Finite Group Databasebeta

← C59×#14872 #28426981

Subgroups — C59×#14872 #28426981

Order 15104.

1426 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C59×#395C211yesmaximal, characteristic
2C2×C59×#391C211yesmaximal, characteristic
3C2×C59×#387C211yesmaximal, characteristic
4C2×C4×C4⋊C4×C59C211yesmaximal, characteristic
5C59×#1446C211yesmaximal, characteristic
6C59×#1444C211yesmaximal, characteristic
7C59×#1441C211yesmaximal, characteristic
8C59×#1441C212yesmaximal
9C59×#1441C212yesmaximal
10C59×#1436C212yesmaximal
11C59×C4⋊#95C212yesmaximal
12C23×Q8×C59C2211yescharacteristic
13C22×C4⋊C4×C59C2211yescharacteristic
14C22×C4⋊C4×C59C2212yes—
15C22×C4⋊C4×C59C2212yes—
16C22×C4⋊C4×C59C2211yescharacteristic
17C22×C4⋊C4×C59C2211yescharacteristic
18C22×C4⋊C4×C59C2212yes—
19C22×C42×C59C2212yes—
20C22×C42×C59C2211yescharacteristic
21C59×#395—24no—
22C59×#391—24no—
23C59×#387—24no—
24C4×C4⋊C4×C59—24no—
25C2×#95×C59C2211yescharacteristic
26C2×#95×C59C2211yescharacteristic
27C2×#95×C59C2211yescharacteristic
28C2×#95×C59C2211yescharacteristic
29C2×#95×C59C2211yescharacteristic
30C2×#95×C59C2212yes—
31C2×#95×C59C2212yes—
32C2×#95×C59C2212yes—
33C2×#95×C59C2212yes—
34C2×#95×C59C2212yes—
35C2×#95×C59C2212yes—
36C2×#95×C59C2212yes—
37C2×#95×C59C2212yes—
38C2×#95×C59C2211yescharacteristic
39C22×Q8×C59—22no—
40C22×Q8×C59—22no—
41C22×Q8×C59—24no—
42C22×Q8×C59—22no—
43C22×Q8×C59—42no—
44C23×C4×C59C2311yescharacteristic
45C23×C4×C59C2312yes—
46C23×C4×C59C2311yescharacteristic
47C23×C4×C59C2311yescharacteristic
48C23×C4×C59C2312yes—
49C23×C4×C59C2311yescharacteristic
50C23×C4×C59C2312yes—
51C23×C4×C59C2311yescharacteristic
52C23×C4×C59C2311yescharacteristic
53C23×C4×C59C2311yescharacteristic
54C23×C4×C59C2312yes—
55C2×C4⋊C4×C59—24no—
56C2×C4⋊C4×C59—22no—
57C2×C4⋊C4×C59—24no—
58C2×C4⋊C4×C59—22no—
59C2×C4⋊C4×C59—22no—
60C2×C4⋊C4×C59—22no—
61C2×C4⋊C4×C59—24no—
62C2×C4⋊C4×C59—22no—
63C2×C4⋊C4×C59—24no—
64C2×C4⋊C4×C59—24no—
65C2×C4⋊C4×C59—22no—
66C2×C4⋊C4×C59—42no—
67C2×C4⋊C4×C59—42no—
68C2×C4⋊C4×C59—42no—
69C2×C4⋊C4×C59—42no—
70C2×C4⋊C4×C59Q814yescomplemented
71C2×C4⋊C4×C59Q818yescomplemented
72C2×C42×C59—22no—
73C2×C42×C59—22no—
74C2×C42×C59—24no—
75C2×C42×C59—24no—
76C2×C42×C59—42no—
77C2×C42×C59D414yes—
78#95×C59—22no—
79#95×C59—22no—
80#95×C59—22no—
81#95×C59—22no—
82#95×C59—22no—
83#95×C59—24no—
84#95×C59—24no—
85#95×C59—24no—
86#95×C59—24no—
87#95×C59—24no—
88#95×C59—42no—
89#95×C59—42no—
90#95×C59—42no—
91#95×C59D414yes—
92C24×C59C2411yescharacteristic
93C2×Q8×C59—28no—
94C2×Q8×C59—48no—
95C2×Q8×C59—48no—
96C2×Q8×C59—44no—
97C2×Q8×C59—44no—
98C22×C4×C59—21no—
99C22×C4×C59—21no—
100C22×C4×C59—21no—
101C22×C4×C59—21no—
102C22×C4×C59—22no—
103C22×C4×C59—22no—
104C22×C4×C59—22no—
105C22×C4×C59—22no—
106C22×C4×C59—21no—
107C22×C4×C59—22no—
108C22×C4×C59—22no—
109C22×C4×C59—22no—
110C22×C4×C59—21no—
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—22no—
118C22×C4×C59—22no—
119C22×C4×C59—22no—
120C22×C4×C59—22no—
121C22×C4×C59—21no—
122C22×C4×C59—22no—
123C22×C4×C59—21no—
124C22×C4×C59—21no—
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—21no—
133C22×C4×C59—21no—
134C22×C4×C59—21no—
135C22×C4×C59—22no—
136C22×C4×C59—21no—
137C22×C4×C59—22no—
138C22×C4×C59—21no—
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—21no—
148C22×C4×C59—21no—
149C22×C4×C59—22no—
150C22×C4×C59C2×D412yes—
151C22×C4×C59C2×D412yes—
152C22×C4×C59C2×D412yes—
153C22×C4×C59C2×D414yes—
154C22×C4×C59C2×D412yes—
155C22×C4×C59C2×Q812yes—
156C22×C4×C59C2×Q812yes—
157C22×C4×C59C2×Q814yes—
158C22×C4×C59C2×Q812yes—
159C22×C4×C59C2×Q814yes—
160C22×C4×C59C2×Q814yes—
161C22×C4×C59#4114yes—
162C22×C4×C59#4112yes—
163C22×C4×C59#4114yes—
164C22×C4×C59#4112yes—
165C4⋊C4×C59—216no—
166C4⋊C4×C59—28no—
167C4⋊C4×C59—48no—
168C4⋊C4×C59—44no—
169C4⋊C4×C59—48no—
170C4⋊C4×C59—44no—
171C42×C59—28no—
172C42×C59—48no—
173C23×C59C22×D411yescharacteristic
174C23×C59C22×D411yescharacteristic
175C23×C59C22×Q812yes—
176C23×C59C22×Q811yescharacteristic
177C23×C59C2×#4111yescharacteristic
178C23×C59C2×#4111yescharacteristic
179C23×C59C2×#4112yes—
180C23×C59C2×#4112yes—
181C23×C59H(5,𝔽2)12yes—
182C23×C59H(5,𝔽2)11yescharacteristic
183C23×C592−1+411yescharacteristic
184Q8×C59—416no—
185C2×C4×C59—22no—
186C2×C4×C59—22no—
187C2×C4×C59—24no—
188C2×C4×C59—22no—
189C2×C4×C59—24no—
190C2×C4×C59—22no—
191C2×C4×C59—24no—
192C2×C4×C59—22no—
193C2×C4×C59—22no—
194C2×C4×C59—24no—
195C2×C4×C59—22no—
196C2×C4×C59—24no—
197C2×C4×C59—24no—
198C2×C4×C59—24no—
199C2×C4×C59—22no—
200C2×C4×C59—24no—
201C2×C4×C59—22no—
202C2×C4×C59—22no—
203C2×C4×C59—24no—
204C2×C4×C59—24no—
205C2×C4×C59—22no—
206C2×C4×C59—22no—
207C2×C4×C59—24no—
208C2×C4×C59—24no—
209C2×C4×C59—24no—
210C2×C4×C59—24no—
211C2×C4×C59—22no—
212C2×C4×C59—24no—
213C2×C4×C59—22no—
214C2×C4×C59—24no—
215C2×C4×C59—24no—
216C2×C4×C59—41no—
217C2×C4×C59—42no—
218C2×C4×C59—41no—
219C2×C4×C59—42no—
220C2×C4×C59—42no—
221C2×C4×C59—41no—
222C2×C4×C59—42no—
223C2×C4×C59—41no—
224C2×C4×C59—42no—
225C2×C4×C59—42no—
226C2×C4×C59—41no—
227C2×C4×C59—42no—
228C2×C4×C59—42no—
229C2×C4×C59—42no—
230C2×C4×C59—41no—
231C2×C4×C59—41no—
232C2×C4×C59—41no—
233C2×C4×C59—41no—
234C2×C4×C59—42no—
235C2×C4×C59—42no—
236C2×C4×C59—41no—
237C2×C4×C59—41no—
238C2×C4×C59—41no—
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#12114yes—
249C2×C4×C59C22⋊Q814yes—
250C2×C4×C59C22⋊Q818yes—
251C2×C4×C59C4⋊Q814yes—
252#14872C5911yesmaximal, characteristic, direct product factor, Sylow
253C22×C59C2×#12111yescharacteristic
254C22×C59C2×C22⋊Q811yescharacteristic
255C22×C59C2×C22⋊Q812yes—
256C22×C59#52511yescharacteristic
257C22×C59#52912yes—
258C22×C59C2×C4⋊Q811yescharacteristic
259C22×C59#53211yescharacteristic
260C22×C59#53312yes—
261C22×C59#53312yes—
262C22×C59#53511yescharacteristic
263C22×C59#53711yescharacteristic
264C22×C59#53812yes—
265C22×C59#54212yes—
266C22×C59#54612yes—
267C22×C59#54611yescharacteristic
268C22×C59D4×Q811yescharacteristic
269C22×C59#55112yes—
270C22×C59#55211yescharacteristic
271C22×C59#55412yes—
272C22×C59#55412yes—
273C22×C59#55411yescharacteristic
274C22×C59#55712yes—
275C22×C59Q8212yes—
276C4×C59—24no—
277C4×C59—24no—
278C4×C59—24no—
279C4×C59—28no—
280C4×C59—42no—
281C4×C59—44no—
282C4×C59—42no—
283C4×C59—44no—
284C4×C59—82no—
285C4×C59—81no—
286C4×C59—81no—
287C2×#395C2×C5911yescharacteristic
288C2×#391C2×C5911yescharacteristic
289C2×#387C2×C5911yescharacteristic
290C2×C4×C4⋊C4C2×C5911yescharacteristic
291#1446C2×C5911yescharacteristic
292#1444C2×C5911yescharacteristic
293#1441C2×C5911yescharacteristic
294#1441C2×C5912yes—
295#1441C2×C5912yes—
296#1436C2×C5912yes—
297C4⋊#95C2×C5912yes—
298C2×C59#239611yescharacteristic
299C2×C59#241111yescharacteristic
300C2×C59#241711yescharacteristic
301C2×C59#245012yes—
302C2×C59#245112yes—
303C2×C59#252012yes—
304C2×C59#256711yescharacteristic
305C2×C59#258411yescharacteristic
306C2×C59#258612yes—
307C2×C59#266211yescharacteristic
308C2×C59#285711yescharacteristic
309C23×Q8C22×C5911yescharacteristic
310C22×C4⋊C4C22×C5911yescharacteristic
311C22×C4⋊C4C22×C5912yes—
312C22×C4⋊C4C22×C5911yescharacteristic
313C22×C4⋊C4C22×C5912yes—
314C22×C4⋊C4C22×C5912yes—
315C22×C4⋊C4C22×C5911yescharacteristic
316C22×C42C22×C5912yes—
317C22×C42C22×C5911yescharacteristic
318#395—24no—
319#391—24no—
320#387—24no—
321C4×C4⋊C4—24no—
322C2×#95C22×C5912yes—
323C2×#95C22×C5911yescharacteristic
324C2×#95C22×C5912yes—
325C2×#95C22×C5912yes—
326C2×#95C22×C5912yes—
327C2×#95C22×C5911yescharacteristic
328C2×#95C22×C5911yescharacteristic
329C2×#95C22×C5912yes—
330C2×#95C22×C5911yescharacteristic
331C2×#95C22×C5911yescharacteristic
332C2×#95C22×C5912yes—
333C2×#95C22×C5912yes—
334C2×#95C22×C5912yes—
335C2×#95C22×C5911yescharacteristic
336C59#1487211yescharacteristic, direct product factor, Sylow
337C22×Q8—22no—
338C22×Q8—22no—
339C22×Q8—24no—
340C22×Q8—22no—
341C22×Q8—42no—
342C23×C4C23×C5911yescharacteristic
343C23×C4C23×C5911yescharacteristic
344C23×C4C23×C5912yes—
345C23×C4C23×C5911yescharacteristic
346C23×C4C23×C5911yescharacteristic
347C23×C4C23×C5912yes—
348C23×C4C23×C5912yes—
349C23×C4C23×C5911yescharacteristic
350C23×C4C23×C5911yescharacteristic
351C23×C4C23×C5912yes—
352C23×C4C23×C5911yescharacteristic
353C2×C4⋊C4—24no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—24no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—24no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—24no—
362C2×C4⋊C4—24no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—42no—
365C2×C4⋊C4—42no—
366C2×C4⋊C4—42no—
367C2×C4⋊C4—42no—
368C2×C4⋊C4Q8×C5914yescomplemented
369C2×C4⋊C4Q8×C5918yescomplemented
370C2×C42—22no—
371C2×C42—22no—
372C2×C42—24no—
373C2×C42—24no—
374C2×C42—42no—
375C2×C42D4×C5914yes—
376#95—22no—
377#95—22no—
378#95—22no—
379#95—22no—
380#95—22no—
381#95—24no—
382#95—24no—
383#95—24no—
384#95—24no—
385#95—24no—
386#95—42no—
387#95—42no—
388#95—42no—
389#95D4×C5914yes—
390C24C24×C5911yescharacteristic
391C2×Q8—28no—
392C2×Q8—48no—
393C2×Q8—48no—
394C2×Q8—44no—
395C2×Q8—44no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—21no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—21no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—21no—
420C22×C4—22no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—21no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—22no—
434C22×C4—21no—
435C22×C4—22no—
436C22×C4—21no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—22no—
448C22×C4C2×D4×C5912yes—
449C22×C4C2×D4×C5912yes—
450C22×C4C2×D4×C5912yes—
451C22×C4C2×D4×C5914yes—
452C22×C4C2×D4×C5912yes—
453C22×C4C2×Q8×C5912yes—
454C22×C4C2×Q8×C5912yes—
455C22×C4C2×Q8×C5914yes—
456C22×C4C2×Q8×C5912yes—
457C22×C4C2×Q8×C5914yes—
458C22×C4C2×Q8×C5914yes—
459C22×C4#41×C5914yes—
460C22×C4#41×C5912yes—
461C22×C4#41×C5914yes—
462C22×C4#41×C5912yes—
463C4⋊C4—216no—
464C4⋊C4—28no—
465C4⋊C4—48no—
466C4⋊C4—44no—
467C4⋊C4—48no—
468C4⋊C4—44no—
469C42—28no—
470C42—48no—
471C23C22×D4×C5911yescharacteristic
472C23C22×D4×C5911yescharacteristic
473C23C22×Q8×C5912yes—
474C23C22×Q8×C5911yescharacteristic
475C23C2×#41×C5911yescharacteristic
476C23C2×#41×C5911yescharacteristic
477C23C2×#41×C5912yes—
478C23C2×#41×C5912yes—
479C23H(5,𝔽2)×C5912yes—
480C23H(5,𝔽2)×C5911yescharacteristic
481C232−1+4×C5911yescharacteristic
482Q8—416no—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—24no—
486C2×C4—22no—
487C2×C4—24no—
488C2×C4—22no—
489C2×C4—24no—
490C2×C4—22no—
491C2×C4—22no—
492C2×C4—24no—
493C2×C4—22no—
494C2×C4—24no—
495C2×C4—24no—
496C2×C4—24no—
497C2×C4—22no—
498C2×C4—24no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—24no—
502C2×C4—24no—
503C2×C4—22no—
504C2×C4—22no—
505C2×C4—24no—
506C2×C4—24no—
507C2×C4—24no—
508C2×C4—24no—
509C2×C4—22no—
510C2×C4—24no—
511C2×C4—22no—
512C2×C4—24no—
513C2×C4—24no—
514C2×C4—41no—
515C2×C4—42no—
516C2×C4—41no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—41no—
520C2×C4—42no—
521C2×C4—41no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—41no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4#121×C5914yes—
547C2×C4C22⋊Q8×C5914yes—
548C2×C4C22⋊Q8×C5918yes—
549C2×C4C4⋊Q8×C5914yes—
550C22C2×#121×C5911yescharacteristic
551C22C2×C22⋊Q8×C5911yescharacteristic
552C22C2×C22⋊Q8×C5912yes—
553C22C59×#52511yescharacteristic
554C22C59×#52912yes—
555C22C2×C4⋊Q8×C5911yescharacteristic
556C22C59×#53211yescharacteristic
557C22C59×#53312yes—
558C22C59×#53312yes—
559C22C59×#53511yescharacteristic
560C22C59×#53711yescharacteristic
561C22C59×#53812yes—
562C22C59×#54212yes—
563C22C59×#54612yes—
564C22C59×#54611yescharacteristic
565C22D4×Q8×C5911yescharacteristic
566C22C59×#55112yes—
567C22C59×#55211yescharacteristic
568C22C59×#55412yes—
569C22C59×#55412yes—
570C22C59×#55411yescharacteristic
571C22C59×#55712yes—
572C22Q82×C5912yes—
573C4—24no—
574C4—24no—
575C4—24no—
576C4—28no—
577C4—42no—
578C4—44no—
579C4—42no—
580C4—44no—
581C4—82no—
582C4—81no—
583C4—81no—
584C2C59×#239611yescharacteristic
585C2C59×#241111yescharacteristic
586C2C59×#241711yescharacteristic
587C2C59×#245012yes—
588C2C59×#245112yes—
589C2C59×#252012yes—
590C2C59×#256711yescharacteristic
591C2C59×#258411yescharacteristic
592C2C59×#258612yes—
593C2C59×#266211yescharacteristic
594C2C59×#285711yescharacteristic
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
70. C2×C4⋊C4×C59Q8semidirect
71. C2×C4⋊C4×C59Q8semidirect
252. #14872C59direct (N × H)
336. C59#14872direct (N × H)
368. C2×C4⋊C4Q8×C59semidirect
369. C2×C4⋊C4Q8×C59semidirect

Maximal subgroups

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

subgroupindex
C2×C59×#3952
C2×C59×#3912
C2×C59×#3872
C2×C4×C4⋊C4×C592
C59×#14462
C59×#14442
C59×#14412
C59×#14362
C59×C4⋊#952
#1487259