Finite Group Databasebeta

← C59×#24464 #28436573

Subgroups — C59×#24464 #28436573

Order 15104.

1600 conjugacy classes of subgroups.

The subgroup lattice has 1100 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C59×#3488C211yesmaximal, characteristic, complemented
2C59×#3055C211yesmaximal, characteristic, complemented
3C2×C59×#453C211yesmaximal, characteristic, complemented
4C59×#3006C211yesmaximal, characteristic, complemented
5C22×#104×C59C211yesmaximal, characteristic, complemented
6C59×#2856C211yesmaximal, characteristic, complemented
7C59×#2039C211yesmaximal, characteristic, complemented
8C59×#2037C211yesmaximal, characteristic, complemented
9C59×#2006C211yesmaximal, characteristic, complemented
10C59×#2002C211yesmaximal, characteristic, complemented
11C59×#1900C211yesmaximal, characteristic, complemented
12C59×#1896C211yesmaximal, characteristic, complemented
13C59×#1883C211yesmaximal, characteristic, complemented
14C59×#1859C211yesmaximal, characteristic, complemented
15C59×#1792C211yesmaximal, characteristic, complemented
16C2×H(5,𝔽2)×C59C2211yescharacteristic
17C22×#41×C59C2211yescharacteristic
18C2×AGL(1,ℤ/8)×C59C2211yescharacteristic
19C2×AGL(1,ℤ/8)×C59C2211yescharacteristic, complemented
20C2×AGL(1,ℤ/8)×C59C2211yescharacteristic, complemented
21C22×M16×C59C2211yescharacteristic, complemented
22C59×#550—21no—
23C59×#548—21no—
24C59×#546—21no—
25C59×#546—22no—
26D42×C59—22no—
27D42×C59—21no—
28C59×#537—21no—
29C59×#537C2211yescharacteristic
30C59×#535—21no—
31C59×#535C2211yescharacteristic
32C2×#127×C59C2211yescharacteristic, complemented
33C59×#525—21no—
34C59×#525C2211yescharacteristic
35C2×#121×C59—21no—
36C2×#121×C59—22no—
37C2×#121×C59C2211yescharacteristic
38C2×#121×C59C2211yescharacteristic, complemented
39C59×#520C2211yescharacteristic
40C22×C42×C59C2211yescharacteristic, complemented
41C59×#469—21no—
42C59×#468—21no—
43C59×#466—21no—
44C59×#465—21no—
45C59×#453—24no—
46C59×#449—21no—
47C59×#449—21no—
48C59×#448—21no—
49C59×#447—21no—
50C59×#428C2211yescharacteristic, complemented
51C2×#104×C59—24no—
52C2×#104×C59C2211yescharacteristic
53C2×#104×C59C2211yescharacteristic
54C2×#104×C59C2211yescharacteristic, complemented
55C2×#104×C59C2211yescharacteristic, complemented
56C2×#104×C59C2211yescharacteristic, complemented
57C2×#104×C59C2211yescharacteristic, complemented
58C59×#418C2211yescharacteristic, complemented
59C59×#417C2211yescharacteristic
60C59×#417C2211yescharacteristic, complemented
61C59×#417C2211yescharacteristic, complemented
62C2×#100×C59C2211yescharacteristic, complemented
63C2×#100×C59C2211yescharacteristic, complemented
64C59×#407C2211yescharacteristic, complemented
65C59×#390—22no—
66C59×#390C2211yescharacteristic, complemented
67C59×#390C2211yescharacteristic, complemented
68C59×#384C2211yescharacteristic, complemented
69C59×#343C2211yescharacteristic, complemented
70C59×#343C2211yescharacteristic, complemented
71C59×#339C2211yescharacteristic, complemented
72C59×#339C2211yescharacteristic, complemented
73H(5,𝔽2)×C59—22no—
74H(5,𝔽2)×C59—22no—
75H(5,𝔽2)×C59—41no—
76H(5,𝔽2)×C59—41no—
77C2×#41×C59—21no—
78C2×#41×C59—21no—
79C2×#41×C59—21no—
80C2×#41×C59—21no—
81C2×#41×C59—22no—
82C2×#41×C59—22no—
83C2×#41×C59—41no—
84C2×#41×C59—41no—
85C2×#41×C59D411yescharacteristic, complemented
86C2×#41×C59D411yescharacteristic, complemented
87C2×#41×C59C2311yescharacteristic
88C2×#41×C59C2311yescharacteristic
89C2×#41×C59C2311yescharacteristic
90C22×Q8×C59D411yescharacteristic, complemented
91C22×D4×C59—21no—
92C22×D4×C59—22no—
93C22×D4×C59—22no—
94C22×D4×C59—21no—
95C22×D4×C59—21no—
96C22×D4×C59—22no—
97C22×D4×C59—21no—
98C22×D4×C59D412yes—
99C22×D4×C59D411yescharacteristic, complemented
100C22×D4×C59C2311yescharacteristic
101C22×D4×C59C2311yescharacteristic
102C23×C4×C59—21no—
103C23×C4×C59—21no—
104C23×C4×C59C2311yescharacteristic
105AGL(1,ℤ/8)×C59—22no—
106AGL(1,ℤ/8)×C59—22no—
107AGL(1,ℤ/8)×C59—22no—
108AGL(1,ℤ/8)×C59—41no—
109AGL(1,ℤ/8)×C59—41no—
110AGL(1,ℤ/8)×C59—41no—
111C2×SD16×C59—21no—
112C2×SD16×C59—21no—
113C2×SD16×C59—21no—
114C2×D8×C59—21no—
115C2×D8×C59—21no—
116C2×D8×C59—21no—
117C2×M16×C59—21no—
118C2×M16×C59—22no—
119C2×M16×C59—41no—
120C2×M16×C59C2311yescharacteristic
121C2×M16×C59C2311yescharacteristic
122C2×M16×C59C2311yescharacteristic
123C2×M16×C59C2311yescharacteristic
124C22×C8×C59—21no—
125#127×C59—22no—
126#127×C59—21no—
127#127×C59—22no—
128#127×C59—41no—
129#124×C59—22no—
130#124×C59—21no—
131#123×C59—22no—
132#123×C59—21no—
133C22⋊Q8×C59—22no—
134C22⋊Q8×C59—21no—
135C22⋊Q8×C59—21no—
136C22⋊Q8×C59D411yescharacteristic, complemented
137C22⋊Q8×C59D411yescharacteristic, complemented
138#121×C59—22no—
139#121×C59—22no—
140#121×C59—22no—
141#121×C59—22no—
142#121×C59—22no—
143#121×C59—21no—
144#121×C59—21no—
145#121×C59—21no—
146#121×C59—21no—
147#121×C59—21no—
148#121×C59—21no—
149#121×C59—22no—
150#121×C59—21no—
151#121×C59—21no—
152#121×C59—21no—
153#121×C59—21no—
154#121×C59—21no—
155#121×C59—21no—
156#121×C59—48no—
157#121×C59D411yescharacteristic, complemented
158#121×C59D411yescharacteristic, complemented
159#120×C59—22no—
160#120×C59—22no—
161#120×C59—22no—
162#120×C59—21no—
163#120×C59—22no—
164C4×Q8×C59—21no—
165C4×D4×C59—22no—
166C4×D4×C59—22no—
167C4×D4×C59—21no—
168C4×D4×C59—22no—
169C4×D4×C59—21no—
170C4×D4×C59—21no—
171#117×C59—21no—
172#117×C59C2311yescharacteristic
173C2×C4⋊C4×C59—21no—
174C2×C4⋊C4×C59—22no—
175C2×C4⋊C4×C59C2311yescharacteristic
176C2×C4⋊C4×C59C2311yescharacteristic
177C2×C22⋊C4×C59—22no—
178C2×C22⋊C4×C59—22no—
179C2×C22⋊C4×C59—21no—
180C2×C22⋊C4×C59—22no—
181C2×C22⋊C4×C59D412yes—
182C2×C42×C59—22no—
183C2×C42×C59—21no—
184C2×C42×C59—41no—
185C2×C42×C59C2311yescharacteristic
186C2×C42×C59C2311yescharacteristic
187#107×C59—21no—
188#106×C59—21no—
189#104×C59—22no—
190#104×C59—22no—
191#104×C59—22no—
192#104×C59—22no—
193#104×C59—41no—
194#104×C59D414yescomplemented
195#103×C59—21no—
196#103×C59—21no—
197#103×C59—21no—
198#102×C59—21no—
199#102×C59—21no—
200#102×C59—21no—
201#102×C59—21no—
202#102×C59—21no—
203#100×C59—22no—
204#100×C59—41no—
205C22⋊C8×C59—21no—
206C22⋊C8×C59—21no—
207C24×C59—22no—
208C24×C59—21no—
209C24×C59—21no—
210C24×C59C2×D411yescharacteristic
211C24×C59C2×D412yes—
212#41×C59—21no—
213#41×C59—21no—
214#41×C59—22no—
215#41×C59—22no—
216#41×C59—21no—
217#41×C59—21no—
218#41×C59—21no—
219#41×C59—21no—
220#41×C59—21no—
221#41×C59—21no—
222#41×C59—21no—
223#41×C59—21no—
224#41×C59—42no—
225#41×C59—42no—
226#41×C59—41no—
227#41×C59—41no—
228#41×C59—42no—
229#41×C59—42no—
230#41×C59—42no—
231#41×C59—42no—
232#41×C59—42no—
233#41×C59—42no—
234#41×C59C2×D412yes—
235#41×C59#4112yes—
236C2×Q8×C59—21no—
237C2×Q8×C59—22no—
238C2×Q8×C59—41no—
239C2×Q8×C59C2×D411yescharacteristic
240C2×Q8×C59C2×D411yescharacteristic
241C2×Q8×C59C2×D411yescharacteristic
242C2×D4×C59—21no—
243C2×D4×C59—22no—
244C2×D4×C59—22no—
245C2×D4×C59—22no—
246C2×D4×C59—22no—
247C2×D4×C59—21no—
248C2×D4×C59—21no—
249C2×D4×C59—21no—
250C2×D4×C59—21no—
251C2×D4×C59—21no—
252C2×D4×C59—22no—
253C2×D4×C59—22no—
254C2×D4×C59—22no—
255C2×D4×C59—21no—
256C2×D4×C59—22no—
257C2×D4×C59—21no—
258C2×D4×C59—21no—
259C2×D4×C59—21no—
260C2×D4×C59—21no—
261C2×D4×C59—21no—
262C2×D4×C59—21no—
263C2×D4×C59—21no—
264C2×D4×C59—21no—
265C2×D4×C59—21no—
266C2×D4×C59—21no—
267C2×D4×C59—21no—
268C2×D4×C59—21no—
269C2×D4×C59—21no—
270C2×D4×C59—41no—
271C2×D4×C59—42no—
272C2×D4×C59—42no—
273C2×D4×C59—44no—
274C2×D4×C59—44no—
275C2×D4×C59—44no—
276C2×D4×C59—42no—
277C2×D4×C59—42no—
278C2×D4×C59—44no—
279C2×D4×C59—44no—
280C2×D4×C59—42no—
281C2×D4×C59—42no—
282C2×D4×C59—44no—
283C2×D4×C59—44no—
284C2×D4×C59—41no—
285C2×D4×C59—41no—
286C2×D4×C59—84no—
287C2×D4×C59C2×D411yescharacteristic
288C2×D4×C59C2×D411yescharacteristic
289C2×D4×C59C2×D411yescharacteristic
290C22×C4×C59—21no—
291C22×C4×C59—21no—
292C22×C4×C59—21no—
293C22×C4×C59—21no—
294C22×C4×C59—21no—
295C22×C4×C59—21no—
296C22×C4×C59—22no—
297C22×C4×C59—24no—
298C22×C4×C59—21no—
299C22×C4×C59—21no—
300C22×C4×C59—22no—
301C22×C4×C59—21no—
302C22×C4×C59—21no—
303C22×C4×C59—21no—
304C22×C4×C59—21no—
305C22×C4×C59—21no—
306C22×C4×C59—42no—
307C22×C4×C59—42no—
308C22×C4×C59—42no—
309C22×C4×C59—42no—
310C22×C4×C59C2×D411yescharacteristic
311C22×C4×C59C2×D411yescharacteristic
312C22×C4×C59C2×D411yescharacteristic
313C22×C4×C59C2×D411yescharacteristic
314C22×C4×C59C2×D411yescharacteristic
315C22×C4×C59C2×D412yes—
316C22×C4×C59C2411yescharacteristic
317SD16×C59—42no—
318SD16×C59—42no—
319SD16×C59—42no—
320D8×C59—42no—
321D8×C59—42no—
322D8×C59—42no—
323M16×C59—21no—
324M16×C59—21no—
325M16×C59—21no—
326M16×C59—21no—
327M16×C59—21no—
328M16×C59—21no—
329M16×C59—21no—
330M16×C59—42no—
331M16×C59C2×D412yescomplemented
332C2×C8×C59—21no—
333C2×C8×C59—21no—
334C2×C8×C59—21no—
335C2×C8×C59—21no—
336C2×C8×C59—42no—
337C4⋊C4×C59—22no—
338C4⋊C4×C59—22no—
339C4⋊C4×C59—21no—
340C4⋊C4×C59—21no—
341C4⋊C4×C59—21no—
342C4⋊C4×C59—21no—
343C4⋊C4×C59—21no—
344C4⋊C4×C59—21no—
345C4⋊C4×C59—44no—
346C4⋊C4×C59C2×D411yescharacteristic
347C4⋊C4×C59C2×D411yescharacteristic
348C22⋊C4×C59—22no—
349C22⋊C4×C59—22no—
350C22⋊C4×C59—22no—
351C22⋊C4×C59—22no—
352C22⋊C4×C59—22no—
353C22⋊C4×C59—21no—
354C22⋊C4×C59—21no—
355C22⋊C4×C59—21no—
356C22⋊C4×C59—21no—
357C22⋊C4×C59—22no—
358C22⋊C4×C59—22no—
359C22⋊C4×C59—21no—
360C22⋊C4×C59—44no—
361C22⋊C4×C59—44no—
362C22⋊C4×C59—41no—
363C22⋊C4×C59—41no—
364C42×C59—22no—
365C42×C59—21no—
366C42×C59—21no—
367C42×C59—21no—
368C42×C59—21no—
369C42×C59—42no—
370C42×C59C2×D412yescomplemented
371C23×C59—21no—
372C23×C59—21no—
373C23×C59—21no—
374C23×C59—22no—
375C23×C59—22no—
376C23×C59—21no—
377C23×C59—21no—
378C23×C59—22no—
379C23×C59—22no—
380C23×C59—41no—
381C23×C59—42no—
382C23×C59—44no—
383C23×C59—42no—
384C23×C59—42no—
385C23×C59—42no—
386C23×C59—42no—
387C23×C59—42no—
388C23×C59—41no—
389C23×C59—41no—
390C23×C59—41no—
391C23×C59—81no—
392C23×C59—82no—
393C23×C59—82no—
394C23×C59#12011yescharacteristic
395C23×C59#12011yescharacteristic
396C23×C59C22×D411yescharacteristic
397Q8×C59—21no—
398Q8×C59—21no—
399Q8×C59—21no—
400Q8×C59—21no—
401Q8×C59—21no—
402Q8×C59—42no—
403Q8×C59#12112yescomplemented
404D4×C59—22no—
405D4×C59—22no—
406D4×C59—21no—
407D4×C59—21no—
408D4×C59—21no—
409D4×C59—21no—
410D4×C59—21no—
411D4×C59—42no—
412D4×C59—42no—
413D4×C59—44no—
414D4×C59—42no—
415D4×C59—44no—
416D4×C59—41no—
417D4×C59—41no—
418D4×C59—41no—
419D4×C59—41no—
420D4×C59—44no—
421D4×C59—42no—
422D4×C59—41no—
423D4×C59—41no—
424D4×C59—41no—
425D4×C59—41no—
426D4×C59—41no—
427D4×C59—41no—
428D4×C59—41no—
429D4×C59—41no—
430D4×C59—88no—
431D4×C59—81no—
432D4×C59—82no—
433D4×C59—82no—
434D4×C59—82no—
435D4×C59—82no—
436D4×C59—82no—
437D4×C59—82no—
438D4×C59#12112yescomplemented
439C2×C4×C59—22no—
440C2×C4×C59—22no—
441C2×C4×C59—21no—
442C2×C4×C59—22no—
443C2×C4×C59—21no—
444C2×C4×C59—21no—
445C2×C4×C59—21no—
446C2×C4×C59—21no—
447C2×C4×C59—21no—
448C2×C4×C59—21no—
449C2×C4×C59—21no—
450C2×C4×C59—21no—
451C2×C4×C59—22no—
452C2×C4×C59—21no—
453C2×C4×C59—21no—
454C2×C4×C59—22no—
455C2×C4×C59—22no—
456C2×C4×C59—21no—
457C2×C4×C59—22no—
458C2×C4×C59—21no—
459C2×C4×C59—21no—
460C2×C4×C59—21no—
461C2×C4×C59—42no—
462C2×C4×C59—42no—
463C2×C4×C59—42no—
464C2×C4×C59—48no—
465C2×C4×C59—44no—
466C2×C4×C59—41no—
467C2×C4×C59—41no—
468C2×C4×C59—41no—
469C2×C4×C59—41no—
470C2×C4×C59—41no—
471C2×C4×C59—41no—
472C2×C4×C59—42no—
473C2×C4×C59—42no—
474C2×C4×C59—41no—
475C2×C4×C59—82no—
476C2×C4×C59#12011yescharacteristic
477C2×C4×C59#12011yescharacteristic
478C2×C4×C59C22×D411yescharacteristic
479C2×C4×C59C22×D411yescharacteristic
480C2×C4×C59C22×D411yescharacteristic
481C2×C4×C59C2×#4111yescharacteristic
482C2×C4×C59H(5,𝔽2)11yescharacteristic
483C2×C4×C59H(5,𝔽2)11yescharacteristic
484C8×C59—22no—
485C8×C59—41no—
486C8×C59—41no—
487C8×C59—41no—
488#24464C5911yesmaximal, characteristic, direct product factor, Sylow
489C22×C59—21no—
490C22×C59—21no—
491C22×C59—21no—
492C22×C59—21no—
493C22×C59—21no—
494C22×C59—22no—
495C22×C59—21no—
496C22×C59—21no—
497C22×C59—42no—
498C22×C59—42no—
499C22×C59—41no—
500C22×C59—41no—
501C22×C59—41no—
502C22×C59—41no—
503C22×C59—42no—
504C22×C59—42no—
505C22×C59—41no—
506C22×C59—41no—
507C22×C59—41no—
508C22×C59—42no—
509C22×C59—41no—
510C22×C59—84no—
511C22×C59—82no—
512C22×C59—82no—
513C22×C59—82no—
514C22×C59—82no—
515C22×C59—81no—
516C22×C59—81no—
517C22×C59—81no—
518C22×C59—164no—
519C22×C59#45312yescomplemented
520C22×C59C2×#12011yescharacteristic
521C22×C59D4211yescharacteristic
522C22×C59#54611yescharacteristic
523C4×C59—24no—
524C4×C59—21no—
525C4×C59—21no—
526C4×C59—22no—
527C4×C59—42no—
528C4×C59—41no—
529C4×C59—41no—
530C4×C59—42no—
531C4×C59—41no—
532C4×C59—41no—
533C4×C59—81no—
534C4×C59C2×#12111yescharacteristic
535C4×C59#53411yescharacteristic
536C4×C59D4211yescharacteristic
537C4×C59#54611yescharacteristic
538#3488C2×C5911yescharacteristic, complemented
539#3055C2×C5911yescharacteristic, complemented
540C2×#453C2×C5911yescharacteristic, complemented
541#3006C2×C5911yescharacteristic, complemented
542C22×#104C2×C5911yescharacteristic, complemented
543#2856C2×C5911yescharacteristic, complemented
544#2039C2×C5911yescharacteristic, complemented
545#2037C2×C5911yescharacteristic, complemented
546#2006C2×C5911yescharacteristic, complemented
547#2002C2×C5911yescharacteristic, complemented
548#1900C2×C5911yescharacteristic, complemented
549#1896C2×C5911yescharacteristic, complemented
550#1883C2×C5911yescharacteristic, complemented
551#1859C2×C5911yescharacteristic, complemented
552#1792C2×C5911yescharacteristic, complemented
553C2×C59—21no—
554C2×C59—21no—
555C2×C59—22no—
556C2×C59—41no—
557C2×C59—42no—
558C2×C59—81no—
559C2×C59—82no—
560C2×C59—81no—
561C2×C59—161no—
562C2×C59#241011yescharacteristic
563C2×C59C2×#45311yescharacteristic
564C2×C59#301811yescharacteristic
565C2×H(5,𝔽2)C22×C5911yescharacteristic
566C22×#41C22×C5911yescharacteristic
567C2×AGL(1,ℤ/8)C22×C5911yescharacteristic
568C2×AGL(1,ℤ/8)C22×C5911yescharacteristic, complemented
569C2×AGL(1,ℤ/8)C22×C5911yescharacteristic, complemented
570C22×M16C22×C5911yescharacteristic, complemented
571#550—21no—
572#548—21no—
573#546—21no—
574#546—22no—
575D42—22no—
576D42—21no—
577#537—21no—
578#537C22×C5911yescharacteristic
579#535—21no—
580#535C22×C5911yescharacteristic
581C2×#127C22×C5911yescharacteristic, complemented
582#525—21no—
583#525C22×C5911yescharacteristic
584C2×#121—21no—
585C2×#121—22no—
586C2×#121C22×C5911yescharacteristic
587C2×#121C22×C5911yescharacteristic, complemented
588#520C22×C5911yescharacteristic
589C22×C42C22×C5911yescharacteristic, complemented
590#469—21no—
591#468—21no—
592#466—21no—
593#465—21no—
594#453—24no—
595#449—21no—
596#449—21no—
597#448—21no—
598#447—21no—
599#428C22×C5911yescharacteristic, complemented
600C2×#104—24no—
601C2×#104C22×C5911yescharacteristic
602C2×#104C22×C5911yescharacteristic
603C2×#104C22×C5911yescharacteristic, complemented
604C2×#104C22×C5911yescharacteristic, complemented
605C2×#104C22×C5911yescharacteristic, complemented
606C2×#104C22×C5911yescharacteristic, complemented
607#418C22×C5911yescharacteristic, complemented
608#417C22×C5911yescharacteristic
609#417C22×C5911yescharacteristic, complemented
610#417C22×C5911yescharacteristic, complemented
611C2×#100C22×C5911yescharacteristic, complemented
612C2×#100C22×C5911yescharacteristic, complemented
613#407C22×C5911yescharacteristic, complemented
614#390—22no—
615#390C22×C5911yescharacteristic, complemented
616#390C22×C5911yescharacteristic, complemented
617#384C22×C5911yescharacteristic, complemented
618#343C22×C5911yescharacteristic, complemented
619#343C22×C5911yescharacteristic, complemented
620#339C22×C5911yescharacteristic, complemented
621#339C22×C5911yescharacteristic, complemented
622C59#2446411yescharacteristic, direct product factor, Sylow
623H(5,𝔽2)—22no—
624H(5,𝔽2)—22no—
625H(5,𝔽2)—41no—
626H(5,𝔽2)—41no—
627C2×#41—21no—
628C2×#41—21no—
629C2×#41—21no—
630C2×#41—21no—
631C2×#41—22no—
632C2×#41—22no—
633C2×#41—41no—
634C2×#41—41no—
635C2×#41D4×C5911yescharacteristic, complemented
636C2×#41D4×C5911yescharacteristic, complemented
637C2×#41C23×C5911yescharacteristic
638C2×#41C23×C5911yescharacteristic
639C2×#41C23×C5911yescharacteristic
640C22×Q8D4×C5911yescharacteristic, complemented
641C22×D4—21no—
642C22×D4—22no—
643C22×D4—22no—
644C22×D4—21no—
645C22×D4—21no—
646C22×D4—21no—
647C22×D4—22no—
648C22×D4D4×C5912yes—
649C22×D4D4×C5911yescharacteristic, complemented
650C22×D4C23×C5911yescharacteristic
651C22×D4C23×C5911yescharacteristic
652C23×C4—21no—
653C23×C4—21no—
654C23×C4C23×C5911yescharacteristic
655AGL(1,ℤ/8)—22no—
656AGL(1,ℤ/8)—22no—
657AGL(1,ℤ/8)—22no—
658AGL(1,ℤ/8)—41no—
659AGL(1,ℤ/8)—41no—
660AGL(1,ℤ/8)—41no—
661C2×SD16—21no—
662C2×SD16—21no—
663C2×SD16—21no—
664C2×D8—21no—
665C2×D8—21no—
666C2×D8—21no—
667C2×M16—21no—
668C2×M16—22no—
669C2×M16—41no—
670C2×M16C23×C5911yescharacteristic
671C2×M16C23×C5911yescharacteristic
672C2×M16C23×C5911yescharacteristic
673C2×M16C23×C5911yescharacteristic
674C22×C8—21no—
675#127—22no—
676#127—21no—
677#127—22no—
678#127—41no—
679#124—22no—
680#124—21no—
681#123—22no—
682#123—21no—
683C22⋊Q8—22no—
684C22⋊Q8—21no—
685C22⋊Q8—21no—
686C22⋊Q8D4×C5911yescharacteristic, complemented
687C22⋊Q8D4×C5911yescharacteristic, complemented
688#121—22no—
689#121—22no—
690#121—22no—
691#121—22no—
692#121—22no—
693#121—21no—
694#121—21no—
695#121—21no—
696#121—21no—
697#121—21no—
698#121—21no—
699#121—22no—
700#121—21no—
701#121—21no—
702#121—21no—
703#121—21no—
704#121—21no—
705#121—21no—
706#121—48no—
707#121D4×C5911yescharacteristic, complemented
708#121D4×C5911yescharacteristic, complemented
709#120—22no—
710#120—22no—
711#120—22no—
712#120—21no—
713#120—22no—
714C4×Q8—21no—
715C4×D4—22no—
716C4×D4—22no—
717C4×D4—21no—
718C4×D4—22no—
719C4×D4—21no—
720C4×D4—21no—
721#117—21no—
722#117C23×C5911yescharacteristic
723C2×C4⋊C4—21no—
724C2×C4⋊C4—22no—
725C2×C4⋊C4C23×C5911yescharacteristic
726C2×C4⋊C4C23×C5911yescharacteristic
727C2×C22⋊C4—22no—
728C2×C22⋊C4—22no—
729C2×C22⋊C4—22no—
730C2×C22⋊C4—21no—
731C2×C22⋊C4D4×C5912yes—
732C2×C42—22no—
733C2×C42—21no—
734C2×C42—41no—
735C2×C42C23×C5911yescharacteristic
736C2×C42C23×C5911yescharacteristic
737#107—21no—
738#106—21no—
739#104—22no—
740#104—22no—
741#104—22no—
742#104—22no—
743#104—41no—
744#104D4×C5914yescomplemented
745#103—21no—
746#103—21no—
747#103—21no—
748#102—21no—
749#102—21no—
750#102—21no—
751#102—21no—
752#102—21no—
753#100—22no—
754#100—41no—
755C22⋊C8—21no—
756C22⋊C8—21no—
757C24—22no—
758C24—21no—
759C24—21no—
760C24C2×D4×C5911yescharacteristic
761C24C2×D4×C5912yes—
762#41—21no—
763#41—21no—
764#41—22no—
765#41—22no—
766#41—21no—
767#41—21no—
768#41—21no—
769#41—21no—
770#41—21no—
771#41—21no—
772#41—21no—
773#41—21no—
774#41—42no—
775#41—42no—
776#41—41no—
777#41—41no—
778#41—42no—
779#41—42no—
780#41—42no—
781#41—42no—
782#41—42no—
783#41—42no—
784#41C2×D4×C5912yes—
785#41#41×C5912yes—
786C2×Q8—21no—
787C2×Q8—22no—
788C2×Q8—41no—
789C2×Q8C2×D4×C5911yescharacteristic
790C2×Q8C2×D4×C5911yescharacteristic
791C2×Q8C2×D4×C5911yescharacteristic
792C2×D4—21no—
793C2×D4—22no—
794C2×D4—22no—
795C2×D4—22no—
796C2×D4—22no—
797C2×D4—21no—
798C2×D4—21no—
799C2×D4—21no—
800C2×D4—21no—
801C2×D4—21no—
802C2×D4—22no—
803C2×D4—22no—
804C2×D4—22no—
805C2×D4—21no—
806C2×D4—22no—
807C2×D4—21no—
808C2×D4—21no—
809C2×D4—21no—
810C2×D4—21no—
811C2×D4—21no—
812C2×D4—21no—
813C2×D4—21no—
814C2×D4—21no—
815C2×D4—21no—
816C2×D4—21no—
817C2×D4—21no—
818C2×D4—21no—
819C2×D4—21no—
820C2×D4—41no—
821C2×D4—42no—
822C2×D4—42no—
823C2×D4—44no—
824C2×D4—44no—
825C2×D4—44no—
826C2×D4—42no—
827C2×D4—42no—
828C2×D4—44no—
829C2×D4—44no—
830C2×D4—42no—
831C2×D4—42no—
832C2×D4—44no—
833C2×D4—44no—
834C2×D4—41no—
835C2×D4—41no—
836C2×D4—84no—
837C2×D4C2×D4×C5911yescharacteristic
838C2×D4C2×D4×C5911yescharacteristic
839C2×D4C2×D4×C5911yescharacteristic
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—22no—
847C22×C4—24no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—22no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—42no—
857C22×C4—42no—
858C22×C4—42no—
859C22×C4—42no—
860C22×C4C2×D4×C5911yescharacteristic
861C22×C4C2×D4×C5911yescharacteristic
862C22×C4C2×D4×C5911yescharacteristic
863C22×C4C2×D4×C5911yescharacteristic
864C22×C4C2×D4×C5911yescharacteristic
865C22×C4C2×D4×C5912yes—
866C22×C4C24×C5911yescharacteristic
867SD16—42no—
868SD16—42no—
869SD16—42no—
870D8—42no—
871D8—42no—
872D8—42no—
873M16—21no—
874M16—21no—
875M16—21no—
876M16—21no—
877M16—21no—
878M16—21no—
879M16—21no—
880M16—42no—
881M16C2×D4×C5912yescomplemented
882C2×C8—21no—
883C2×C8—21no—
884C2×C8—21no—
885C2×C8—21no—
886C2×C8—42no—
887C4⋊C4—22no—
888C4⋊C4—22no—
889C4⋊C4—21no—
890C4⋊C4—21no—
891C4⋊C4—21no—
892C4⋊C4—21no—
893C4⋊C4—21no—
894C4⋊C4—21no—
895C4⋊C4—44no—
896C4⋊C4C2×D4×C5911yescharacteristic
897C4⋊C4C2×D4×C5911yescharacteristic
898C22⋊C4—22no—
899C22⋊C4—22no—
900C22⋊C4—22no—
901C22⋊C4—22no—
902C22⋊C4—22no—
903C22⋊C4—21no—
904C22⋊C4—21no—
905C22⋊C4—21no—
906C22⋊C4—21no—
907C22⋊C4—22no—
908C22⋊C4—22no—
909C22⋊C4—21no—
910C22⋊C4—44no—
911C22⋊C4—44no—
912C22⋊C4—41no—
913C22⋊C4—41no—
914C42—22no—
915C42—21no—
916C42—21no—
917C42—21no—
918C42—21no—
919C42—42no—
920C42C2×D4×C5912yescomplemented
921C23—22no—
922C23—21no—
923C23—21no—
924C23—21no—
925C23—22no—
926C23—21no—
927C23—21no—
928C23—22no—
929C23—22no—
930C23—41no—
931C23—42no—
932C23—44no—
933C23—42no—
934C23—42no—
935C23—42no—
936C23—42no—
937C23—42no—
938C23—41no—
939C23—41no—
940C23—41no—
941C23—81no—
942C23—82no—
943C23—82no—
944C23#120×C5911yescharacteristic
945C23#120×C5911yescharacteristic
946C23C22×D4×C5911yescharacteristic
947Q8—21no—
948Q8—21no—
949Q8—21no—
950Q8—21no—
951Q8—21no—
952Q8—42no—
953Q8#121×C5912yescomplemented
954D4—22no—
955D4—22no—
956D4—21no—
957D4—21no—
958D4—21no—
959D4—21no—
960D4—21no—
961D4—42no—
962D4—42no—
963D4—44no—
964D4—42no—
965D4—44no—
966D4—44no—
967D4—42no—
968D4—41no—
969D4—41no—
970D4—41no—
971D4—41no—
972D4—41no—
973D4—41no—
974D4—41no—
975D4—41no—
976D4—41no—
977D4—41no—
978D4—41no—
979D4—41no—
980D4—88no—
981D4—81no—
982D4—82no—
983D4—82no—
984D4—82no—
985D4—82no—
986D4—82no—
987D4—82no—
988D4#121×C5912yescomplemented
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—21no—
992C2×C4—22no—
993C2×C4—21no—
994C2×C4—21no—
995C2×C4—21no—
996C2×C4—21no—
997C2×C4—21no—
998C2×C4—21no—
999C2×C4—21no—
1000C2×C4—21no—
1001C2×C4—22no—
1002C2×C4—21no—
1003C2×C4—21no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—21no—
1007C2×C4—22no—
1008C2×C4—21no—
1009C2×C4—21no—
1010C2×C4—21no—
1011C2×C4—42no—
1012C2×C4—42no—
1013C2×C4—42no—
1014C2×C4—48no—
1015C2×C4—44no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—42no—
1023C2×C4—42no—
1024C2×C4—41no—
1025C2×C4—82no—
1026C2×C4#120×C5911yescharacteristic
1027C2×C4#120×C5911yescharacteristic
1028C2×C4C22×D4×C5911yescharacteristic
1029C2×C4C22×D4×C5911yescharacteristic
1030C2×C4C22×D4×C5911yescharacteristic
1031C2×C4C2×#41×C5911yescharacteristic
1032C2×C4H(5,𝔽2)×C5911yescharacteristic
1033C2×C4H(5,𝔽2)×C5911yescharacteristic
1034C8—22no—
1035C8—41no—
1036C8—41no—
1037C8—41no—
1038C22—21no—
1039C22—21no—
1040C22—21no—
1041C22—21no—
1042C22—21no—
1043C22—21no—
1044C22—21no—
1045C22—22no—
1046C22—42no—
1047C22—42no—
1048C22—41no—
1049C22—41no—
1050C22—42no—
1051C22—41no—
1052C22—41no—
1053C22—41no—
1054C22—42no—
1055C22—41no—
1056C22—41no—
1057C22—41no—
1058C22—42no—
1059C22—84no—
1060C22—82no—
1061C22—82no—
1062C22—82no—
1063C22—82no—
1064C22—81no—
1065C22—81no—
1066C22—81no—
1067C22—164no—
1068C22C59×#45312yescomplemented
1069C22C2×#120×C5911yescharacteristic
1070C22D42×C5911yescharacteristic
1071C22C59×#54611yescharacteristic
1072C4—24no—
1073C4—21no—
1074C4—21no—
1075C4—22no—
1076C4—42no—
1077C4—42no—
1078C4—41no—
1079C4—41no—
1080C4—41no—
1081C4—41no—
1082C4—81no—
1083C4C2×#121×C5911yescharacteristic
1084C4C59×#53411yescharacteristic
1085C4D42×C5911yescharacteristic
1086C4C59×#54611yescharacteristic
1087C2—21no—
1088C2—21no—
1089C2—22no—
1090C2—41no—
1091C2—42no—
1092C2—81no—
1093C2—82no—
1094C2—81no—
1095C2—161no—
1096C2C59×#241011yescharacteristic
1097C2C2×C59×#45311yescharacteristic
1098C2C59×#301811yescharacteristic
subgroupG/H
center, socleC22×C59C2×#120
commutator, Frattini, cosocleC22×C4C24×C59
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C59 ◁ C23×C4×C59 ◁ G

Complements

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

NH ≅ G/Ntype
1. C59×#3488C2semidirect
2. C59×#3055C2semidirect
3. C2×C59×#453C2semidirect
4. C59×#3006C2semidirect
5. C22×#104×C59C2semidirect
6. C59×#2856C2semidirect
7. C59×#2039C2semidirect
8. C59×#2037C2semidirect
9. C59×#2006C2semidirect
10. C59×#2002C2semidirect
11. C59×#1900C2semidirect
12. C59×#1896C2semidirect
13. C59×#1883C2semidirect
14. C59×#1859C2semidirect
15. C59×#1792C2semidirect
19. C2×AGL(1,ℤ/8)×C59C22semidirect
20. C2×AGL(1,ℤ/8)×C59C22semidirect
21. C22×M16×C59C22semidirect
32. C2×#127×C59C22semidirect
38. C2×#121×C59C22semidirect
40. C22×C42×C59C22semidirect
50. C59×#428C22semidirect
54. C2×#104×C59C22semidirect
55. C2×#104×C59C22semidirect
56. C2×#104×C59C22semidirect
57. C2×#104×C59C22semidirect
58. C59×#418C22semidirect
60. C59×#417C22semidirect
61. C59×#417C22semidirect
62. C2×#100×C59C22semidirect
63. C2×#100×C59C22semidirect
64. C59×#407C22semidirect
66. C59×#390C22semidirect
67. C59×#390C22semidirect
68. C59×#384C22semidirect
69. C59×#343C22semidirect
70. C59×#343C22semidirect
71. C59×#339C22semidirect
72. C59×#339C22semidirect
85. C2×#41×C59D4semidirect
86. C2×#41×C59D4semidirect
90. C22×Q8×C59D4semidirect
99. C22×D4×C59D4semidirect
136. C22⋊Q8×C59D4semidirect
137. C22⋊Q8×C59D4semidirect
157. #121×C59D4semidirect
158. #121×C59D4semidirect
194. #104×C59D4semidirect
331. M16×C59C2×D4semidirect
370. C42×C59C2×D4semidirect
403. Q8×C59#121semidirect
438. D4×C59#121semidirect
488. #24464C59direct (N × H)
519. C22×C59#453semidirect
538. #3488C2×C59semidirect
539. #3055C2×C59semidirect
540. C2×#453C2×C59semidirect
541. #3006C2×C59semidirect
542. C22×#104C2×C59semidirect
543. #2856C2×C59semidirect
544. #2039C2×C59semidirect
545. #2037C2×C59semidirect
546. #2006C2×C59semidirect
547. #2002C2×C59semidirect
548. #1900C2×C59semidirect
549. #1896C2×C59semidirect
550. #1883C2×C59semidirect
551. #1859C2×C59semidirect
552. #1792C2×C59semidirect
568. C2×AGL(1,ℤ/8)C22×C59semidirect
569. C2×AGL(1,ℤ/8)C22×C59semidirect
570. C22×M16C22×C59semidirect
581. C2×#127C22×C59semidirect
587. C2×#121C22×C59semidirect
589. C22×C42C22×C59semidirect
599. #428C22×C59semidirect
603. C2×#104C22×C59semidirect
604. C2×#104C22×C59semidirect
605. C2×#104C22×C59semidirect
606. C2×#104C22×C59semidirect
607. #418C22×C59semidirect
609. #417C22×C59semidirect
610. #417C22×C59semidirect
611. C2×#100C22×C59semidirect
612. C2×#100C22×C59semidirect
613. #407C22×C59semidirect
615. #390C22×C59semidirect
616. #390C22×C59semidirect
617. #384C22×C59semidirect
618. #343C22×C59semidirect
619. #343C22×C59semidirect
620. #339C22×C59semidirect
621. #339C22×C59semidirect
622. C59#24464direct (N × H)
635. C2×#41D4×C59semidirect
636. C2×#41D4×C59semidirect
640. C22×Q8D4×C59semidirect
649. C22×D4D4×C59semidirect
686. C22⋊Q8D4×C59semidirect
687. C22⋊Q8D4×C59semidirect
707. #121D4×C59semidirect
708. #121D4×C59semidirect
744. #104D4×C59semidirect
881. M16C2×D4×C59semidirect
920. C42C2×D4×C59semidirect
953. Q8#121×C59semidirect
988. D4#121×C59semidirect
1068. C22C59×#453semidirect

Maximal subgroups

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

subgroupindex
C59×#34882
C59×#30552
C2×C59×#4532
C59×#30062
C22×#104×C592
C59×#28562
C59×#20392
C59×#20372
C59×#20062
C59×#20022
C59×#19002
C59×#18962
C59×#18832
C59×#18592
C59×#17922
#2446459