Finite Group Databasebeta

← C59×#24467 #28436576

Subgroups — C59×#24467 #28436576

Order 15104.

1486 conjugacy classes of subgroups.

The subgroup lattice has 1068 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C59×#3488C211yesmaximal, characteristic
2C59×#3056C211yesmaximal, characteristic, complemented
3C2×C59×#455C211yesmaximal, characteristic, complemented
4C59×#3007C211yesmaximal, characteristic, complemented
5C22×#104×C59C211yesmaximal, characteristic, complemented
6C59×#2850C211yesmaximal, characteristic, complemented
7C59×#2040C211yesmaximal, characteristic, complemented
8C59×#2037C211yesmaximal, characteristic, complemented
9C59×#2007C211yesmaximal, characteristic, complemented
10C59×#2004C211yesmaximal, characteristic, complemented
11C59×#1900C211yesmaximal, characteristic, complemented
12C59×#1896C211yesmaximal, characteristic, complemented
13C59×#1882C211yesmaximal, characteristic, complemented
14C59×#1860C211yesmaximal, characteristic, complemented
15C59×#1792C211yesmaximal, characteristic, complemented
16C2×H(5,𝔽2)×C59C2211yescharacteristic
17C22×#41×C59C2211yescharacteristic
18C2×#137×C59C2211yescharacteristic
19C2×#137×C59C2211yescharacteristic, complemented
20C2×#137×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×#124×C59C2211yescharacteristic, complemented
33C59×#525—21no—
34C59×#525C2211yescharacteristic
35C2×C22⋊Q8×C59C2211yescharacteristic, complemented
36C2×#121×C59—21no—
37C2×#121×C59C2211yescharacteristic
38C59×#520C2211yescharacteristic
39C22×C42×C59C2211yescharacteristic, complemented
40C59×#470—21no—
41C59×#468—21no—
42C59×#467—21no—
43C59×#465—21no—
44C59×#455—24no—
45C59×#452—21no—
46C59×#452—21no—
47C59×#451—21no—
48C59×#450—21no—
49C59×#428C2211yescharacteristic, complemented
50C2×#104×C59—24no—
51C2×#104×C59C2211yescharacteristic
52C2×#104×C59C2211yescharacteristic
53C2×#104×C59C2211yescharacteristic, complemented
54C2×#104×C59C2211yescharacteristic, complemented
55C2×#104×C59C2211yescharacteristic, complemented
56C2×#104×C59C2211yescharacteristic, complemented
57C59×#419C2211yescharacteristic, complemented
58C59×#417C2211yescharacteristic
59C59×#417C2211yescharacteristic, complemented
60C59×#417C2211yescharacteristic, complemented
61C2×#100×C59C2211yescharacteristic, complemented
62C2×#100×C59C2211yescharacteristic, complemented
63C59×#407C2211yescharacteristic, complemented
64C59×#391C2211yescharacteristic, complemented
65C59×#390C2211yescharacteristic, complemented
66C59×#388—22no—
67C59×#386—22no—
68C59×#382C2211yescharacteristic, 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
86C2×#41×C59D411yescharacteristic
87C2×#41×C59C2311yescharacteristic
88C2×#41×C59C2311yescharacteristic
89C2×#41×C59C2311yescharacteristic
90C22×Q8×C59D411yescharacteristic
91C22×Q8×C59C2311yescharacteristic
92C22×D4×C59—21no—
93C22×D4×C59—22no—
94C22×D4×C59—22no—
95C22×D4×C59—21no—
96C22×D4×C59—21no—
97C22×D4×C59D411yescharacteristic
98C22×D4×C59D412yes—
99C22×D4×C59C2311yescharacteristic
100C23×C4×C59—21no—
101C23×C4×C59—21no—
102C23×C4×C59C2311yescharacteristic
103#137×C59—22no—
104#137×C59—22no—
105#137×C59—22no—
106#137×C59—41no—
107#137×C59—41no—
108#137×C59—41no—
109C2×Q16×C59—21no—
110C2×Q16×C59—21no—
111C2×Q16×C59—21no—
112C2×SD16×C59—21no—
113C2×SD16×C59—21no—
114C2×SD16×C59—21no—
115C2×M16×C59—21no—
116C2×M16×C59—22no—
117C2×M16×C59—41no—
118C2×M16×C59C2311yescharacteristic
119C2×M16×C59C2311yescharacteristic
120C2×M16×C59C2311yescharacteristic
121C2×M16×C59C2311yescharacteristic
122C22×C8×C59—21no—
123#127×C59—22no—
124#127×C59—21no—
125#124×C59—22no—
126#124×C59—21no—
127#124×C59—22no—
128#124×C59—41no—
129#123×C59—22no—
130#123×C59—21no—
131C22⋊Q8×C59—22no—
132C22⋊Q8×C59—21no—
133C22⋊Q8×C59—21no—
134C22⋊Q8×C59—21no—
135C22⋊Q8×C59—21no—
136C22⋊Q8×C59—21no—
137C22⋊Q8×C59—21no—
138C22⋊Q8×C59D411yescharacteristic
139C22⋊Q8×C59D411yescharacteristic
140#121×C59—22no—
141#121×C59—22no—
142#121×C59—22no—
143#121×C59—22no—
144#121×C59—22no—
145#121×C59—21no—
146#121×C59—21no—
147#121×C59—21no—
148#121×C59—21no—
149#121×C59—21no—
150#121×C59—21no—
151#121×C59—22no—
152#121×C59—21no—
153#121×C59—21no—
154#121×C59D411yescharacteristic
155#121×C59D411yescharacteristic
156#120×C59—22no—
157#120×C59—22no—
158#120×C59—22no—
159#120×C59—21no—
160#120×C59—22no—
161C4×Q8×C59—21no—
162C4×D4×C59—22no—
163C4×D4×C59—22no—
164C4×D4×C59—21no—
165C4×D4×C59—22no—
166C4×D4×C59—21no—
167C4×D4×C59—21no—
168#117×C59—21no—
169#117×C59C2311yescharacteristic
170C2×C4⋊C4×C59—21no—
171C2×C4⋊C4×C59—21no—
172C2×C4⋊C4×C59C2311yescharacteristic
173C2×C4⋊C4×C59C2311yescharacteristic
174C2×C22⋊C4×C59—22no—
175C2×C22⋊C4×C59—21no—
176C2×C22⋊C4×C59—22no—
177C2×C22⋊C4×C59—22no—
178C2×C22⋊C4×C59D412yes—
179C2×C42×C59—22no—
180C2×C42×C59—21no—
181C2×C42×C59—41no—
182C2×C42×C59C2311yescharacteristic
183C2×C42×C59C2311yescharacteristic
184#107×C59—21no—
185#106×C59—21no—
186#104×C59—22no—
187#104×C59—22no—
188#104×C59—22no—
189#104×C59—22no—
190#104×C59—41no—
191#104×C59D414yescomplemented
192#103×C59—21no—
193#103×C59—21no—
194#103×C59—21no—
195#103×C59—21no—
196#103×C59—21no—
197#102×C59—21no—
198#102×C59—21no—
199#102×C59—21no—
200#100×C59—22no—
201#100×C59—41no—
202C22⋊C8×C59—21no—
203C22⋊C8×C59—21no—
204#95×C59—22no—
205#95×C59—22no—
206C24×C59—22no—
207C24×C59—21no—
208C24×C59C2×D411yescharacteristic
209C24×C59C2×D412yes—
210#41×C59—21no—
211#41×C59—21no—
212#41×C59—22no—
213#41×C59—22no—
214#41×C59—21no—
215#41×C59—21no—
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—42no—
223#41×C59—42no—
224#41×C59—41no—
225#41×C59—41no—
226#41×C59—42no—
227#41×C59—42no—
228#41×C59—42no—
229#41×C59—42no—
230#41×C59—42no—
231#41×C59—42no—
232#41×C59C2×D412yes—
233#41×C59#4112yes—
234C2×Q8×C59—21no—
235C2×Q8×C59—22no—
236C2×Q8×C59—21no—
237C2×Q8×C59—21no—
238C2×Q8×C59—21no—
239C2×Q8×C59—21no—
240C2×Q8×C59—21no—
241C2×Q8×C59—21no—
242C2×Q8×C59—41no—
243C2×Q8×C59C2×D411yescharacteristic
244C2×Q8×C59C2×D411yescharacteristic
245C2×Q8×C59C2×D411yescharacteristic
246C2×D4×C59—21no—
247C2×D4×C59—22no—
248C2×D4×C59—22no—
249C2×D4×C59—22no—
250C2×D4×C59—22no—
251C2×D4×C59—21no—
252C2×D4×C59—21no—
253C2×D4×C59—21no—
254C2×D4×C59—21no—
255C2×D4×C59—21no—
256C2×D4×C59—22no—
257C2×D4×C59—22no—
258C2×D4×C59—22no—
259C2×D4×C59—21no—
260C2×D4×C59—22no—
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—41no—
269C2×D4×C59—42no—
270C2×D4×C59—42no—
271C2×D4×C59—42no—
272C2×D4×C59—42no—
273C2×D4×C59—44no—
274C2×D4×C59—44no—
275C2×D4×C59—42no—
276C2×D4×C59—42no—
277C2×D4×C59—44no—
278C2×D4×C59—84no—
279C2×D4×C59C2×D411yescharacteristic
280C2×D4×C59C2×D411yescharacteristic
281C2×D4×C59C2×D411yescharacteristic
282C22×C4×C59—21no—
283C22×C4×C59—21no—
284C22×C4×C59—21no—
285C22×C4×C59—21no—
286C22×C4×C59—21no—
287C22×C4×C59—22no—
288C22×C4×C59—21no—
289C22×C4×C59—21no—
290C22×C4×C59—21no—
291C22×C4×C59—22no—
292C22×C4×C59—21no—
293C22×C4×C59—21no—
294C22×C4×C59—21no—
295C22×C4×C59—21no—
296C22×C4×C59—21no—
297C22×C4×C59—21no—
298C22×C4×C59—42no—
299C22×C4×C59—42no—
300C22×C4×C59—42no—
301C22×C4×C59—42no—
302C22×C4×C59—42no—
303C22×C4×C59C2×D411yescharacteristic
304C22×C4×C59C2×D411yescharacteristic
305C22×C4×C59C2×D411yescharacteristic
306C22×C4×C59C2×D411yescharacteristic
307C22×C4×C59C2×D411yescharacteristic
308C22×C4×C59C2×D412yes—
309C22×C4×C59C2411yescharacteristic
310Q16×C59—42no—
311Q16×C59—42no—
312Q16×C59—42no—
313SD16×C59—42no—
314SD16×C59—42no—
315SD16×C59—42no—
316M16×C59—21no—
317M16×C59—21no—
318M16×C59—21no—
319M16×C59—21no—
320M16×C59—21no—
321M16×C59—21no—
322M16×C59—21no—
323M16×C59—42no—
324M16×C59C2×D412yescomplemented
325C2×C8×C59—21no—
326C2×C8×C59—21no—
327C2×C8×C59—21no—
328C2×C8×C59—21no—
329C2×C8×C59—42no—
330C4⋊C4×C59—22no—
331C4⋊C4×C59—22no—
332C4⋊C4×C59—21no—
333C4⋊C4×C59—21no—
334C4⋊C4×C59—21no—
335C4⋊C4×C59—21no—
336C4⋊C4×C59—21no—
337C4⋊C4×C59—21no—
338C4⋊C4×C59—41no—
339C4⋊C4×C59—41no—
340C4⋊C4×C59C2×D411yescharacteristic
341C4⋊C4×C59C2×D411yescharacteristic
342C22⋊C4×C59—22no—
343C22⋊C4×C59—22no—
344C22⋊C4×C59—22no—
345C22⋊C4×C59—22no—
346C22⋊C4×C59—22no—
347C22⋊C4×C59—21no—
348C22⋊C4×C59—21no—
349C22⋊C4×C59—21no—
350C22⋊C4×C59—21no—
351C22⋊C4×C59—22no—
352C22⋊C4×C59—22no—
353C22⋊C4×C59—21no—
354C22⋊C4×C59—44no—
355C22⋊C4×C59—44no—
356C22⋊C4×C59—41no—
357C22⋊C4×C59—41no—
358C42×C59—22no—
359C42×C59—21no—
360C42×C59—21no—
361C42×C59—21no—
362C42×C59—21no—
363C42×C59—42no—
364C42×C59C2×D412yescomplemented
365C23×C59—21no—
366C23×C59—21no—
367C23×C59—21no—
368C23×C59—22no—
369C23×C59—22no—
370C23×C59—21no—
371C23×C59—21no—
372C23×C59—22no—
373C23×C59—22no—
374C23×C59—41no—
375C23×C59—42no—
376C23×C59—44no—
377C23×C59—42no—
378C23×C59—42no—
379C23×C59—42no—
380C23×C59—81no—
381C23×C59—82no—
382C23×C59—82no—
383C23×C59#12011yescharacteristic
384C23×C59#12011yescharacteristic
385C23×C59C22×D411yescharacteristic
386Q8×C59—21no—
387Q8×C59—21no—
388Q8×C59—21no—
389Q8×C59—21no—
390Q8×C59—21no—
391Q8×C59—42no—
392Q8×C59—41no—
393Q8×C59—41no—
394Q8×C59—41no—
395Q8×C59—41no—
396Q8×C59#12112yes—
397D4×C59—22no—
398D4×C59—22no—
399D4×C59—21no—
400D4×C59—21no—
401D4×C59—21no—
402D4×C59—21no—
403D4×C59—21no—
404D4×C59—42no—
405D4×C59—42no—
406D4×C59—44no—
407D4×C59—42no—
408D4×C59—44no—
409D4×C59—41no—
410D4×C59—41no—
411D4×C59—41no—
412D4×C59—41no—
413D4×C59—44no—
414D4×C59—42no—
415D4×C59—41no—
416D4×C59—41no—
417D4×C59—41no—
418D4×C59—41no—
419D4×C59—81no—
420D4×C59—82no—
421D4×C59—82no—
422D4×C59—82no—
423D4×C59—82no—
424D4×C59#12112yes—
425C2×C4×C59—21no—
426C2×C4×C59—21no—
427C2×C4×C59—21no—
428C2×C4×C59—21no—
429C2×C4×C59—21no—
430C2×C4×C59—21no—
431C2×C4×C59—21no—
432C2×C4×C59—21no—
433C2×C4×C59—21no—
434C2×C4×C59—22no—
435C2×C4×C59—21no—
436C2×C4×C59—21no—
437C2×C4×C59—22no—
438C2×C4×C59—22no—
439C2×C4×C59—21no—
440C2×C4×C59—22no—
441C2×C4×C59—21no—
442C2×C4×C59—21no—
443C2×C4×C59—21no—
444C2×C4×C59—22no—
445C2×C4×C59—42no—
446C2×C4×C59—42no—
447C2×C4×C59—42no—
448C2×C4×C59—44no—
449C2×C4×C59—41no—
450C2×C4×C59—41no—
451C2×C4×C59—41no—
452C2×C4×C59—48no—
453C2×C4×C59—41no—
454C2×C4×C59—41no—
455C2×C4×C59—41no—
456C2×C4×C59—41no—
457C2×C4×C59—41no—
458C2×C4×C59—42no—
459C2×C4×C59—42no—
460C2×C4×C59—41no—
461C2×C4×C59—41no—
462C2×C4×C59—41no—
463C2×C4×C59—41no—
464C2×C4×C59—82no—
465C2×C4×C59#12011yescharacteristic
466C2×C4×C59#12011yescharacteristic
467C2×C4×C59C22×D411yescharacteristic
468C2×C4×C59C22×D411yescharacteristic
469C2×C4×C59C22×D411yescharacteristic
470C2×C4×C59C2×#4111yescharacteristic
471C2×C4×C59H(5,𝔽2)11yescharacteristic
472C2×C4×C59H(5,𝔽2)11yescharacteristic
473C8×C59—22no—
474C8×C59—41no—
475C8×C59—41no—
476C8×C59—41no—
477#24467C5911yesmaximal, characteristic, direct product factor, Sylow
478C22×C59—21no—
479C22×C59—21no—
480C22×C59—21no—
481C22×C59—21no—
482C22×C59—21no—
483C22×C59—22no—
484C22×C59—21no—
485C22×C59—21no—
486C22×C59—42no—
487C22×C59—42no—
488C22×C59—41no—
489C22×C59—41no—
490C22×C59—41no—
491C22×C59—41no—
492C22×C59—42no—
493C22×C59—42no—
494C22×C59—41no—
495C22×C59—41no—
496C22×C59—41no—
497C22×C59—42no—
498C22×C59—41no—
499C22×C59—84no—
500C22×C59—82no—
501C22×C59—82no—
502C22×C59—164no—
503C22×C59#45512yescomplemented
504C22×C59C2×#12011yescharacteristic
505C22×C59D4211yescharacteristic
506C22×C59#54611yescharacteristic
507C4×C59—21no—
508C4×C59—21no—
509C4×C59—22no—
510C4×C59—42no—
511C4×C59—42no—
512C4×C59—41no—
513C4×C59—41no—
514C4×C59—42no—
515C4×C59—41no—
516C4×C59—41no—
517C4×C59—81no—
518C4×C59—81no—
519C4×C59C2×#12111yescharacteristic
520C4×C59#53411yescharacteristic
521C4×C59D4211yescharacteristic
522C4×C59#54611yescharacteristic
523#3488C2×C5911yescharacteristic
524#3056C2×C5911yescharacteristic, complemented
525C2×#455C2×C5911yescharacteristic, complemented
526#3007C2×C5911yescharacteristic, complemented
527C22×#104C2×C5911yescharacteristic, complemented
528#2850C2×C5911yescharacteristic, complemented
529#2040C2×C5911yescharacteristic, complemented
530#2037C2×C5911yescharacteristic, complemented
531#2007C2×C5911yescharacteristic, complemented
532#2004C2×C5911yescharacteristic, complemented
533#1900C2×C5911yescharacteristic, complemented
534#1896C2×C5911yescharacteristic, complemented
535#1882C2×C5911yescharacteristic, complemented
536#1860C2×C5911yescharacteristic, complemented
537#1792C2×C5911yescharacteristic, complemented
538C2×C59—21no—
539C2×C59—21no—
540C2×C59—22no—
541C2×C59—41no—
542C2×C59—42no—
543C2×C59—81no—
544C2×C59—82no—
545C2×C59—81no—
546C2×C59#241011yescharacteristic
547C2×C59C2×#45511yescharacteristic
548C2×C59#301811yescharacteristic
549C2×H(5,𝔽2)C22×C5911yescharacteristic
550C22×#41C22×C5911yescharacteristic
551C2×#137C22×C5911yescharacteristic
552C2×#137C22×C5911yescharacteristic, complemented
553C2×#137C22×C5911yescharacteristic, complemented
554C22×M16C22×C5911yescharacteristic, complemented
555#550—21no—
556#548—21no—
557#546—21no—
558#546—22no—
559D42—22no—
560D42—21no—
561#537—21no—
562#537C22×C5911yescharacteristic
563#535—21no—
564#535C22×C5911yescharacteristic
565C2×#124C22×C5911yescharacteristic, complemented
566#525—21no—
567#525C22×C5911yescharacteristic
568C2×C22⋊Q8C22×C5911yescharacteristic, complemented
569C2×#121—21no—
570C2×#121C22×C5911yescharacteristic
571#520C22×C5911yescharacteristic
572C22×C42C22×C5911yescharacteristic, complemented
573#470—21no—
574#468—21no—
575#467—21no—
576#465—21no—
577#455—24no—
578#452—21no—
579#452—21no—
580#451—21no—
581#450—21no—
582#428C22×C5911yescharacteristic, complemented
583C2×#104—24no—
584C2×#104C22×C5911yescharacteristic
585C2×#104C22×C5911yescharacteristic
586C2×#104C22×C5911yescharacteristic, complemented
587C2×#104C22×C5911yescharacteristic, complemented
588C2×#104C22×C5911yescharacteristic, complemented
589C2×#104C22×C5911yescharacteristic, complemented
590#419C22×C5911yescharacteristic, complemented
591#417C22×C5911yescharacteristic
592#417C22×C5911yescharacteristic, complemented
593#417C22×C5911yescharacteristic, complemented
594C2×#100C22×C5911yescharacteristic, complemented
595C2×#100C22×C5911yescharacteristic, complemented
596#407C22×C5911yescharacteristic, complemented
597#391C22×C5911yescharacteristic, complemented
598#390C22×C5911yescharacteristic, complemented
599#388—22no—
600#386—22no—
601#382C22×C5911yescharacteristic, complemented
602#343C22×C5911yescharacteristic, complemented
603#343C22×C5911yescharacteristic, complemented
604#339C22×C5911yescharacteristic, complemented
605#339C22×C5911yescharacteristic, complemented
606C59#2446711yescharacteristic, direct product factor, Sylow
607H(5,𝔽2)—22no—
608H(5,𝔽2)—22no—
609H(5,𝔽2)—41no—
610H(5,𝔽2)—41no—
611C2×#41—21no—
612C2×#41—21no—
613C2×#41—21no—
614C2×#41—21no—
615C2×#41—22no—
616C2×#41—22no—
617C2×#41—41no—
618C2×#41—41no—
619C2×#41D4×C5911yescharacteristic
620C2×#41D4×C5911yescharacteristic
621C2×#41C23×C5911yescharacteristic
622C2×#41C23×C5911yescharacteristic
623C2×#41C23×C5911yescharacteristic
624C22×Q8D4×C5911yescharacteristic
625C22×Q8C23×C5911yescharacteristic
626C22×D4—21no—
627C22×D4—22no—
628C22×D4—22no—
629C22×D4—21no—
630C22×D4—21no—
631C22×D4D4×C5911yescharacteristic
632C22×D4D4×C5912yes—
633C22×D4C23×C5911yescharacteristic
634C23×C4—21no—
635C23×C4—21no—
636C23×C4C23×C5911yescharacteristic
637#137—22no—
638#137—22no—
639#137—22no—
640#137—41no—
641#137—41no—
642#137—41no—
643C2×Q16—21no—
644C2×Q16—21no—
645C2×Q16—21no—
646C2×SD16—21no—
647C2×SD16—21no—
648C2×SD16—21no—
649C2×M16—21no—
650C2×M16—22no—
651C2×M16—41no—
652C2×M16C23×C5911yescharacteristic
653C2×M16C23×C5911yescharacteristic
654C2×M16C23×C5911yescharacteristic
655C2×M16C23×C5911yescharacteristic
656C22×C8—21no—
657#127—22no—
658#127—21no—
659#124—22no—
660#124—21no—
661#124—22no—
662#124—41no—
663#123—22no—
664#123—21no—
665C22⋊Q8—22no—
666C22⋊Q8—21no—
667C22⋊Q8—21no—
668C22⋊Q8—21no—
669C22⋊Q8—21no—
670C22⋊Q8—21no—
671C22⋊Q8—21no—
672C22⋊Q8D4×C5911yescharacteristic
673C22⋊Q8D4×C5911yescharacteristic
674#121—22no—
675#121—22no—
676#121—22no—
677#121—22no—
678#121—22no—
679#121—21no—
680#121—21no—
681#121—21no—
682#121—21no—
683#121—21no—
684#121—21no—
685#121—22no—
686#121—21no—
687#121—21no—
688#121D4×C5911yescharacteristic
689#121D4×C5911yescharacteristic
690#120—22no—
691#120—22no—
692#120—22no—
693#120—21no—
694#120—22no—
695C4×Q8—21no—
696C4×D4—22no—
697C4×D4—22no—
698C4×D4—21no—
699C4×D4—22no—
700C4×D4—21no—
701C4×D4—21no—
702#117—21no—
703#117C23×C5911yescharacteristic
704C2×C4⋊C4—21no—
705C2×C4⋊C4—21no—
706C2×C4⋊C4C23×C5911yescharacteristic
707C2×C4⋊C4C23×C5911yescharacteristic
708C2×C22⋊C4—22no—
709C2×C22⋊C4—21no—
710C2×C22⋊C4—22no—
711C2×C22⋊C4—22no—
712C2×C22⋊C4D4×C5912yes—
713C2×C42—22no—
714C2×C42—21no—
715C2×C42—41no—
716C2×C42C23×C5911yescharacteristic
717C2×C42C23×C5911yescharacteristic
718#107—21no—
719#106—21no—
720#104—22no—
721#104—22no—
722#104—22no—
723#104—22no—
724#104—41no—
725#104D4×C5914yescomplemented
726#103—21no—
727#103—21no—
728#103—21no—
729#103—21no—
730#103—21no—
731#102—21no—
732#102—21no—
733#102—21no—
734#100—22no—
735#100—41no—
736C22⋊C8—21no—
737C22⋊C8—21no—
738#95—22no—
739#95—22no—
740C24—22no—
741C24—21no—
742C24C2×D4×C5911yescharacteristic
743C24C2×D4×C5912yes—
744#41—21no—
745#41—21no—
746#41—22no—
747#41—22no—
748#41—21no—
749#41—21no—
750#41—21no—
751#41—21no—
752#41—21no—
753#41—21no—
754#41—21no—
755#41—21no—
756#41—42no—
757#41—42no—
758#41—41no—
759#41—41no—
760#41—42no—
761#41—42no—
762#41—42no—
763#41—42no—
764#41—42no—
765#41—42no—
766#41C2×D4×C5912yes—
767#41#41×C5912yes—
768C2×Q8—21no—
769C2×Q8—22no—
770C2×Q8—21no—
771C2×Q8—21no—
772C2×Q8—21no—
773C2×Q8—21no—
774C2×Q8—21no—
775C2×Q8—21no—
776C2×Q8—41no—
777C2×Q8C2×D4×C5911yescharacteristic
778C2×Q8C2×D4×C5911yescharacteristic
779C2×Q8C2×D4×C5911yescharacteristic
780C2×D4—21no—
781C2×D4—22no—
782C2×D4—22no—
783C2×D4—22no—
784C2×D4—22no—
785C2×D4—21no—
786C2×D4—21no—
787C2×D4—21no—
788C2×D4—21no—
789C2×D4—21no—
790C2×D4—22no—
791C2×D4—22no—
792C2×D4—22no—
793C2×D4—21no—
794C2×D4—22no—
795C2×D4—21no—
796C2×D4—21no—
797C2×D4—21no—
798C2×D4—21no—
799C2×D4—21no—
800C2×D4—21no—
801C2×D4—21no—
802C2×D4—41no—
803C2×D4—42no—
804C2×D4—42no—
805C2×D4—42no—
806C2×D4—42no—
807C2×D4—44no—
808C2×D4—44no—
809C2×D4—42no—
810C2×D4—42no—
811C2×D4—44no—
812C2×D4—84no—
813C2×D4C2×D4×C5911yescharacteristic
814C2×D4C2×D4×C5911yescharacteristic
815C2×D4C2×D4×C5911yescharacteristic
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—22no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—22no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—42no—
833C22×C4—42no—
834C22×C4—42no—
835C22×C4—42no—
836C22×C4—42no—
837C22×C4C2×D4×C5911yescharacteristic
838C22×C4C2×D4×C5911yescharacteristic
839C22×C4C2×D4×C5911yescharacteristic
840C22×C4C2×D4×C5911yescharacteristic
841C22×C4C2×D4×C5911yescharacteristic
842C22×C4C2×D4×C5912yes—
843C22×C4C24×C5911yescharacteristic
844Q16—42no—
845Q16—42no—
846Q16—42no—
847SD16—42no—
848SD16—42no—
849SD16—42no—
850M16—21no—
851M16—21no—
852M16—21no—
853M16—21no—
854M16—21no—
855M16—21no—
856M16—21no—
857M16—42no—
858M16C2×D4×C5912yescomplemented
859C2×C8—21no—
860C2×C8—21no—
861C2×C8—21no—
862C2×C8—21no—
863C2×C8—42no—
864C4⋊C4—22no—
865C4⋊C4—22no—
866C4⋊C4—21no—
867C4⋊C4—21no—
868C4⋊C4—21no—
869C4⋊C4—21no—
870C4⋊C4—21no—
871C4⋊C4—21no—
872C4⋊C4—41no—
873C4⋊C4—41no—
874C4⋊C4C2×D4×C5911yescharacteristic
875C4⋊C4C2×D4×C5911yescharacteristic
876C22⋊C4—22no—
877C22⋊C4—22no—
878C22⋊C4—22no—
879C22⋊C4—22no—
880C22⋊C4—22no—
881C22⋊C4—21no—
882C22⋊C4—21no—
883C22⋊C4—21no—
884C22⋊C4—21no—
885C22⋊C4—22no—
886C22⋊C4—22no—
887C22⋊C4—21no—
888C22⋊C4—44no—
889C22⋊C4—44no—
890C22⋊C4—41no—
891C22⋊C4—41no—
892C42—22no—
893C42—21no—
894C42—21no—
895C42—21no—
896C42—21no—
897C42—42no—
898C42C2×D4×C5912yescomplemented
899C23—22no—
900C23—21no—
901C23—21no—
902C23—21no—
903C23—22no—
904C23—21no—
905C23—21no—
906C23—22no—
907C23—22no—
908C23—41no—
909C23—42no—
910C23—44no—
911C23—42no—
912C23—42no—
913C23—42no—
914C23—81no—
915C23—82no—
916C23—82no—
917C23#120×C5911yescharacteristic
918C23#120×C5911yescharacteristic
919C23C22×D4×C5911yescharacteristic
920Q8—21no—
921Q8—21no—
922Q8—21no—
923Q8—21no—
924Q8—21no—
925Q8—42no—
926Q8—41no—
927Q8—41no—
928Q8—41no—
929Q8—41no—
930Q8#121×C5912yes—
931D4—22no—
932D4—22no—
933D4—21no—
934D4—21no—
935D4—21no—
936D4—21no—
937D4—21no—
938D4—42no—
939D4—42no—
940D4—44no—
941D4—42no—
942D4—44no—
943D4—44no—
944D4—42no—
945D4—41no—
946D4—41no—
947D4—41no—
948D4—41no—
949D4—41no—
950D4—41no—
951D4—41no—
952D4—41no—
953D4—81no—
954D4—82no—
955D4—82no—
956D4—82no—
957D4—82no—
958D4#121×C5912yes—
959C2×C4—21no—
960C2×C4—21no—
961C2×C4—21no—
962C2×C4—21no—
963C2×C4—21no—
964C2×C4—21no—
965C2×C4—21no—
966C2×C4—21no—
967C2×C4—21no—
968C2×C4—22no—
969C2×C4—21no—
970C2×C4—21no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—21no—
974C2×C4—22no—
975C2×C4—21no—
976C2×C4—21no—
977C2×C4—21no—
978C2×C4—22no—
979C2×C4—42no—
980C2×C4—42no—
981C2×C4—42no—
982C2×C4—44no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—41no—
986C2×C4—48no—
987C2×C4—41no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—42no—
993C2×C4—42no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—82no—
999C2×C4#120×C5911yescharacteristic
1000C2×C4#120×C5911yescharacteristic
1001C2×C4C22×D4×C5911yescharacteristic
1002C2×C4C22×D4×C5911yescharacteristic
1003C2×C4C22×D4×C5911yescharacteristic
1004C2×C4C2×#41×C5911yescharacteristic
1005C2×C4H(5,𝔽2)×C5911yescharacteristic
1006C2×C4H(5,𝔽2)×C5911yescharacteristic
1007C8—22no—
1008C8—41no—
1009C8—41no—
1010C8—41no—
1011C22—21no—
1012C22—21no—
1013C22—21no—
1014C22—21no—
1015C22—21no—
1016C22—21no—
1017C22—21no—
1018C22—22no—
1019C22—42no—
1020C22—42no—
1021C22—41no—
1022C22—41no—
1023C22—42no—
1024C22—41no—
1025C22—41no—
1026C22—41no—
1027C22—42no—
1028C22—41no—
1029C22—41no—
1030C22—41no—
1031C22—42no—
1032C22—84no—
1033C22—82no—
1034C22—82no—
1035C22—164no—
1036C22C59×#45512yescomplemented
1037C22C2×#120×C5911yescharacteristic
1038C22D42×C5911yescharacteristic
1039C22C59×#54611yescharacteristic
1040C4—21no—
1041C4—21no—
1042C4—22no—
1043C4—42no—
1044C4—42no—
1045C4—42no—
1046C4—41no—
1047C4—41no—
1048C4—41no—
1049C4—41no—
1050C4—81no—
1051C4—81no—
1052C4C2×#121×C5911yescharacteristic
1053C4C59×#53411yescharacteristic
1054C4D42×C5911yescharacteristic
1055C4C59×#54611yescharacteristic
1056C2—21no—
1057C2—22no—
1058C2—21no—
1059C2—41no—
1060C2—42no—
1061C2—81no—
1062C2—82no—
1063C2—81no—
1064C2C59×#241011yescharacteristic
1065C2C2×C59×#45511yescharacteristic
1066C2C59×#301811yescharacteristic
subgroupG/H
center, socleC22×C59C2×#120
commutator, Frattini, cosocleC22×C4C24×C59
prime radicalC59×#3488C2
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
2. C59×#3056C2semidirect
3. C2×C59×#455C2semidirect
4. C59×#3007C2semidirect
5. C22×#104×C59C2semidirect
6. C59×#2850C2semidirect
7. C59×#2040C2semidirect
8. C59×#2037C2semidirect
9. C59×#2007C2semidirect
10. C59×#2004C2semidirect
11. C59×#1900C2semidirect
12. C59×#1896C2semidirect
13. C59×#1882C2semidirect
14. C59×#1860C2semidirect
15. C59×#1792C2semidirect
19. C2×#137×C59C22semidirect
20. C2×#137×C59C22semidirect
21. C22×M16×C59C22semidirect
32. C2×#124×C59C22semidirect
35. C2×C22⋊Q8×C59C22semidirect
39. C22×C42×C59C22semidirect
49. C59×#428C22semidirect
53. C2×#104×C59C22semidirect
54. C2×#104×C59C22semidirect
55. C2×#104×C59C22semidirect
56. C2×#104×C59C22semidirect
57. C59×#419C22semidirect
59. C59×#417C22semidirect
60. C59×#417C22semidirect
61. C2×#100×C59C22semidirect
62. C2×#100×C59C22semidirect
63. C59×#407C22semidirect
64. C59×#391C22semidirect
65. C59×#390C22semidirect
68. C59×#382C22semidirect
69. C59×#343C22semidirect
70. C59×#343C22semidirect
71. C59×#339C22semidirect
72. C59×#339C22semidirect
191. #104×C59D4semidirect
324. M16×C59C2×D4semidirect
364. C42×C59C2×D4semidirect
477. #24467C59direct (N × H)
503. C22×C59#455semidirect
524. #3056C2×C59semidirect
525. C2×#455C2×C59semidirect
526. #3007C2×C59semidirect
527. C22×#104C2×C59semidirect
528. #2850C2×C59semidirect
529. #2040C2×C59semidirect
530. #2037C2×C59semidirect
531. #2007C2×C59semidirect
532. #2004C2×C59semidirect
533. #1900C2×C59semidirect
534. #1896C2×C59semidirect
535. #1882C2×C59semidirect
536. #1860C2×C59semidirect
537. #1792C2×C59semidirect
552. C2×#137C22×C59semidirect
553. C2×#137C22×C59semidirect
554. C22×M16C22×C59semidirect
565. C2×#124C22×C59semidirect
568. C2×C22⋊Q8C22×C59semidirect
572. C22×C42C22×C59semidirect
582. #428C22×C59semidirect
586. C2×#104C22×C59semidirect
587. C2×#104C22×C59semidirect
588. C2×#104C22×C59semidirect
589. C2×#104C22×C59semidirect
590. #419C22×C59semidirect
592. #417C22×C59semidirect
593. #417C22×C59semidirect
594. C2×#100C22×C59semidirect
595. C2×#100C22×C59semidirect
596. #407C22×C59semidirect
597. #391C22×C59semidirect
598. #390C22×C59semidirect
601. #382C22×C59semidirect
602. #343C22×C59semidirect
603. #343C22×C59semidirect
604. #339C22×C59semidirect
605. #339C22×C59semidirect
606. C59#24467direct (N × H)
725. #104D4×C59semidirect
858. M16C2×D4×C59semidirect
898. C42C2×D4×C59semidirect
1036. C22C59×#455semidirect

Maximal subgroups

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

subgroupindex
C59×#34882
C59×#30562
C2×C59×#4552
C59×#30072
C22×#104×C592
C59×#28502
C59×#20402
C59×#20372
C59×#20072
C59×#20042
C59×#19002
C59×#18962
C59×#18822
C59×#18602
C59×#17922
#2446759