Finite Group Databasebeta

← C59×#10394 #28422503

Subgroups — C59×#10394 #28422503

Order 15104.

772 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C59×#2617C211yesmaximal, characteristic
2C59×#1874C211yesmaximal, characteristic, complemented
3C59×#1852C211yesmaximal, characteristic, complemented
4C2×C59×#327C211yesmaximal, characteristic, complemented
5C2×C59×#323C211yesmaximal, characteristic, complemented
6C59×#1439C211yesmaximal, characteristic, complemented
7C59×#1294C211yesmaximal, characteristic, complemented
8C2×#121×C59C2211yescharacteristic
9C2×#120×C59—21no—
10C22×C4⋊C4×C59C2211yescharacteristic
11C22×C22⋊C4×C59—21no—
12C22×C22⋊C4×C59C2211yescharacteristic
13C2×#107×C59—21no—
14C2×#102×C59—21no—
15C2×C22⋊C8×C59C2211yescharacteristic
16C2×C22⋊C8×C59C2211yescharacteristic
17C59×#397—21no—
18C59×#394—21no—
19C59×#394—21no—
20C59×#392—21no—
21C59×#386—21no—
22C59×#380C2211yescharacteristic
23C2×#95×C59—21no—
24C2×#95×C59C2211yescharacteristic
25C59×#340—21no—
26C59×#340—21no—
27C59×#327—22no—
28C59×#323—22no—
29C25×C59D411yescharacteristic
30C22×D4×C59—21no—
31C22×D4×C59—21no—
32C22×D4×C59—21no—
33C22×D4×C59D411yescharacteristic
34C23×C4×C59—21no—
35C23×C4×C59—21no—
36C23×C4×C59D411yescharacteristic
37C23×C4×C59C2311yescharacteristic
38C22×C8×C59—21no—
39C22×C8×C59—21no—
40#121×C59—21no—
41#121×C59—21no—
42#121×C59—21no—
43#121×C59—21no—
44#120×C59—42no—
45#120×C59—42no—
46C2×C4⋊C4×C59—21no—
47C2×C4⋊C4×C59—21no—
48C2×C4⋊C4×C59—42no—
49C2×C4⋊C4×C59D411yescharacteristic
50C2×C4⋊C4×C59D411yescharacteristic
51C2×C4⋊C4×C59D411yescharacteristic
52C2×C22⋊C4×C59—21no—
53C2×C22⋊C4×C59—21no—
54C2×C22⋊C4×C59—21no—
55C2×C22⋊C4×C59—21no—
56C2×C22⋊C4×C59—21no—
57C2×C22⋊C4×C59—21no—
58C2×C22⋊C4×C59—21no—
59C2×C22⋊C4×C59—21no—
60C2×C22⋊C4×C59—21no—
61C2×C22⋊C4×C59—21no—
62C2×C22⋊C4×C59—21no—
63C2×C22⋊C4×C59—21no—
64C2×C22⋊C4×C59—42no—
65C2×C22⋊C4×C59—42no—
66C2×C22⋊C4×C59—42no—
67#107×C59—42no—
68#102×C59—42no—
69C22⋊C8×C59—21no—
70C22⋊C8×C59—21no—
71C22⋊C8×C59—21no—
72C22⋊C8×C59D412yescomplemented
73#95×C59—21no—
74#95×C59—21no—
75#95×C59—21no—
76#95×C59—21no—
77#95×C59—21no—
78#95×C59—42no—
79C24×C59—21no—
80C24×C59—21no—
81C24×C59—21no—
82C24×C59—21no—
83C24×C59—21no—
84C24×C59—21no—
85C24×C59—21no—
86C24×C59—41no—
87C24×C59—41no—
88C24×C59—41no—
89C24×C59—41no—
90C24×C59D812yes—
91C24×C59C2×D411yescharacteristic
92C2×D4×C59—21no—
93C2×D4×C59—21no—
94C2×D4×C59—41no—
95C2×D4×C59—41no—
96C2×D4×C59—42no—
97C2×D4×C59—42no—
98C2×D4×C59—41no—
99C2×D4×C59—41no—
100C2×D4×C59—41no—
101C2×D4×C59—41no—
102C2×D4×C59—41no—
103C2×D4×C59—41no—
104C2×D4×C59—81no—
105C2×D4×C59—81no—
106C2×D4×C59—81no—
107C2×D4×C59—81no—
108C22×C4×C59—22no—
109C22×C4×C59—22no—
110C22×C4×C59—21no—
111C22×C4×C59—21no—
112C22×C4×C59—21no—
113C22×C4×C59—21no—
114C22×C4×C59—21no—
115C22×C4×C59—21no—
116C22×C4×C59—41no—
117C22×C4×C59—41no—
118C22×C4×C59—41no—
119C22×C4×C59—41no—
120C22×C4×C59—41no—
121C22×C4×C59—41no—
122C22×C4×C59—41no—
123C22×C4×C59—41no—
124C22×C4×C59—41no—
125C22×C4×C59—41no—
126C22×C4×C59—41no—
127C22×C4×C59—41no—
128C22×C4×C59—41no—
129C22×C4×C59—41no—
130C22×C4×C59—41no—
131C22×C4×C59—41no—
132C22×C4×C59C2×D411yescharacteristic
133C22×C4×C59C2×D411yescharacteristic
134C22×C4×C59C2×D411yescharacteristic
135C22×C4×C59#4111yescharacteristic
136C22×C4×C59#4111yescharacteristic
137C22×C4×C59#4111yescharacteristic
138C2×C8×C59—22no—
139C2×C8×C59—41no—
140C2×C8×C59—41no—
141C2×C8×C59—41no—
142C2×C8×C59—41no—
143C2×C8×C59—41no—
144C4⋊C4×C59—22no—
145C4⋊C4×C59—22no—
146C4⋊C4×C59—21no—
147C4⋊C4×C59—21no—
148C4⋊C4×C59—41no—
149C4⋊C4×C59—41no—
150C4⋊C4×C59—41no—
151C4⋊C4×C59—41no—
152C22⋊C4×C59—42no—
153C22⋊C4×C59—42no—
154C22⋊C4×C59—48no—
155C22⋊C4×C59—41no—
156C22⋊C4×C59—41no—
157C22⋊C4×C59—41no—
158C22⋊C4×C59—41no—
159C22⋊C4×C59—41no—
160C22⋊C4×C59—41no—
161C22⋊C4×C59—41no—
162C22⋊C4×C59—41no—
163C22⋊C4×C59—81no—
164C22⋊C4×C59—81no—
165C23×C59—21no—
166C23×C59—21no—
167C23×C59—21no—
168C23×C59—21no—
169C23×C59—22no—
170C23×C59—22no—
171C23×C59—22no—
172C23×C59—42no—
173C23×C59—42no—
174C23×C59—42no—
175C23×C59—42no—
176C23×C59—42no—
177C23×C59—42no—
178C23×C59—41no—
179C23×C59—41no—
180C23×C59—41no—
181C23×C59—41no—
182C23×C59—41no—
183C23×C59—41no—
184C23×C59—41no—
185C23×C59—41no—
186C23×C59—41no—
187C23×C59—41no—
188C23×C59—41no—
189C23×C59—41no—
190C23×C59—41no—
191C23×C59—41no—
192C23×C59—41no—
193C23×C59—81no—
194C23×C59—81no—
195C23×C59—81no—
196C23×C59—81no—
197C23×C59—81no—
198C23×C59—81no—
199C23×C59#12011yescharacteristic
200C23×C59#12111yescharacteristic
201C23×C59#12311yescharacteristic
202C23×C59C2×D811yescharacteristic
203C23×C59#13511yescharacteristic
204C23×C59AGL(1,ℤ/8)11yescharacteristic
205C23×C59#13711yescharacteristic
206D4×C59—42no—
207D4×C59—81no—
208D4×C59—84no—
209D4×C59—84no—
210D4×C59—81no—
211D4×C59—81no—
212D4×C59—81no—
213D4×C59—81no—
214C2×C4×C59—21no—
215C2×C4×C59—21no—
216C2×C4×C59—21no—
217C2×C4×C59—21no—
218C2×C4×C59—41no—
219C2×C4×C59—41no—
220C2×C4×C59—41no—
221C2×C4×C59—41no—
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—41no—
229C2×C4×C59—41no—
230C2×C4×C59—41no—
231C2×C4×C59—41no—
232C2×C4×C59—41no—
233C2×C4×C59—41no—
234C2×C4×C59—41no—
235C2×C4×C59—41no—
236C2×C4×C59—41no—
237C2×C4×C59—41no—
238C2×C4×C59—42no—
239C2×C4×C59—41no—
240C2×C4×C59—41no—
241C2×C4×C59—81no—
242C2×C4×C59—81no—
243C2×C4×C59—81no—
244C2×C4×C59—81no—
245C2×C4×C59—81no—
246C2×C4×C59—81no—
247C2×C4×C59—81no—
248C2×C4×C59—81no—
249C2×C4×C59—81no—
250C2×C4×C59#12111yescharacteristic
251C2×C4×C59#12111yescharacteristic
252C2×C4×C59#12311yescharacteristic
253C2×C4×C59#12411yescharacteristic
254C8×C59—42no—
255C8×C59—81no—
256#10394C5911yesmaximal, characteristic, direct product factor, Sylow
257C22×C59—21no—
258C22×C59—21no—
259C22×C59—21no—
260C22×C59—21no—
261C22×C59—21no—
262C22×C59—21no—
263C22×C59—21no—
264C22×C59—21no—
265C22×C59—21no—
266C22×C59—21no—
267C22×C59—21no—
268C22×C59—21no—
269C22×C59—44no—
270C22×C59—42no—
271C22×C59—42no—
272C22×C59—42no—
273C22×C59—82no—
274C22×C59—82no—
275C22×C59—82no—
276C22×C59—81no—
277C22×C59—81no—
278C22×C59—81no—
279C22×C59—81no—
280C22×C59—81no—
281C22×C59—81no—
282C22×C59—81no—
283C22×C59—81no—
284C22×C59—81no—
285C22×C59—81no—
286C22×C59—81no—
287C22×C59#39411yescharacteristic
288C22×C59#44711yescharacteristic
289C22×C59#45211yescharacteristic
290C22×C59#45311yescharacteristic
291C22×C59#45511yescharacteristic
292C22×C59B(4,𝔽2)11yescharacteristic
293C22×C59#45811yescharacteristic
294C22×C59#46611yescharacteristic
295C22×C59#46811yescharacteristic
296C22×C59#48011yescharacteristic
297C22×C59#48211yescharacteristic
298C4×C59—21no—
299C4×C59—21no—
300C4×C59—21no—
301C4×C59—21no—
302C4×C59—82no—
303C4×C59—82no—
304C4×C59—81no—
305C4×C59—81no—
306C4×C59—81no—
307C4×C59—81no—
308#2617C2×C5911yescharacteristic
309#1874C2×C5911yescharacteristic, complemented
310#1852C2×C5911yescharacteristic, complemented
311C2×#327C2×C5911yescharacteristic, complemented
312C2×#323C2×C5911yescharacteristic, complemented
313#1439C2×C5911yescharacteristic, complemented
314#1294C2×C5911yescharacteristic, complemented
315C2×C59—21no—
316C2×C59—21no—
317C2×C59—21no—
318C2×C59—21no—
319C2×C59—82no—
320C2×C59—161no—
321C2×C59#159511yescharacteristic
322C2×C59#160611yescharacteristic
323C2×C59#160711yescharacteristic
324C2×C59#161811yescharacteristic
325C2×C59#203311yescharacteristic
326C2×C59#203711yescharacteristic
327C2×C59#204411yescharacteristic
328C2×#121C22×C5911yescharacteristic
329C2×#120—21no—
330C22×C4⋊C4C22×C5911yescharacteristic
331C22×C22⋊C4—21no—
332C22×C22⋊C4C22×C5911yescharacteristic
333C2×#107—21no—
334C2×#102—21no—
335C2×C22⋊C8C22×C5911yescharacteristic
336C2×C22⋊C8C22×C5911yescharacteristic
337#397—21no—
338#394—21no—
339#394—21no—
340#392—21no—
341#386—21no—
342#380C22×C5911yescharacteristic
343C2×#95—21no—
344C2×#95C22×C5911yescharacteristic
345#340—21no—
346#340—21no—
347#327—22no—
348#323—22no—
349C59#1039411yescharacteristic, direct product factor, Sylow
350C25D4×C5911yescharacteristic
351C22×D4—21no—
352C22×D4—21no—
353C22×D4—21no—
354C22×D4D4×C5911yescharacteristic
355C23×C4—21no—
356C23×C4—21no—
357C23×C4D4×C5911yescharacteristic
358C23×C4C23×C5911yescharacteristic
359C22×C8—21no—
360C22×C8—21no—
361#121—21no—
362#121—21no—
363#121—21no—
364#121—21no—
365#120—42no—
366#120—42no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—42no—
370C2×C4⋊C4D4×C5911yescharacteristic
371C2×C4⋊C4D4×C5911yescharacteristic
372C2×C4⋊C4D4×C5911yescharacteristic
373C2×C22⋊C4—21no—
374C2×C22⋊C4—21no—
375C2×C22⋊C4—21no—
376C2×C22⋊C4—21no—
377C2×C22⋊C4—21no—
378C2×C22⋊C4—21no—
379C2×C22⋊C4—21no—
380C2×C22⋊C4—21no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—21no—
384C2×C22⋊C4—21no—
385C2×C22⋊C4—42no—
386C2×C22⋊C4—42no—
387C2×C22⋊C4—42no—
388#107—42no—
389#102—42no—
390C22⋊C8—21no—
391C22⋊C8—21no—
392C22⋊C8—21no—
393C22⋊C8D4×C5912yescomplemented
394#95—21no—
395#95—21no—
396#95—21no—
397#95—21no—
398#95—21no—
399#95—42no—
400C24—21no—
401C24—21no—
402C24—21no—
403C24—21no—
404C24—21no—
405C24—21no—
406C24—21no—
407C24—41no—
408C24—41no—
409C24—41no—
410C24—41no—
411C24D8×C5912yes—
412C24C2×D4×C5911yescharacteristic
413C2×D4—21no—
414C2×D4—21no—
415C2×D4—41no—
416C2×D4—41no—
417C2×D4—42no—
418C2×D4—42no—
419C2×D4—41no—
420C2×D4—41no—
421C2×D4—41no—
422C2×D4—41no—
423C2×D4—41no—
424C2×D4—41no—
425C2×D4—81no—
426C2×D4—81no—
427C2×D4—81no—
428C2×D4—81no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—41no—
438C22×C4—41no—
439C22×C4—41no—
440C22×C4—41no—
441C22×C4—41no—
442C22×C4—41no—
443C22×C4—41no—
444C22×C4—41no—
445C22×C4—41no—
446C22×C4—41no—
447C22×C4—41no—
448C22×C4—41no—
449C22×C4—41no—
450C22×C4—41no—
451C22×C4—41no—
452C22×C4—41no—
453C22×C4C2×D4×C5911yescharacteristic
454C22×C4C2×D4×C5911yescharacteristic
455C22×C4C2×D4×C5911yescharacteristic
456C22×C4#41×C5911yescharacteristic
457C22×C4#41×C5911yescharacteristic
458C22×C4#41×C5911yescharacteristic
459C2×C8—22no—
460C2×C8—41no—
461C2×C8—41no—
462C2×C8—41no—
463C2×C8—41no—
464C2×C8—41no—
465C4⋊C4—22no—
466C4⋊C4—22no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—41no—
470C4⋊C4—41no—
471C4⋊C4—41no—
472C4⋊C4—41no—
473C22⋊C4—42no—
474C22⋊C4—42no—
475C22⋊C4—48no—
476C22⋊C4—41no—
477C22⋊C4—41no—
478C22⋊C4—41no—
479C22⋊C4—41no—
480C22⋊C4—41no—
481C22⋊C4—41no—
482C22⋊C4—41no—
483C22⋊C4—41no—
484C22⋊C4—81no—
485C22⋊C4—81no—
486C23—21no—
487C23—21no—
488C23—21no—
489C23—21no—
490C23—22no—
491C23—22no—
492C23—22no—
493C23—42no—
494C23—42no—
495C23—42no—
496C23—42no—
497C23—42no—
498C23—42no—
499C23—41no—
500C23—41no—
501C23—41no—
502C23—41no—
503C23—41no—
504C23—41no—
505C23—41no—
506C23—41no—
507C23—41no—
508C23—41no—
509C23—41no—
510C23—41no—
511C23—41no—
512C23—41no—
513C23—41no—
514C23—81no—
515C23—81no—
516C23—81no—
517C23—81no—
518C23—81no—
519C23—81no—
520C23#120×C5911yescharacteristic
521C23#121×C5911yescharacteristic
522C23#123×C5911yescharacteristic
523C23C2×D8×C5911yescharacteristic
524C23#135×C5911yescharacteristic
525C23AGL(1,ℤ/8)×C5911yescharacteristic
526C23#137×C5911yescharacteristic
527D4—42no—
528D4—81no—
529D4—84no—
530D4—84no—
531D4—81no—
532D4—81no—
533D4—81no—
534D4—81no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—42no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—81no—
563C2×C4—81no—
564C2×C4—81no—
565C2×C4—81no—
566C2×C4—81no—
567C2×C4—81no—
568C2×C4—81no—
569C2×C4—81no—
570C2×C4—81no—
571C2×C4#121×C5911yescharacteristic
572C2×C4#121×C5911yescharacteristic
573C2×C4#123×C5911yescharacteristic
574C2×C4#124×C5911yescharacteristic
575C8—42no—
576C8—81no—
577C22—21no—
578C22—21no—
579C22—21no—
580C22—21no—
581C22—21no—
582C22—21no—
583C22—21no—
584C22—21no—
585C22—21no—
586C22—21no—
587C22—21no—
588C22—21no—
589C22—44no—
590C22—42no—
591C22—42no—
592C22—42no—
593C22—82no—
594C22—82no—
595C22—82no—
596C22—81no—
597C22—81no—
598C22—81no—
599C22—81no—
600C22—81no—
601C22—81no—
602C22—81no—
603C22—81no—
604C22—81no—
605C22—81no—
606C22—81no—
607C22C59×#39411yescharacteristic
608C22C59×#44711yescharacteristic
609C22C59×#45211yescharacteristic
610C22C59×#45311yescharacteristic
611C22C59×#45511yescharacteristic
612C22C59×B(4,𝔽2)11yescharacteristic
613C22C59×#45811yescharacteristic
614C22C59×#46611yescharacteristic
615C22C59×#46811yescharacteristic
616C22C59×#48011yescharacteristic
617C22C59×#48211yescharacteristic
618C4—21no—
619C4—21no—
620C4—21no—
621C4—21no—
622C4—82no—
623C4—81no—
624C4—81no—
625C4—82no—
626C4—81no—
627C4—81no—
628C2—21no—
629C2—21no—
630C2—21no—
631C2—21no—
632C2—82no—
633C2—161no—
634C2C59×#159511yescharacteristic
635C2C59×#160611yescharacteristic
636C2C59×#160711yescharacteristic
637C2C59×#161811yescharacteristic
638C2C59×#203311yescharacteristic
639C2C59×#203711yescharacteristic
640C2C59×#204411yescharacteristic
subgroupG/H
center, socleC23×C59#120
commutator, Frattini, cosocleC23×C4C23×C59
prime radicalC59×#2617C2
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C59 ◁ C23×C4×C59 ◁ G

Complements

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

NH ≅ G/Ntype
2. C59×#1874C2semidirect
3. C59×#1852C2semidirect
4. C2×C59×#327C2semidirect
5. C2×C59×#323C2semidirect
6. C59×#1439C2semidirect
7. C59×#1294C2semidirect
72. C22⋊C8×C59D4semidirect
256. #10394C59direct (N × H)
309. #1874C2×C59semidirect
310. #1852C2×C59semidirect
311. C2×#327C2×C59semidirect
312. C2×#323C2×C59semidirect
313. #1439C2×C59semidirect
314. #1294C2×C59semidirect
349. C59#10394direct (N × H)
393. C22⋊C8D4×C59semidirect

Maximal subgroups

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

subgroupindex
C59×#26172
C59×#18742
C59×#18522
C2×C59×#3272
C2×C59×#3232
C59×#14392
C59×#12942
#1039459