Finite Group Databasebeta

← C59×#24471 #28436580

Subgroups — C59×#24471 #28436580

Order 15104.

1444 conjugacy classes of subgroups.

The subgroup lattice has 1064 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
5C2×C59×#421C211yesmaximal, characteristic, complemented
6C59×#2620C211yesmaximal, characteristic, complemented
7C59×#2039C211yesmaximal, characteristic, complemented
8C59×#2037C211yesmaximal, characteristic, complemented
9C59×#2007C211yesmaximal, characteristic, complemented
10C59×#2004C211yesmaximal, characteristic, complemented
11C59×#1900C211yesmaximal, characteristic, complemented
12C59×#1897C211yesmaximal, characteristic, complemented
13C59×#1882C211yesmaximal, characteristic, complemented
14C59×#1859C211yesmaximal, 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
39C2×#117×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
50C59×#421—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×#396—22no—
65C59×#394—22no—
66C59×#391C2211yescharacteristic, 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
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×C59C2311yescharacteristic
102#137×C59—22no—
103#137×C59—22no—
104#137×C59—22no—
105#137×C59—41no—
106#137×C59—41no—
107#137×C59—41no—
108C2×Q16×C59—21no—
109C2×Q16×C59—21no—
110C2×Q16×C59—21no—
111C2×SD16×C59—21no—
112C2×SD16×C59—21no—
113C2×SD16×C59—21no—
114C2×M16×C59—21no—
115C2×M16×C59—22no—
116C2×M16×C59—41no—
117C2×M16×C59C2311yescharacteristic
118C2×M16×C59C2311yescharacteristic
119C2×M16×C59C2311yescharacteristic
120C2×M16×C59C2311yescharacteristic
121C22×C8×C59—21no—
122#127×C59—22no—
123#127×C59—21no—
124#124×C59—22no—
125#124×C59—21no—
126#124×C59—22no—
127#124×C59—41no—
128#123×C59—22no—
129#123×C59—21no—
130C22⋊Q8×C59—22no—
131C22⋊Q8×C59—21no—
132C22⋊Q8×C59—21no—
133C22⋊Q8×C59—21no—
134C22⋊Q8×C59—21no—
135C22⋊Q8×C59—21no—
136C22⋊Q8×C59—21no—
137C22⋊Q8×C59D411yescharacteristic
138C22⋊Q8×C59D411yescharacteristic
139#121×C59—22no—
140#121×C59—22no—
141#121×C59—22no—
142#121×C59—22no—
143#121×C59—22no—
144#121×C59—21no—
145#121×C59—21no—
146#121×C59—21no—
147#121×C59—21no—
148#121×C59—21no—
149#121×C59—21no—
150#121×C59—22no—
151#121×C59—21no—
152#121×C59—21no—
153#121×C59D411yescharacteristic
154#121×C59D411yescharacteristic
155#120×C59—22no—
156#120×C59—22no—
157#120×C59—22no—
158#120×C59—21no—
159#120×C59—22no—
160C4×Q8×C59—21no—
161C4×D4×C59—22no—
162C4×D4×C59—22no—
163C4×D4×C59—21no—
164C4×D4×C59—22no—
165C4×D4×C59—21no—
166C4×D4×C59—21no—
167#117×C59—21no—
168#117×C59—22no—
169#117×C59—41no—
170#117×C59C2311yescharacteristic
171C2×C4⋊C4×C59—21no—
172C2×C4⋊C4×C59—21no—
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—21no—
179C2×C22⋊C4×C59—21no—
180C2×C22⋊C4×C59—22no—
181C2×C22⋊C4×C59—22no—
182C2×C22⋊C4×C59D412yes—
183C2×C42×C59C2311yescharacteristic
184C2×C42×C59C2311yescharacteristic
185#107×C59—21no—
186#106×C59—21no—
187#104×C59—22no—
188#104×C59—22no—
189#104×C59—22no—
190#104×C59—22no—
191#104×C59—41no—
192#104×C59D414yescomplemented
193#103×C59—21no—
194#103×C59—21no—
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#100×C59—22no—
202#100×C59—41no—
203C22⋊C8×C59—21no—
204C22⋊C8×C59—21no—
205#95×C59—22no—
206C24×C59—22no—
207C24×C59—21no—
208C24×C59C2×D412yes—
209C24×C59C2×D411yescharacteristic
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—82no—
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—22no—
291C22×C4×C59—21no—
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×C59C2×D411yescharacteristic
301C22×C4×C59C2×D411yescharacteristic
302C22×C4×C59C2×D411yescharacteristic
303C22×C4×C59C2×D411yescharacteristic
304C22×C4×C59C2×D411yescharacteristic
305C22×C4×C59C2×D412yes—
306C22×C4×C59C2411yescharacteristic
307Q16×C59—42no—
308Q16×C59—42no—
309Q16×C59—42no—
310SD16×C59—42no—
311SD16×C59—42no—
312SD16×C59—42no—
313M16×C59—21no—
314M16×C59—21no—
315M16×C59—21no—
316M16×C59—21no—
317M16×C59—21no—
318M16×C59—21no—
319M16×C59—21no—
320M16×C59—42no—
321M16×C59C2×D412yescomplemented
322C2×C8×C59—21no—
323C2×C8×C59—21no—
324C2×C8×C59—21no—
325C2×C8×C59—21no—
326C2×C8×C59—42no—
327C4⋊C4×C59—22no—
328C4⋊C4×C59—22no—
329C4⋊C4×C59—21no—
330C4⋊C4×C59—21no—
331C4⋊C4×C59—21no—
332C4⋊C4×C59—21no—
333C4⋊C4×C59—21no—
334C4⋊C4×C59—21no—
335C4⋊C4×C59—42no—
336C4⋊C4×C59—41no—
337C4⋊C4×C59—41no—
338C4⋊C4×C59—82no—
339C4⋊C4×C59C2×D411yescharacteristic
340C4⋊C4×C59C2×D411yescharacteristic
341C22⋊C4×C59—22no—
342C22⋊C4×C59—22no—
343C22⋊C4×C59—22no—
344C22⋊C4×C59—22no—
345C22⋊C4×C59—22no—
346C22⋊C4×C59—21no—
347C22⋊C4×C59—21no—
348C22⋊C4×C59—21no—
349C22⋊C4×C59—21no—
350C22⋊C4×C59—22no—
351C22⋊C4×C59—22no—
352C22⋊C4×C59—21no—
353C22⋊C4×C59—42no—
354C22⋊C4×C59—44no—
355C22⋊C4×C59—41no—
356C22⋊C4×C59—41no—
357C22⋊C4×C59—82no—
358C42×C59—22no—
359C42×C59—21no—
360C42×C59—21no—
361C42×C59—21no—
362C42×C59—21no—
363C42×C59C2×D412yescomplemented
364C23×C59—21no—
365C23×C59—21no—
366C23×C59—21no—
367C23×C59—22no—
368C23×C59—21no—
369C23×C59—21no—
370C23×C59—22no—
371C23×C59—22no—
372C23×C59—41no—
373C23×C59—41no—
374C23×C59—42no—
375C23×C59—42no—
376C23×C59—44no—
377C23×C59—42no—
378C23×C59—42no—
379C23×C59—81no—
380C23×C59—82no—
381C23×C59—82no—
382C23×C59#12011yescharacteristic
383C23×C59#12011yescharacteristic
384C23×C59C22×D411yescharacteristic
385Q8×C59—21no—
386Q8×C59—21no—
387Q8×C59—21no—
388Q8×C59—21no—
389Q8×C59—21no—
390Q8×C59—42no—
391Q8×C59—41no—
392Q8×C59—41no—
393Q8×C59—41no—
394Q8×C59—41no—
395Q8×C59#12112yes—
396D4×C59—22no—
397D4×C59—22no—
398D4×C59—21no—
399D4×C59—21no—
400D4×C59—21no—
401D4×C59—21no—
402D4×C59—21no—
403D4×C59—42no—
404D4×C59—42no—
405D4×C59—44no—
406D4×C59—42no—
407D4×C59—44no—
408D4×C59—44no—
409D4×C59—42no—
410D4×C59—41no—
411D4×C59—41no—
412D4×C59—41no—
413D4×C59—41no—
414D4×C59—41no—
415D4×C59—41no—
416D4×C59—41no—
417D4×C59—41no—
418D4×C59—81no—
419D4×C59—82no—
420D4×C59—82no—
421D4×C59—82no—
422D4×C59—82no—
423D4×C59#12112yes—
424C2×C4×C59—21no—
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—22no—
434C2×C4×C59—21no—
435C2×C4×C59—21no—
436C2×C4×C59—22no—
437C2×C4×C59—21no—
438C2×C4×C59—22no—
439C2×C4×C59—21no—
440C2×C4×C59—21no—
441C2×C4×C59—21no—
442C2×C4×C59—22no—
443C2×C4×C59—42no—
444C2×C4×C59—42no—
445C2×C4×C59—42no—
446C2×C4×C59—44no—
447C2×C4×C59—41no—
448C2×C4×C59—41no—
449C2×C4×C59—41no—
450C2×C4×C59—41no—
451C2×C4×C59—41no—
452C2×C4×C59—41no—
453C2×C4×C59—42no—
454C2×C4×C59—41no—
455C2×C4×C59—42no—
456C2×C4×C59—41no—
457C2×C4×C59—41no—
458C2×C4×C59—41no—
459C2×C4×C59—41no—
460C2×C4×C59—41no—
461C2×C4×C59—41no—
462C2×C4×C59—82no—
463C2×C4×C59#12011yescharacteristic
464C2×C4×C59#12011yescharacteristic
465C2×C4×C59C22×D411yescharacteristic
466C2×C4×C59C22×D411yescharacteristic
467C2×C4×C59C22×D411yescharacteristic
468C2×C4×C59C2×#4111yescharacteristic
469C2×C4×C59H(5,𝔽2)11yescharacteristic
470C2×C4×C59H(5,𝔽2)11yescharacteristic
471C8×C59—22no—
472C8×C59—41no—
473C8×C59—41no—
474C8×C59—41no—
475#24471C5911yesmaximal, characteristic, direct product factor, Sylow
476C22×C59—21no—
477C22×C59—21no—
478C22×C59—21no—
479C22×C59—21no—
480C22×C59—22no—
481C22×C59—21no—
482C22×C59—21no—
483C22×C59—21no—
484C22×C59—21no—
485C22×C59—41no—
486C22×C59—41no—
487C22×C59—41no—
488C22×C59—41no—
489C22×C59—42no—
490C22×C59—42no—
491C22×C59—41no—
492C22×C59—41no—
493C22×C59—41no—
494C22×C59—42no—
495C22×C59—41no—
496C22×C59—81no—
497C22×C59—81no—
498C22×C59—82no—
499C22×C59—82no—
500C22×C59—84no—
501C22×C59—164no—
502C22×C59C2×#12011yescharacteristic
503C22×C59D4211yescharacteristic
504C22×C59#54611yescharacteristic
505C4×C59—21no—
506C4×C59—21no—
507C4×C59—22no—
508C4×C59—42no—
509C4×C59—41no—
510C4×C59—41no—
511C4×C59—42no—
512C4×C59—41no—
513C4×C59—41no—
514C4×C59—81no—
515C4×C59—81no—
516C4×C59—81no—
517C4×C59C2×#12111yescharacteristic
518C4×C59#53411yescharacteristic
519C4×C59D4211yescharacteristic
520C4×C59#54611yescharacteristic
521#3488C2×C5911yescharacteristic
522#3056C2×C5911yescharacteristic, complemented
523C2×#455C2×C5911yescharacteristic, complemented
524#3007C2×C5911yescharacteristic, complemented
525C2×#421C2×C5911yescharacteristic, complemented
526#2620C2×C5911yescharacteristic, complemented
527#2039C2×C5911yescharacteristic, complemented
528#2037C2×C5911yescharacteristic, complemented
529#2007C2×C5911yescharacteristic, complemented
530#2004C2×C5911yescharacteristic, complemented
531#1900C2×C5911yescharacteristic, complemented
532#1897C2×C5911yescharacteristic, complemented
533#1882C2×C5911yescharacteristic, complemented
534#1859C2×C5911yescharacteristic, complemented
535#1792C2×C5911yescharacteristic, complemented
536C2×C59—21no—
537C2×C59—21no—
538C2×C59—41no—
539C2×C59—41no—
540C2×C59—42no—
541C2×C59—81no—
542C2×C59—82no—
543C2×C59—81no—
544C2×C59#241011yescharacteristic
545C2×C59#301911yescharacteristic
546C2×C59#302211yescharacteristic
547C2×H(5,𝔽2)C22×C5911yescharacteristic
548C22×#41C22×C5911yescharacteristic
549C2×#137C22×C5911yescharacteristic
550C2×#137C22×C5911yescharacteristic, complemented
551C2×#137C22×C5911yescharacteristic, complemented
552C22×M16C22×C5911yescharacteristic, complemented
553#550—21no—
554#548—21no—
555#546—21no—
556#546—22no—
557D42—22no—
558D42—21no—
559#537—21no—
560#537C22×C5911yescharacteristic
561#535—21no—
562#535C22×C5911yescharacteristic
563C2×#124C22×C5911yescharacteristic, complemented
564#525—21no—
565#525C22×C5911yescharacteristic
566C2×C22⋊Q8C22×C5911yescharacteristic, complemented
567C2×#121—21no—
568C2×#121C22×C5911yescharacteristic
569#520C22×C5911yescharacteristic
570C2×#117C22×C5911yescharacteristic, complemented
571#470—21no—
572#468—21no—
573#467—21no—
574#465—21no—
575#455—24no—
576#452—21no—
577#452—21no—
578#451—21no—
579#450—21no—
580#428C22×C5911yescharacteristic, complemented
581#421—24no—
582C2×#104C22×C5911yescharacteristic
583C2×#104C22×C5911yescharacteristic
584C2×#104C22×C5911yescharacteristic, complemented
585C2×#104C22×C5911yescharacteristic, complemented
586C2×#104C22×C5911yescharacteristic, complemented
587C2×#104C22×C5911yescharacteristic, complemented
588#419C22×C5911yescharacteristic, complemented
589#417C22×C5911yescharacteristic
590#417C22×C5911yescharacteristic, complemented
591#417C22×C5911yescharacteristic, complemented
592C2×#100C22×C5911yescharacteristic, complemented
593C2×#100C22×C5911yescharacteristic, complemented
594#407C22×C5911yescharacteristic, complemented
595#396—22no—
596#394—22no—
597#391C22×C5911yescharacteristic, complemented
598#390C22×C5911yescharacteristic, complemented
599#384C22×C5911yescharacteristic, complemented
600#343C22×C5911yescharacteristic, complemented
601#343C22×C5911yescharacteristic, complemented
602#339C22×C5911yescharacteristic, complemented
603#339C22×C5911yescharacteristic, complemented
604C59#2447111yescharacteristic, direct product factor, Sylow
605H(5,𝔽2)—22no—
606H(5,𝔽2)—22no—
607H(5,𝔽2)—41no—
608H(5,𝔽2)—41no—
609C2×#41—21no—
610C2×#41—21no—
611C2×#41—21no—
612C2×#41—21no—
613C2×#41—22no—
614C2×#41—22no—
615C2×#41—41no—
616C2×#41—41no—
617C2×#41D4×C5911yescharacteristic
618C2×#41D4×C5911yescharacteristic
619C2×#41C23×C5911yescharacteristic
620C2×#41C23×C5911yescharacteristic
621C2×#41C23×C5911yescharacteristic
622C22×Q8D4×C5911yescharacteristic
623C22×Q8C23×C5911yescharacteristic
624C22×D4—21no—
625C22×D4—22no—
626C22×D4—22no—
627C22×D4—21no—
628C22×D4—21no—
629C22×D4D4×C5911yescharacteristic
630C22×D4D4×C5912yes—
631C22×D4C23×C5911yescharacteristic
632C23×C4—21no—
633C23×C4C23×C5911yescharacteristic
634#137—22no—
635#137—22no—
636#137—22no—
637#137—41no—
638#137—41no—
639#137—41no—
640C2×Q16—21no—
641C2×Q16—21no—
642C2×Q16—21no—
643C2×SD16—21no—
644C2×SD16—21no—
645C2×SD16—21no—
646C2×M16—21no—
647C2×M16—22no—
648C2×M16—41no—
649C2×M16C23×C5911yescharacteristic
650C2×M16C23×C5911yescharacteristic
651C2×M16C23×C5911yescharacteristic
652C2×M16C23×C5911yescharacteristic
653C22×C8—21no—
654#127—22no—
655#127—21no—
656#124—22no—
657#124—21no—
658#124—22no—
659#124—41no—
660#123—22no—
661#123—21no—
662C22⋊Q8—22no—
663C22⋊Q8—21no—
664C22⋊Q8—21no—
665C22⋊Q8—21no—
666C22⋊Q8—21no—
667C22⋊Q8—21no—
668C22⋊Q8—21no—
669C22⋊Q8D4×C5911yescharacteristic
670C22⋊Q8D4×C5911yescharacteristic
671#121—22no—
672#121—22no—
673#121—22no—
674#121—22no—
675#121—22no—
676#121—21no—
677#121—21no—
678#121—21no—
679#121—21no—
680#121—21no—
681#121—21no—
682#121—22no—
683#121—21no—
684#121—21no—
685#121D4×C5911yescharacteristic
686#121D4×C5911yescharacteristic
687#120—22no—
688#120—22no—
689#120—22no—
690#120—21no—
691#120—22no—
692C4×Q8—21no—
693C4×D4—22no—
694C4×D4—22no—
695C4×D4—21no—
696C4×D4—22no—
697C4×D4—21no—
698C4×D4—21no—
699#117—21no—
700#117—22no—
701#117—41no—
702#117C23×C5911yescharacteristic
703C2×C4⋊C4—21no—
704C2×C4⋊C4—21no—
705C2×C4⋊C4—21no—
706C2×C4⋊C4—22no—
707C2×C4⋊C4C23×C5911yescharacteristic
708C2×C4⋊C4C23×C5911yescharacteristic
709C2×C22⋊C4—22no—
710C2×C22⋊C4—21no—
711C2×C22⋊C4—21no—
712C2×C22⋊C4—22no—
713C2×C22⋊C4—22no—
714C2×C22⋊C4D4×C5912yes—
715C2×C42C23×C5911yescharacteristic
716C2×C42C23×C5911yescharacteristic
717#107—21no—
718#106—21no—
719#104—22no—
720#104—22no—
721#104—22no—
722#104—22no—
723#104—41no—
724#104D4×C5914yescomplemented
725#103—21no—
726#103—21no—
727#103—21no—
728#103—21no—
729#103—21no—
730#102—21no—
731#102—21no—
732#102—21no—
733#100—22no—
734#100—41no—
735C22⋊C8—21no—
736C22⋊C8—21no—
737#95—22no—
738C24—22no—
739C24—21no—
740C24C2×D4×C5912yes—
741C24C2×D4×C5911yescharacteristic
742#41—21no—
743#41—21no—
744#41—22no—
745#41—22no—
746#41—21no—
747#41—21no—
748#41—21no—
749#41—21no—
750#41—21no—
751#41—21no—
752#41—21no—
753#41—21no—
754#41—42no—
755#41—42no—
756#41—41no—
757#41—41no—
758#41—42no—
759#41—42no—
760#41—42no—
761#41—42no—
762#41—42no—
763#41—42no—
764#41C2×D4×C5912yes—
765#41#41×C5912yes—
766C2×Q8—21no—
767C2×Q8—22no—
768C2×Q8—21no—
769C2×Q8—21no—
770C2×Q8—21no—
771C2×Q8—21no—
772C2×Q8—21no—
773C2×Q8—21no—
774C2×Q8—41no—
775C2×Q8C2×D4×C5911yescharacteristic
776C2×Q8C2×D4×C5911yescharacteristic
777C2×Q8C2×D4×C5911yescharacteristic
778C2×D4—21no—
779C2×D4—22no—
780C2×D4—22no—
781C2×D4—22no—
782C2×D4—22no—
783C2×D4—21no—
784C2×D4—21no—
785C2×D4—21no—
786C2×D4—21no—
787C2×D4—21no—
788C2×D4—22no—
789C2×D4—22no—
790C2×D4—22no—
791C2×D4—21no—
792C2×D4—22no—
793C2×D4—21no—
794C2×D4—21no—
795C2×D4—21no—
796C2×D4—21no—
797C2×D4—21no—
798C2×D4—21no—
799C2×D4—21no—
800C2×D4—41no—
801C2×D4—42no—
802C2×D4—42no—
803C2×D4—42no—
804C2×D4—42no—
805C2×D4—44no—
806C2×D4—44no—
807C2×D4—42no—
808C2×D4—42no—
809C2×D4—82no—
810C2×D4—84no—
811C2×D4C2×D4×C5911yescharacteristic
812C2×D4C2×D4×C5911yescharacteristic
813C2×D4C2×D4×C5911yescharacteristic
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—22no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—22no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—42no—
831C22×C4—42no—
832C22×C4C2×D4×C5911yescharacteristic
833C22×C4C2×D4×C5911yescharacteristic
834C22×C4C2×D4×C5911yescharacteristic
835C22×C4C2×D4×C5911yescharacteristic
836C22×C4C2×D4×C5911yescharacteristic
837C22×C4C2×D4×C5912yes—
838C22×C4C24×C5911yescharacteristic
839Q16—42no—
840Q16—42no—
841Q16—42no—
842SD16—42no—
843SD16—42no—
844SD16—42no—
845M16—21no—
846M16—21no—
847M16—21no—
848M16—21no—
849M16—21no—
850M16—21no—
851M16—21no—
852M16—42no—
853M16C2×D4×C5912yescomplemented
854C2×C8—21no—
855C2×C8—21no—
856C2×C8—21no—
857C2×C8—21no—
858C2×C8—42no—
859C4⋊C4—22no—
860C4⋊C4—22no—
861C4⋊C4—21no—
862C4⋊C4—21no—
863C4⋊C4—21no—
864C4⋊C4—21no—
865C4⋊C4—21no—
866C4⋊C4—21no—
867C4⋊C4—42no—
868C4⋊C4—41no—
869C4⋊C4—41no—
870C4⋊C4—82no—
871C4⋊C4C2×D4×C5911yescharacteristic
872C4⋊C4C2×D4×C5911yescharacteristic
873C22⋊C4—22no—
874C22⋊C4—22no—
875C22⋊C4—22no—
876C22⋊C4—22no—
877C22⋊C4—22no—
878C22⋊C4—21no—
879C22⋊C4—21no—
880C22⋊C4—21no—
881C22⋊C4—21no—
882C22⋊C4—22no—
883C22⋊C4—22no—
884C22⋊C4—21no—
885C22⋊C4—42no—
886C22⋊C4—44no—
887C22⋊C4—41no—
888C22⋊C4—41no—
889C22⋊C4—82no—
890C42—22no—
891C42—21no—
892C42—21no—
893C42—21no—
894C42—21no—
895C42C2×D4×C5912yescomplemented
896C23—21no—
897C23—21no—
898C23—21no—
899C23—22no—
900C23—21no—
901C23—21no—
902C23—22no—
903C23—22no—
904C23—41no—
905C23—41no—
906C23—42no—
907C23—42no—
908C23—44no—
909C23—42no—
910C23—42no—
911C23—81no—
912C23—82no—
913C23—82no—
914C23#120×C5911yescharacteristic
915C23#120×C5911yescharacteristic
916C23C22×D4×C5911yescharacteristic
917Q8—21no—
918Q8—21no—
919Q8—21no—
920Q8—21no—
921Q8—21no—
922Q8—42no—
923Q8—41no—
924Q8—41no—
925Q8—41no—
926Q8—41no—
927Q8#121×C5912yes—
928D4—22no—
929D4—22no—
930D4—21no—
931D4—21no—
932D4—21no—
933D4—21no—
934D4—21no—
935D4—42no—
936D4—42no—
937D4—44no—
938D4—42no—
939D4—44no—
940D4—44no—
941D4—42no—
942D4—41no—
943D4—41no—
944D4—41no—
945D4—41no—
946D4—41no—
947D4—41no—
948D4—41no—
949D4—41no—
950D4—81no—
951D4—82no—
952D4—82no—
953D4—82no—
954D4—82no—
955D4#121×C5912yes—
956C2×C4—21no—
957C2×C4—21no—
958C2×C4—21no—
959C2×C4—21no—
960C2×C4—21no—
961C2×C4—21no—
962C2×C4—21no—
963C2×C4—21no—
964C2×C4—21no—
965C2×C4—22no—
966C2×C4—21no—
967C2×C4—21no—
968C2×C4—22no—
969C2×C4—21no—
970C2×C4—22no—
971C2×C4—21no—
972C2×C4—21no—
973C2×C4—21no—
974C2×C4—22no—
975C2×C4—42no—
976C2×C4—42no—
977C2×C4—42no—
978C2×C4—44no—
979C2×C4—41no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—42no—
986C2×C4—41no—
987C2×C4—42no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—82no—
995C2×C4#120×C5911yescharacteristic
996C2×C4#120×C5911yescharacteristic
997C2×C4C22×D4×C5911yescharacteristic
998C2×C4C22×D4×C5911yescharacteristic
999C2×C4C22×D4×C5911yescharacteristic
1000C2×C4C2×#41×C5911yescharacteristic
1001C2×C4H(5,𝔽2)×C5911yescharacteristic
1002C2×C4H(5,𝔽2)×C5911yescharacteristic
1003C8—22no—
1004C8—41no—
1005C8—41no—
1006C8—41no—
1007C22—21no—
1008C22—21no—
1009C22—21no—
1010C22—21no—
1011C22—21no—
1012C22—21no—
1013C22—21no—
1014C22—21no—
1015C22—22no—
1016C22—41no—
1017C22—41no—
1018C22—42no—
1019C22—41no—
1020C22—41no—
1021C22—41no—
1022C22—42no—
1023C22—41no—
1024C22—41no—
1025C22—41no—
1026C22—42no—
1027C22—81no—
1028C22—81no—
1029C22—82no—
1030C22—82no—
1031C22—84no—
1032C22—164no—
1033C22C2×#120×C5911yescharacteristic
1034C22D42×C5911yescharacteristic
1035C22C59×#54611yescharacteristic
1036C4—21no—
1037C4—21no—
1038C4—22no—
1039C4—42no—
1040C4—42no—
1041C4—41no—
1042C4—41no—
1043C4—41no—
1044C4—41no—
1045C4—81no—
1046C4—81no—
1047C4—81no—
1048C4C2×#121×C5911yescharacteristic
1049C4C59×#53411yescharacteristic
1050C4D42×C5911yescharacteristic
1051C4C59×#54611yescharacteristic
1052C2—21no—
1053C2—21no—
1054C2—41no—
1055C2—41no—
1056C2—42no—
1057C2—81no—
1058C2—82no—
1059C2—81no—
1060C2C59×#241011yescharacteristic
1061C2C59×#301911yescharacteristic
1062C2C59×#302211yescharacteristic
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. C2×C59×#421C2semidirect
6. C59×#2620C2semidirect
7. C59×#2039C2semidirect
8. C59×#2037C2semidirect
9. C59×#2007C2semidirect
10. C59×#2004C2semidirect
11. C59×#1900C2semidirect
12. C59×#1897C2semidirect
13. C59×#1882C2semidirect
14. C59×#1859C2semidirect
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. C2×#117×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
66. C59×#391C22semidirect
67. C59×#390C22semidirect
68. C59×#384C22semidirect
69. C59×#343C22semidirect
70. C59×#343C22semidirect
71. C59×#339C22semidirect
72. C59×#339C22semidirect
192. #104×C59D4semidirect
321. M16×C59C2×D4semidirect
363. C42×C59C2×D4semidirect
475. #24471C59direct (N × H)
522. #3056C2×C59semidirect
523. C2×#455C2×C59semidirect
524. #3007C2×C59semidirect
525. C2×#421C2×C59semidirect
526. #2620C2×C59semidirect
527. #2039C2×C59semidirect
528. #2037C2×C59semidirect
529. #2007C2×C59semidirect
530. #2004C2×C59semidirect
531. #1900C2×C59semidirect
532. #1897C2×C59semidirect
533. #1882C2×C59semidirect
534. #1859C2×C59semidirect
535. #1792C2×C59semidirect
550. C2×#137C22×C59semidirect
551. C2×#137C22×C59semidirect
552. C22×M16C22×C59semidirect
563. C2×#124C22×C59semidirect
566. C2×C22⋊Q8C22×C59semidirect
570. C2×#117C22×C59semidirect
580. #428C22×C59semidirect
584. C2×#104C22×C59semidirect
585. C2×#104C22×C59semidirect
586. C2×#104C22×C59semidirect
587. C2×#104C22×C59semidirect
588. #419C22×C59semidirect
590. #417C22×C59semidirect
591. #417C22×C59semidirect
592. C2×#100C22×C59semidirect
593. C2×#100C22×C59semidirect
594. #407C22×C59semidirect
597. #391C22×C59semidirect
598. #390C22×C59semidirect
599. #384C22×C59semidirect
600. #343C22×C59semidirect
601. #343C22×C59semidirect
602. #339C22×C59semidirect
603. #339C22×C59semidirect
604. C59#24471direct (N × H)
724. #104D4×C59semidirect
853. M16C2×D4×C59semidirect
895. C42C2×D4×C59semidirect

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
C2×C59×#4212
C59×#26202
C59×#20392
C59×#20372
C59×#20072
C59×#20042
C59×#19002
C59×#18972
C59×#18822
C59×#18592
C59×#17922
#2447159