59×#233912yes—
661C2C59×#237411yescharacteristic
662C2C59×#237611yescharacteristic
663C2C59×#270312yes—
664C2C59×#270612yes—
665C2C59×#271012yes—
666C2C59×#271812yes—
subgroupG/H
center, socleC24×C59C24
commutatorC23C23×C4×C59
Frattini, cosocleC24C24×C59
prime radicalC23×D4×C59C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C59 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C59×#388C2semidirect
3. C59×#1445C2semidirect
4. C59×#1439C2semidirect
7. C59×#1437C2semidirect
8. C59×C4⋊#95C2semidirect
9. C59×C22⋊#95C2semidirect
13. C2×#123×C59C4semidirect
174. C22⋊C4×C59C22⋊C4semidirect
276. #14506C59direct (N × H)
324. C2×#388C2×C59semidirect
325. #1445C2×C59semidirect
326. #1439C2×C59semidirect
329. #1437C2×C59semidirect
330. C4⋊#95C2×C59semidirect
331. C22⋊#95C2×C59semidirect
346. C2×#123C4×C59semidirect
367. C59#14506direct (N × H)
508. C22⋊C4C22⋊C4×C59semidirect

Maximal subgroups

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

subgroupindex
C22×#123×C592
C2×C59×#3882
C59×#14452
C59×#14392
C59×#14382
C59×#14372
C59×C4⋊#952
C59×C22⋊#952
#1450659