Finite Group Databasebeta

← C59×#14879 #28426988

Subgroups — C59×#14879 #28426988

Order 15104.

1634 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×Q8×C59C211yesmaximal, characteristic
2C2×C59×#398C211yesmaximal, characteristic
3C2×C59×#395C211yesmaximal, characteristic
4C2×C59×#387C211yesmaximal, characteristic
5C59×#1446C211yesmaximal, characteristic
6C59×#1445C211yesmaximal, characteristic
7C59×#1444C212yesmaximal
8C59×#1441C212yesmaximal
9C59×#1436C212yesmaximal
10C59×#1436C212yesmaximal
11C59×#1434C211yesmaximal, characteristic
12C23×Q8×C59C2211yescharacteristic
13C2×C4×Q8×C59—24no—
14C2×C4×Q8×C59—24no—
15C2×C4×Q8×C59—24no—
16C22×C4⋊C4×C59C2211yescharacteristic
17C22×C4⋊C4×C59C2211yescharacteristic
18C22×C4⋊C4×C59C2212yes—
19C22×C4⋊C4×C59C2212yes—
20C22×C4⋊C4×C59C2212yes—
21C22×C4⋊C4×C59C2211yescharacteristic
22C22×C42×C59C2212yes—
23C22×C42×C59C2211yescharacteristic
24C59×#398—24no—
25C59×#395—24no—
26C59×#387—24no—
27C2×#95×C59C2211yescharacteristic
28C2×#95×C59C2211yescharacteristic
29C2×#95×C59C2211yescharacteristic
30C2×#95×C59C2211yescharacteristic
31C2×#95×C59C2211yescharacteristic
32C2×#95×C59C2212yes—
33C2×#95×C59C2211yescharacteristic
34C2×#95×C59C2212yes—
35C2×#95×C59C2212yes—
36C2×#95×C59C2212yes—
37C2×#95×C59C2212yes—
38C2×#95×C59C2212yes—
39C2×#95×C59C2212yes—
40C2×#95×C59C2212yes—
41C22×Q8×C59—22no—
42C22×Q8×C59—22no—
43C22×Q8×C59—24no—
44C22×Q8×C59—24no—
45C22×Q8×C59D414yes—
46C23×C4×C59C2311yescharacteristic
47C23×C4×C59C2311yescharacteristic
48C23×C4×C59C2312yes—
49C23×C4×C59C2311yescharacteristic
50C23×C4×C59C2312yes—
51C23×C4×C59C2312yes—
52C23×C4×C59C2311yescharacteristic
53C23×C4×C59C2311yescharacteristic
54C23×C4×C59C2311yescharacteristic
55C23×C4×C59C2311yescharacteristic
56C23×C4×C59C2312yes—
57C4×Q8×C59—232no—
58C2×C4⋊C4×C59—22no—
59C2×C4⋊C4×C59—24no—
60C2×C4⋊C4×C59—24no—
61C2×C4⋊C4×C59—24no—
62C2×C4⋊C4×C59—22no—
63C2×C4⋊C4×C59—22no—
64C2×C4⋊C4×C59—22no—
65C2×C4⋊C4×C59—22no—
66C2×C4⋊C4×C59—22no—
67C2×C4⋊C4×C59—22no—
68C2×C4⋊C4×C59—24no—
69C2×C4⋊C4×C59—24no—
70C2×C4⋊C4×C59—22no—
71C2×C4⋊C4×C59—24no—
72C2×C4⋊C4×C59—24no—
73C2×C4⋊C4×C59—24no—
74C2×C4⋊C4×C59—42no—
75C2×C4⋊C4×C59D414yes—
76C2×C42×C59—24no—
77C2×C42×C59—24no—
78C2×C42×C59—24no—
79C2×C42×C59—22no—
80C2×C42×C59—22no—
81C2×C42×C59D414yes—
82#95×C59—22no—
83#95×C59—22no—
84#95×C59—22no—
85#95×C59—22no—
86#95×C59—22no—
87#95×C59—24no—
88#95×C59—22no—
89#95×C59—24no—
90#95×C59—24no—
91#95×C59—24no—
92#95×C59—24no—
93#95×C59—42no—
94#95×C59—42no—
95#95×C59Q818yescomplemented
96C24×C59C2411yescharacteristic
97C2×Q8×C59—28no—
98C2×Q8×C59—28no—
99C2×Q8×C59—216no—
100C2×Q8×C59—28no—
101C2×Q8×C59—216no—
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—21no—
112C22×C4×C59—21no—
113C22×C4×C59—22no—
114C22×C4×C59—22no—
115C22×C4×C59—21no—
116C22×C4×C59—22no—
117C22×C4×C59—21no—
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—21no—
127C22×C4×C59—21no—
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—21no—
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—21no—
142C22×C4×C59—22no—
143C22×C4×C59—22no—
144C22×C4×C59—22no—
145C22×C4×C59—21no—
146C22×C4×C59—21no—
147C22×C4×C59—21no—
148C22×C4×C59—21no—
149C22×C4×C59—22no—
150C22×C4×C59—22no—
151C22×C4×C59—22no—
152C22×C4×C59—21no—
153C22×C4×C59—22no—
154C22×C4×C59—21no—
155C22×C4×C59C2×D414yes—
156C22×C4×C59C2×D412yes—
157C22×C4×C59C2×D412yes—
158C22×C4×C59C2×D412yes—
159C22×C4×C59C2×D412yes—
160C22×C4×C59C2×D414yes—
161C22×C4×C59C2×D412yes—
162C22×C4×C59C2×Q814yes—
163C22×C4×C59C2×Q814yes—
164C22×C4×C59C2×Q814yes—
165C22×C4×C59#4112yes—
166C22×C4×C59#4112yes—
167C22×C4×C59#4114yes—
168C22×C4×C59#4114yes—
169C4⋊C4×C59—28no—
170C4⋊C4×C59—216no—
171C4⋊C4×C59—28no—
172C4⋊C4×C59—48no—
173C4⋊C4×C59—44no—
174C4⋊C4×C59—48no—
175C42×C59—216no—
176C42×C59—28no—
177C23×C59C22×D411yescharacteristic
178C23×C59C22×D411yescharacteristic
179C23×C59C22×D411yescharacteristic
180C23×C59C22×Q812yes—
181C23×C59C2×#4112yes—
182C23×C59C2×#4112yes—
183C23×C59C2×#4111yescharacteristic
184C23×C59C2×#4111yescharacteristic
185C23×C59H(5,𝔽2)11yescharacteristic
186C23×C592−1+412yes—
187C23×C592−1+411yescharacteristic
188Q8×C59—232no—
189C2×C4×C59—22no—
190C2×C4×C59—24no—
191C2×C4×C59—24no—
192C2×C4×C59—24no—
193C2×C4×C59—22no—
194C2×C4×C59—22no—
195C2×C4×C59—24no—
196C2×C4×C59—24no—
197C2×C4×C59—24no—
198C2×C4×C59—24no—
199C2×C4×C59—24no—
200C2×C4×C59—22no—
201C2×C4×C59—24no—
202C2×C4×C59—24no—
203C2×C4×C59—24no—
204C2×C4×C59—22no—
205C2×C4×C59—22no—
206C2×C4×C59—22no—
207C2×C4×C59—22no—
208C2×C4×C59—24no—
209C2×C4×C59—24no—
210C2×C4×C59—22no—
211C2×C4×C59—22no—
212C2×C4×C59—24no—
213C2×C4×C59—24no—
214C2×C4×C59—22no—
215C2×C4×C59—24no—
216C2×C4×C59—24no—
217C2×C4×C59—24no—
218C2×C4×C59—24no—
219C2×C4×C59—24no—
220C2×C4×C59—41no—
221C2×C4×C59—42no—
222C2×C4×C59—41no—
223C2×C4×C59—42no—
224C2×C4×C59—42no—
225C2×C4×C59—41no—
226C2×C4×C59—41no—
227C2×C4×C59—42no—
228C2×C4×C59—42no—
229C2×C4×C59—42no—
230C2×C4×C59—42no—
231C2×C4×C59—41no—
232C2×C4×C59—41no—
233C2×C4×C59—41no—
234C2×C4×C59—41no—
235C2×C4×C59—42no—
236C2×C4×C59—41no—
237C2×C4×C59—42no—
238C2×C4×C59—41no—
239C2×C4×C59—42no—
240C2×C4×C59—42no—
241C2×C4×C59—42no—
242C2×C4×C59—42no—
243C2×C4×C59—41no—
244C2×C4×C59—42no—
245C2×C4×C59—41no—
246C2×C4×C59—41no—
247C2×C4×C59—42no—
248C2×C4×C59—41no—
249C2×C4×C59—41no—
250C2×C4×C59—41no—
251C2×C4×C59—42no—
252C2×C4×C59—42no—
253C2×C4×C59#12014yes—
254C2×C4×C59#12318yes—
255C2×C4×C59C4⋊Q814yes—
256#14879C5911yesmaximal, characteristic, direct product factor, Sylow
257C22×C59C2×#12011yescharacteristic
258C22×C59C2×#12312yes—
259C22×C59#52511yescharacteristic
260C22×C59#52511yescharacteristic
261C22×C59#52512yes—
262C22×C59#52511yescharacteristic
263C22×C59C2×C4⋊Q811yescharacteristic
264C22×C59#53312yes—
265C22×C59#53312yes—
266C22×C59#53611yescharacteristic
267C22×C59#53711yescharacteristic
268C22×C59#54112yes—
269C22×C59#54212yes—
270C22×C59#54611yescharacteristic
271C22×C59#54711yescharacteristic
272C22×C59#54811yescharacteristic
273C22×C59D4×Q812yes—
274C22×C59D4×Q812yes—
275C22×C59#55011yescharacteristic
276C22×C59#55212yes—
277C22×C59#55412yes—
278C22×C59#55612yes—
279C22×C59#55712yes—
280C4×C59—24no—
281C4×C59—28no—
282C4×C59—24no—
283C4×C59—42no—
284C4×C59—42no—
285C4×C59—44no—
286C4×C59—42no—
287C4×C59—44no—
288C4×C59—44no—
289C4×C59—81no—
290C4×C59—81no—
291C22×C4×Q8C2×C5911yescharacteristic
292C2×#398C2×C5911yescharacteristic
293C2×#395C2×C5911yescharacteristic
294C2×#387C2×C5911yescharacteristic
295#1446C2×C5911yescharacteristic
296#1445C2×C5911yescharacteristic
297#1444C2×C5912yes—
298#1441C2×C5912yes—
299#1436C2×C5912yes—
300#1436C2×C5912yes—
301#1434C2×C5911yescharacteristic
302C2×C59#239911yescharacteristic
303C2×C59#240711yescharacteristic
304C2×C59#242312yes—
305C2×C59#243411yescharacteristic
306C2×C59#244612yes—
307C2×C59#246212yes—
308C2×C59#246512yes—
309C2×C59#258411yescharacteristic
310C2×C59#259911yescharacteristic
311C2×C59#263711yescharacteristic
312C2×C59#284911yescharacteristic
313C23×Q8C22×C5911yescharacteristic
314C2×C4×Q8—24no—
315C2×C4×Q8—24no—
316C2×C4×Q8—24no—
317C22×C4⋊C4C22×C5911yescharacteristic
318C22×C4⋊C4C22×C5912yes—
319C22×C4⋊C4C22×C5912yes—
320C22×C4⋊C4C22×C5911yescharacteristic
321C22×C4⋊C4C22×C5912yes—
322C22×C4⋊C4C22×C5911yescharacteristic
323C22×C42C22×C5912yes—
324C22×C42C22×C5911yescharacteristic
325#398—24no—
326#395—24no—
327#387—24no—
328C2×#95C22×C5911yescharacteristic
329C2×#95C22×C5912yes—
330C2×#95C22×C5911yescharacteristic
331C2×#95C22×C5912yes—
332C2×#95C22×C5911yescharacteristic
333C2×#95C22×C5911yescharacteristic
334C2×#95C22×C5912yes—
335C2×#95C22×C5912yes—
336C2×#95C22×C5912yes—
337C2×#95C22×C5911yescharacteristic
338C2×#95C22×C5911yescharacteristic
339C2×#95C22×C5912yes—
340C2×#95C22×C5912yes—
341C2×#95C22×C5912yes—
342C59#1487911yescharacteristic, direct product factor, Sylow
343C22×Q8—22no—
344C22×Q8—22no—
345C22×Q8—24no—
346C22×Q8—24no—
347C22×Q8D4×C5914yes—
348C23×C4C23×C5911yescharacteristic
349C23×C4C23×C5911yescharacteristic
350C23×C4C23×C5912yes—
351C23×C4C23×C5911yescharacteristic
352C23×C4C23×C5912yes—
353C23×C4C23×C5912yes—
354C23×C4C23×C5911yescharacteristic
355C23×C4C23×C5911yescharacteristic
356C23×C4C23×C5911yescharacteristic
357C23×C4C23×C5911yescharacteristic
358C23×C4C23×C5912yes—
359C4×Q8—232no—
360C2×C4⋊C4—24no—
361C2×C4⋊C4—24no—
362C2×C4⋊C4—24no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—24no—
371C2×C4⋊C4—24no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—24no—
374C2×C4⋊C4—24no—
375C2×C4⋊C4—24no—
376C2×C4⋊C4—42no—
377C2×C4⋊C4D4×C5914yes—
378C2×C42—24no—
379C2×C42—24no—
380C2×C42—24no—
381C2×C42—22no—
382C2×C42—22no—
383C2×C42D4×C5914yes—
384#95—22no—
385#95—22no—
386#95—22no—
387#95—22no—
388#95—22no—
389#95—24no—
390#95—22no—
391#95—24no—
392#95—24no—
393#95—24no—
394#95—24no—
395#95—42no—
396#95—42no—
397#95Q8×C5918yescomplemented
398C24C24×C5911yescharacteristic
399C2×Q8—28no—
400C2×Q8—28no—
401C2×Q8—216no—
402C2×Q8—28no—
403C2×Q8—216no—
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—21no—
418C22×C4—22no—
419C22×C4—21no—
420C22×C4—22no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—21no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—22no—
443C22×C4—21no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—21no—
455C22×C4—22no—
456C22×C4—21no—
457C22×C4C2×D4×C5914yes—
458C22×C4C2×D4×C5912yes—
459C22×C4C2×D4×C5912yes—
460C22×C4C2×D4×C5912yes—
461C22×C4C2×D4×C5912yes—
462C22×C4C2×D4×C5914yes—
463C22×C4C2×D4×C5912yes—
464C22×C4C2×Q8×C5914yes—
465C22×C4C2×Q8×C5914yes—
466C22×C4C2×Q8×C5914yes—
467C22×C4#41×C5912yes—
468C22×C4#41×C5912yes—
469C22×C4#41×C5914yes—
470C22×C4#41×C5914yes—
471C4⋊C4—216no—
472C4⋊C4—28no—
473C4⋊C4—28no—
474C4⋊C4—48no—
475C4⋊C4—44no—
476C4⋊C4—48no—
477C42—216no—
478C42—28no—
479C23C22×D4×C5911yescharacteristic
480C23C22×D4×C5911yescharacteristic
481C23C22×D4×C5911yescharacteristic
482C23C22×Q8×C5912yes—
483C23C2×#41×C5912yes—
484C23C2×#41×C5912yes—
485C23C2×#41×C5911yescharacteristic
486C23C2×#41×C5911yescharacteristic
487C23H(5,𝔽2)×C5911yescharacteristic
488C232−1+4×C5912yes—
489C232−1+4×C5911yescharacteristic
490Q8—232no—
491C2×C4—22no—
492C2×C4—24no—
493C2×C4—24no—
494C2×C4—24no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—24no—
498C2×C4—24no—
499C2×C4—24no—
500C2×C4—24no—
501C2×C4—24no—
502C2×C4—22no—
503C2×C4—24no—
504C2×C4—24no—
505C2×C4—24no—
506C2×C4—22no—
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—24no—
511C2×C4—24no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—24no—
515C2×C4—24no—
516C2×C4—22no—
517C2×C4—24no—
518C2×C4—24no—
519C2×C4—24no—
520C2×C4—24no—
521C2×C4—24no—
522C2×C4—41no—
523C2×C4—42no—
524C2×C4—41no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—42no—
538C2×C4—41no—
539C2×C4—42no—
540C2×C4—41no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—41no—
546C2×C4—42no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—42no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4#120×C5914yes—
556C2×C4#123×C5918yes—
557C2×C4C4⋊Q8×C5914yes—
558C22C2×#120×C5911yescharacteristic
559C22C2×#123×C5912yes—
560C22C59×#52511yescharacteristic
561C22C59×#52511yescharacteristic
562C22C59×#52512yes—
563C22C59×#52511yescharacteristic
564C22C2×C4⋊Q8×C5911yescharacteristic
565C22C59×#53312yes—
566C22C59×#53312yes—
567C22C59×#53611yescharacteristic
568C22C59×#53711yescharacteristic
569C22C59×#54112yes—
570C22C59×#54212yes—
571C22C59×#54611yescharacteristic
572C22C59×#54711yescharacteristic
573C22C59×#54811yescharacteristic
574C22D4×Q8×C5912yes—
575C22D4×Q8×C5912yes—
576C22C59×#55011yescharacteristic
577C22C59×#55212yes—
578C22C59×#55412yes—
579C22C59×#55612yes—
580C22C59×#55712yes—
581C4—24no—
582C4—28no—
583C4—24no—
584C4—42no—
585C4—42no—
586C4—44no—
587C4—42no—
588C4—44no—
589C4—44no—
590C4—81no—
591C4—81no—
592C2C59×#239911yescharacteristic
593C2C59×#240711yescharacteristic
594C2C59×#242312yes—
595C2C59×#243411yescharacteristic
596C2C59×#244612yes—
597C2C59×#246212yes—
598C2C59×#246512yes—
599C2C59×#258411yescharacteristic
600C2C59×#259911yescharacteristic
601C2C59×#263711yescharacteristic
602C2C59×#284911yescharacteristic
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
95. #95×C59Q8semidirect
256. #14879C59direct (N × H)
342. C59#14879direct (N × H)
397. #95Q8×C59semidirect

Maximal subgroups

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

subgroupindex
C22×C4×Q8×C592
C2×C59×#3982
C2×C59×#3952
C2×C59×#3872
C59×#14462
C59×#14452
C59×#14442
C59×#14412
C59×#14362
C59×#14342
#1487959