Finite Group Databasebeta

← C59×#16305 #28428414

Subgroups — C59×#16305 #28428414

Order 15104.

1618 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C59×#398C212yesmaximal, complemented
2C2×C59×#396C212yesmaximal
3C2×C59×#380C212yesmaximal
4C59×#1444C212yesmaximal, complemented
5C59×#1444C212yesmaximal, complemented
6C59×#1441C212yesmaximal, complemented
7C59×#1439C211yesmaximal, characteristic
8C59×#1439C211yesmaximal, characteristic
9C59×C22⋊#95C211yesmaximal, characteristic
10C24×C4×C59C2211yescharacteristic
11C22×C4⋊C4×C59C2212yes—
12C22×C4⋊C4×C59C2212yes—
13C22×C4⋊C4×C59C2212yes—
14C22×C4⋊C4×C59C2212yes—
15C22×C4⋊C4×C59C2211yescharacteristic
16C22×C4⋊C4×C59C2212yes—
17C22×C4⋊C4×C59C2211yescharacteristic
18C22×C22⋊C4×C59C2212yes—
19C22×C22⋊C4×C59C2212yes—
20C22×C22⋊C4×C59C2211yescharacteristic
21C22×C22⋊C4×C59C2211yescharacteristic
22C59×#398—28no—
23C59×#396—28no—
24C59×#380—28no—
25C2×#95×C59C2212yes—
26C2×#95×C59C2212yes—
27C2×#95×C59C2212yes—
28C2×#95×C59C2212yes—
29C2×#95×C59C2212yes—
30C2×#95×C59C2211yescharacteristic
31C2×#95×C59C2212yes—
32C2×#95×C59C2211yescharacteristic
33C2×#95×C59C2212yes—
34C25×C59C2311yescharacteristic
35C23×C4×C59—24no—
36C23×C4×C59—24no—
37C23×C4×C59—41no—
38C23×C4×C59—41no—
39C23×C4×C59Q814yes—
40C23×C4×C59C2312yes—
41C23×C4×C59C2312yes—
42C23×C4×C59C2312yes—
43C23×C4×C59C2312yes—
44C23×C4×C59C2312yes—
45C23×C4×C59C2311yescharacteristic
46C23×C4×C59C2311yescharacteristic
47C23×C4×C59C2312yes—
48C2×C4⋊C4×C59—24no—
49C2×C4⋊C4×C59—24no—
50C2×C4⋊C4×C59—24no—
51C2×C4⋊C4×C59—24no—
52C2×C4⋊C4×C59—24no—
53C2×C4⋊C4×C59—24no—
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×C59—42no—
60C2×C4⋊C4×C59—42no—
61C2×C4⋊C4×C59—41no—
62C2×C4⋊C4×C59—42no—
63C2×C4⋊C4×C59—42no—
64C2×C4⋊C4×C59—42no—
65C2×C4⋊C4×C59—42no—
66C2×C4⋊C4×C59—41no—
67C2×C22⋊C4×C59—24no—
68C2×C22⋊C4×C59—24no—
69C2×C22⋊C4×C59—24no—
70C2×C22⋊C4×C59—24no—
71C2×C22⋊C4×C59—41no—
72C2×C22⋊C4×C59—41no—
73C2×C22⋊C4×C59—41no—
74C2×C22⋊C4×C59—41no—
75C2×C22⋊C4×C59—42no—
76C2×C22⋊C4×C59—42no—
77C2×C22⋊C4×C59D414yes—
78C2×C22⋊C4×C59Q814yes—
79#95×C59—24no—
80#95×C59—24no—
81#95×C59—24no—
82#95×C59—24no—
83#95×C59—24no—
84#95×C59—41no—
85#95×C59—41no—
86#95×C59—42no—
87#95×C59D418yes—
88C24×C59—22no—
89C24×C59—22no—
90C24×C59—21no—
91C24×C59—22no—
92C24×C59—21no—
93C24×C59—21no—
94C24×C59—21no—
95C24×C59—22no—
96C24×C59C2×D412yes—
97C24×C59C2×Q812yes—
98C24×C59C2×Q812yes—
99C24×C59C2411yescharacteristic
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—21no—
114C22×C4×C59—22no—
115C22×C4×C59—22no—
116C22×C4×C59—22no—
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—216no—
131C22×C4×C59—22no—
132C22×C4×C59—22no—
133C22×C4×C59—22no—
134C22×C4×C59—22no—
135C22×C4×C59—22no—
136C22×C4×C59—22no—
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—44no—
146C22×C4×C59—44no—
147C22×C4×C59—48no—
148C22×C4×C59—44no—
149C22×C4×C59C2×D414yes—
150C22×C4×C59C2×D414yes—
151C22×C4×C59C2×D414yes—
152C22×C4×C59C2×D414yes—
153C22×C4×C59C2×Q812yes—
154C22×C4×C59C2×Q812yes—
155C22×C4×C59C2×Q814yes—
156C22×C4×C59#4114yes—
157C4⋊C4×C59—48no—
158C4⋊C4×C59—48no—
159C4⋊C4×C59—48no—
160C4⋊C4×C59—48no—
161C4⋊C4×C59—44no—
162C4⋊C4×C59—48no—
163C4⋊C4×C59—44no—
164C22⋊C4×C59—44no—
165C22⋊C4×C59—44no—
166C22⋊C4×C59—48no—
167C22⋊C4×C59—48no—
168C23×C59—24no—
169C23×C59—22no—
170C23×C59—22no—
171C23×C59—22no—
172C23×C59—22no—
173C23×C59—22no—
174C23×C59—22no—
175C23×C59—24no—
176C23×C59—24no—
177C23×C59—24no—
178C23×C59—24no—
179C23×C59—24no—
180C23×C59—42no—
181C23×C59—42no—
182C23×C59—42no—
183C23×C59—42no—
184C23×C59—41no—
185C23×C59—42no—
186C23×C59—41no—
187C23×C59—41no—
188C23×C59—42no—
189C23×C59—41no—
190C23×C59C4⋊Q814yes—
191C23×C59C22×D412yes—
192C23×C59C22×D411yescharacteristic
193C23×C59C22×Q811yescharacteristic
194C23×C59C22×Q811yescharacteristic
195C23×C59C2×#4112yes—
196C23×C59H(5,𝔽2)11yescharacteristic
197C23×C59H(5,𝔽2)11yescharacteristic
198C23×C59H(5,𝔽2)12yes—
199C23×C59H(5,𝔽2)11yescharacteristic
200C23×C592−1+411yescharacteristic
201C23×C592−1+412yes—
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—24no—
209C2×C4×C59—24no—
210C2×C4×C59—24no—
211C2×C4×C59—22no—
212C2×C4×C59—22no—
213C2×C4×C59—24no—
214C2×C4×C59—24no—
215C2×C4×C59—24no—
216C2×C4×C59—24no—
217C2×C4×C59—24no—
218C2×C4×C59—24no—
219C2×C4×C59—24no—
220C2×C4×C59—24no—
221C2×C4×C59—416no—
222C2×C4×C59—42no—
223C2×C4×C59—42no—
224C2×C4×C59—42no—
225C2×C4×C59—42no—
226C2×C4×C59—42no—
227C2×C4×C59—42no—
228C2×C4×C59—42no—
229C2×C4×C59—42no—
230C2×C4×C59—42no—
231C2×C4×C59—41no—
232C2×C4×C59—42no—
233C2×C4×C59—42no—
234C2×C4×C59—41no—
235C2×C4×C59—41no—
236C2×C4×C59—42no—
237C2×C4×C59—42no—
238C2×C4×C59—42no—
239C2×C4×C59—41no—
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×C59C22⋊Q818yes—
255#16305C5911yesmaximal, characteristic, direct product factor, Sylow
256C22×C59—24no—
257C22×C59—28no—
258C22×C59—42no—
259C22×C59—44no—
260C22×C59—44no—
261C22×C59—42no—
262C22×C59—42no—
263C22×C59—42no—
264C22×C59—44no—
265C22×C59—42no—
266C22×C59—42no—
267C22×C59C2×C22⋊Q812yes—
268C22×C59C2×C4⋊Q811yescharacteristic
269C22×C59#53411yescharacteristic
270C22×C59#53712yes—
271C22×C59#53712yes—
272C22×C59#53711yescharacteristic
273C22×C59#54012yes—
274C22×C59#54112yes—
275C22×C59#54311yescharacteristic
276C22×C59#54311yescharacteristic
277C22×C59#54412yes—
278C22×C59#54411yescharacteristic
279C22×C59#54411yescharacteristic
280C22×C59D4212yes—
281C22×C59D4211yescharacteristic
282C22×C59#54612yes—
283C22×C59#54712yes—
284C22×C59D4×Q812yes—
285C22×C59#55111yescharacteristic
286C22×C59#55412yes—
287C22×C59#56011yescharacteristic
288C22×C59#56212yes—
289C22×C59#56311yescharacteristic
290C4×C59—28no—
291C4×C59—44no—
292C4×C59—44no—
293C4×C59—44no—
294C4×C59—42no—
295C4×C59—42no—
296C4×C59—82no—
297C4×C59—82no—
298C2×#398C2×C5912yescomplemented
299C2×#396C2×C5912yes—
300C2×#380C2×C5912yes—
301#1444C2×C5912yescomplemented
302#1444C2×C5912yescomplemented
303#1441C2×C5912yescomplemented
304#1439C2×C5911yescharacteristic
305#1439C2×C5911yescharacteristic
306C22⋊#95C2×C5911yescharacteristic
307C2×C59—44no—
308C2×C59#243711yescharacteristic
309C2×C59#244012yes—
310C2×C59#262912yes—
311C2×C59#265911yescharacteristic
312C2×C59#267112yes—
313C2×C59#267511yescharacteristic
314C2×C59#268311yescharacteristic
315C2×C59#270412yes—
316C2×C59#272211yescharacteristic
317C2×C59#274811yescharacteristic
318C2×C59#284111yescharacteristic
319C24×C4C22×C5911yescharacteristic
320C22×C4⋊C4C22×C5912yes—
321C22×C4⋊C4C22×C5912yes—
322C22×C4⋊C4C22×C5911yescharacteristic
323C22×C4⋊C4C22×C5912yes—
324C22×C4⋊C4C22×C5912yes—
325C22×C4⋊C4C22×C5912yes—
326C22×C4⋊C4C22×C5911yescharacteristic
327C22×C22⋊C4C22×C5912yes—
328C22×C22⋊C4C22×C5912yes—
329C22×C22⋊C4C22×C5911yescharacteristic
330C22×C22⋊C4C22×C5911yescharacteristic
331#398—28no—
332#396—28no—
333#380—28no—
334C2×#95C22×C5912yes—
335C2×#95C22×C5912yes—
336C2×#95C22×C5912yes—
337C2×#95C22×C5912yes—
338C2×#95C22×C5912yes—
339C2×#95C22×C5911yescharacteristic
340C2×#95C22×C5912yes—
341C2×#95C22×C5911yescharacteristic
342C2×#95C22×C5912yes—
343C59#1630511yescharacteristic, direct product factor, Sylow
344C25C23×C5911yescharacteristic
345C23×C4—24no—
346C23×C4—24no—
347C23×C4—41no—
348C23×C4—41no—
349C23×C4Q8×C5914yes—
350C23×C4C23×C5912yes—
351C23×C4C23×C5912yes—
352C23×C4C23×C5912yes—
353C23×C4C23×C5912yes—
354C23×C4C23×C5912yes—
355C23×C4C23×C5911yescharacteristic
356C23×C4C23×C5911yescharacteristic
357C23×C4C23×C5912yes—
358C2×C4⋊C4—24no—
359C2×C4⋊C4—24no—
360C2×C4⋊C4—24no—
361C2×C4⋊C4—24no—
362C2×C4⋊C4—24no—
363C2×C4⋊C4—24no—
364C2×C4⋊C4—24no—
365C2×C4⋊C4—24no—
366C2×C4⋊C4—24no—
367C2×C4⋊C4—24no—
368C2×C4⋊C4—42no—
369C2×C4⋊C4—42no—
370C2×C4⋊C4—42no—
371C2×C4⋊C4—41no—
372C2×C4⋊C4—42no—
373C2×C4⋊C4—42no—
374C2×C4⋊C4—42no—
375C2×C4⋊C4—42no—
376C2×C4⋊C4—41no—
377C2×C22⋊C4—24no—
378C2×C22⋊C4—24no—
379C2×C22⋊C4—24no—
380C2×C22⋊C4—24no—
381C2×C22⋊C4—41no—
382C2×C22⋊C4—41no—
383C2×C22⋊C4—41no—
384C2×C22⋊C4—41no—
385C2×C22⋊C4—42no—
386C2×C22⋊C4—42no—
387C2×C22⋊C4D4×C5914yes—
388C2×C22⋊C4Q8×C5914yes—
389#95—24no—
390#95—24no—
391#95—24no—
392#95—24no—
393#95—24no—
394#95—41no—
395#95—41no—
396#95—42no—
397#95D4×C5918yes—
398C24—22no—
399C24—22no—
400C24—21no—
401C24—22no—
402C24—21no—
403C24—21no—
404C24—21no—
405C24—22no—
406C24C2×D4×C5912yes—
407C24C2×Q8×C5912yes—
408C24C2×Q8×C5912yes—
409C24C24×C5911yescharacteristic
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—21no—
423C22×C4—21no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—216no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—44no—
456C22×C4—44no—
457C22×C4—48no—
458C22×C4—44no—
459C22×C4C2×D4×C5914yes—
460C22×C4C2×D4×C5914yes—
461C22×C4C2×D4×C5914yes—
462C22×C4C2×D4×C5914yes—
463C22×C4C2×Q8×C5912yes—
464C22×C4C2×Q8×C5912yes—
465C22×C4C2×Q8×C5914yes—
466C22×C4#41×C5914yes—
467C4⋊C4—48no—
468C4⋊C4—48no—
469C4⋊C4—48no—
470C4⋊C4—48no—
471C4⋊C4—44no—
472C4⋊C4—48no—
473C4⋊C4—44no—
474C22⋊C4—44no—
475C22⋊C4—44no—
476C22⋊C4—48no—
477C22⋊C4—48no—
478C23—24no—
479C23—22no—
480C23—22no—
481C23—22no—
482C23—22no—
483C23—22no—
484C23—22no—
485C23—24no—
486C23—24no—
487C23—24no—
488C23—24no—
489C23—24no—
490C23—42no—
491C23—42no—
492C23—42no—
493C23—42no—
494C23—41no—
495C23—42no—
496C23—41no—
497C23—41no—
498C23—42no—
499C23—41no—
500C23C4⋊Q8×C5914yes—
501C23C22×D4×C5912yes—
502C23C22×D4×C5911yescharacteristic
503C23C22×Q8×C5911yescharacteristic
504C23C22×Q8×C5911yescharacteristic
505C23C2×#41×C5912yes—
506C23H(5,𝔽2)×C5911yescharacteristic
507C23H(5,𝔽2)×C5911yescharacteristic
508C23H(5,𝔽2)×C5912yes—
509C23H(5,𝔽2)×C5911yescharacteristic
510C232−1+4×C5911yescharacteristic
511C232−1+4×C5912yes—
512C2×C4—24no—
513C2×C4—24no—
514C2×C4—24no—
515C2×C4—24no—
516C2×C4—24no—
517C2×C4—24no—
518C2×C4—24no—
519C2×C4—24no—
520C2×C4—24no—
521C2×C4—22no—
522C2×C4—22no—
523C2×C4—24no—
524C2×C4—24no—
525C2×C4—24no—
526C2×C4—24no—
527C2×C4—24no—
528C2×C4—24no—
529C2×C4—24no—
530C2×C4—24no—
531C2×C4—416no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—41no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—41no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—42no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—42no—
563C2×C4—42no—
564C2×C4C22⋊Q8×C5918yes—
565C22—24no—
566C22—28no—
567C22—42no—
568C22—42no—
569C22—44no—
570C22—44no—
571C22—42no—
572C22—42no—
573C22—42no—
574C22—44no—
575C22—42no—
576C22C2×C22⋊Q8×C5912yes—
577C22C2×C4⋊Q8×C5911yescharacteristic
578C22C59×#53411yescharacteristic
579C22C59×#53712yes—
580C22C59×#53712yes—
581C22C59×#53711yescharacteristic
582C22C59×#54012yes—
583C22C59×#54112yes—
584C22C59×#54311yescharacteristic
585C22C59×#54311yescharacteristic
586C22C59×#54412yes—
587C22C59×#54411yescharacteristic
588C22C59×#54411yescharacteristic
589C22D42×C5912yes—
590C22D42×C5911yescharacteristic
591C22C59×#54612yes—
592C22C59×#54712yes—
593C22D4×Q8×C5912yes—
594C22C59×#55111yescharacteristic
595C22C59×#55412yes—
596C22C59×#56011yescharacteristic
597C22C59×#56212yes—
598C22C59×#56311yescharacteristic
599C4—28no—
600C4—42no—
601C4—44no—
602C4—44no—
603C4—44no—
604C4—42no—
605C4—82no—
606C4—82no—
607C2—44no—
608C2C59×#243711yescharacteristic
609C2C59×#244012yes—
610C2C59×#262912yes—
611C2C59×#265911yescharacteristic
612C2C59×#267112yes—
613C2C59×#267511yescharacteristic
614C2C59×#268311yescharacteristic
615C2C59×#270412yes—
616C2C59×#272211yescharacteristic
617C2C59×#274811yescharacteristic
618C2C59×#284111yescharacteristic
subgroupG/H
center, socleC24×C59C24
commutator, Frattini, cosocleC24C24×C59
prime radicalC25×C59C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C59 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C59×#398C2semidirect
4. C59×#1444C2semidirect
5. C59×#1444C2semidirect
6. C59×#1441C2semidirect
255. #16305C59direct (N × H)
298. C2×#398C2×C59semidirect
301. #1444C2×C59semidirect
302. #1444C2×C59semidirect
303. #1441C2×C59semidirect
343. C59#16305direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C59×#3982
C2×C59×#3962
C2×C59×#3802
C59×#14442
C59×#14412
C59×#14392
C59×C22⋊#952
#1630559