Finite Group Databasebeta

← C59×#24468 #28436577

Subgroups — C59×#24468 #28436577

Order 15104.

1502 conjugacy classes of subgroups.

The subgroup lattice has 1090 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
5C2×C59×#421C211yesmaximal, characteristic, complemented
6C59×#2619C211yesmaximal, characteristic, complemented
7C59×#2040C211yesmaximal, characteristic, complemented
8C59×#2037C211yesmaximal, characteristic, complemented
9C59×#2006C211yesmaximal, characteristic, complemented
10C59×#2002C211yesmaximal, characteristic, complemented
11C59×#1900C211yesmaximal, characteristic, complemented
12C59×#1897C211yesmaximal, characteristic, complemented
13C59×#1883C211yesmaximal, characteristic, complemented
14C59×#1860C211yesmaximal, 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×C59C2211yescharacteristic
37C2×#121×C59C2211yescharacteristic, complemented
38C59×#520C2211yescharacteristic
39C2×#117×C59C2211yescharacteristic, complemented
40C59×#469—21no—
41C59×#468—21no—
42C59×#466—21no—
43C59×#465—21no—
44C59×#453—24no—
45C59×#449—21no—
46C59×#449—21no—
47C59×#448—21no—
48C59×#447—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×#418C2211yescharacteristic, complemented
58C59×#417C2211yescharacteristic
59C59×#417C2211yescharacteristic, complemented
60C59×#417C2211yescharacteristic, complemented
61C2×#100×C59C2211yescharacteristic, complemented
62C2×#100×C59C2211yescharacteristic, complemented
63C59×#407C2211yescharacteristic, complemented
64C59×#394—22no—
65C59×#392—22no—
66C59×#390C2211yescharacteristic, complemented
67C59×#390C2211yescharacteristic, complemented
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, 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—21no—
97C22×D4×C59—22no—
98C22×D4×C59D412yes—
99C22×D4×C59D411yescharacteristic, complemented
100C22×D4×C59C2311yescharacteristic
101C22×D4×C59C2311yescharacteristic
102C23×C4×C59—21no—
103C23×C4×C59C2311yescharacteristic
104AGL(1,ℤ/8)×C59—22no—
105AGL(1,ℤ/8)×C59—22no—
106AGL(1,ℤ/8)×C59—22no—
107AGL(1,ℤ/8)×C59—41no—
108AGL(1,ℤ/8)×C59—41no—
109AGL(1,ℤ/8)×C59—41no—
110C2×SD16×C59—21no—
111C2×SD16×C59—21no—
112C2×SD16×C59—21no—
113C2×D8×C59—21no—
114C2×D8×C59—21no—
115C2×D8×C59—21no—
116C2×M16×C59—21no—
117C2×M16×C59—22no—
118C2×M16×C59—41no—
119C2×M16×C59C2311yescharacteristic
120C2×M16×C59C2311yescharacteristic
121C2×M16×C59C2311yescharacteristic
122C2×M16×C59C2311yescharacteristic
123C22×C8×C59—21no—
124#127×C59—22no—
125#127×C59—21no—
126#127×C59—22no—
127#127×C59—41no—
128#124×C59—22no—
129#124×C59—21no—
130#123×C59—22no—
131#123×C59—21no—
132C22⋊Q8×C59—22no—
133C22⋊Q8×C59—21no—
134C22⋊Q8×C59—21no—
135C22⋊Q8×C59D411yescharacteristic, complemented
136C22⋊Q8×C59D411yescharacteristic, complemented
137#121×C59—22no—
138#121×C59—22no—
139#121×C59—22no—
140#121×C59—22no—
141#121×C59—22no—
142#121×C59—21no—
143#121×C59—21no—
144#121×C59—21no—
145#121×C59—21no—
146#121×C59—21no—
147#121×C59—21no—
148#121×C59—22no—
149#121×C59—21no—
150#121×C59—21no—
151#121×C59—21no—
152#121×C59—21no—
153#121×C59—21no—
154#121×C59—21no—
155#121×C59D411yescharacteristic, complemented
156#121×C59D411yescharacteristic, complemented
157#120×C59—22no—
158#120×C59—22no—
159#120×C59—22no—
160#120×C59—21no—
161#120×C59—22no—
162C4×Q8×C59—21no—
163C4×D4×C59—22no—
164C4×D4×C59—22no—
165C4×D4×C59—21no—
166C4×D4×C59—22no—
167C4×D4×C59—21no—
168C4×D4×C59—21no—
169#117×C59—21no—
170#117×C59—22no—
171#117×C59—41no—
172#117×C59C2311yescharacteristic
173C2×C4⋊C4×C59—21no—
174C2×C4⋊C4×C59—21no—
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#102×C59—21no—
197#102×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×C59—21no—
209C24×C59C2×D412yes—
210C24×C59C2×D411yescharacteristic
211#41×C59—21no—
212#41×C59—21no—
213#41×C59—22no—
214#41×C59—22no—
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—21no—
223#41×C59—42no—
224#41×C59—42no—
225#41×C59—41no—
226#41×C59—41no—
227#41×C59—42no—
228#41×C59—42no—
229#41×C59—42no—
230#41×C59—42no—
231#41×C59—42no—
232#41×C59—42no—
233#41×C59C2×D412yes—
234#41×C59#4112yes—
235C2×Q8×C59—21no—
236C2×Q8×C59—22no—
237C2×Q8×C59—41no—
238C2×Q8×C59C2×D411yescharacteristic
239C2×Q8×C59C2×D411yescharacteristic
240C2×Q8×C59C2×D411yescharacteristic
241C2×D4×C59—21no—
242C2×D4×C59—22no—
243C2×D4×C59—22no—
244C2×D4×C59—22no—
245C2×D4×C59—22no—
246C2×D4×C59—21no—
247C2×D4×C59—21no—
248C2×D4×C59—21no—
249C2×D4×C59—21no—
250C2×D4×C59—21no—
251C2×D4×C59—22no—
252C2×D4×C59—22no—
253C2×D4×C59—22no—
254C2×D4×C59—21no—
255C2×D4×C59—22no—
256C2×D4×C59—21no—
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—41no—
270C2×D4×C59—42no—
271C2×D4×C59—42no—
272C2×D4×C59—44no—
273C2×D4×C59—42no—
274C2×D4×C59—42no—
275C2×D4×C59—44no—
276C2×D4×C59—44no—
277C2×D4×C59—42no—
278C2×D4×C59—42no—
279C2×D4×C59—41no—
280C2×D4×C59—41no—
281C2×D4×C59—82no—
282C2×D4×C59—82no—
283C2×D4×C59—82no—
284C2×D4×C59—82no—
285C2×D4×C59—84no—
286C2×D4×C59C2×D411yescharacteristic
287C2×D4×C59C2×D411yescharacteristic
288C2×D4×C59C2×D411yescharacteristic
289C22×C4×C59—21no—
290C22×C4×C59—21no—
291C22×C4×C59—21no—
292C22×C4×C59—21no—
293C22×C4×C59—21no—
294C22×C4×C59—22no—
295C22×C4×C59—21no—
296C22×C4×C59—21no—
297C22×C4×C59—22no—
298C22×C4×C59—21no—
299C22×C4×C59—21no—
300C22×C4×C59—21no—
301C22×C4×C59—21no—
302C22×C4×C59—21no—
303C22×C4×C59—21no—
304C22×C4×C59—42no—
305C22×C4×C59—42no—
306C22×C4×C59C2×D411yescharacteristic
307C22×C4×C59C2×D411yescharacteristic
308C22×C4×C59C2×D411yescharacteristic
309C22×C4×C59C2×D411yescharacteristic
310C22×C4×C59C2×D411yescharacteristic
311C22×C4×C59C2×D412yes—
312C22×C4×C59C2411yescharacteristic
313SD16×C59—42no—
314SD16×C59—42no—
315SD16×C59—42no—
316D8×C59—42no—
317D8×C59—42no—
318D8×C59—42no—
319M16×C59—21no—
320M16×C59—21no—
321M16×C59—21no—
322M16×C59—21no—
323M16×C59—21no—
324M16×C59—21no—
325M16×C59—21no—
326M16×C59—42no—
327M16×C59C2×D412yescomplemented
328C2×C8×C59—21no—
329C2×C8×C59—21no—
330C2×C8×C59—21no—
331C2×C8×C59—21no—
332C2×C8×C59—42no—
333C4⋊C4×C59—22no—
334C4⋊C4×C59—22no—
335C4⋊C4×C59—21no—
336C4⋊C4×C59—21no—
337C4⋊C4×C59—21no—
338C4⋊C4×C59—21no—
339C4⋊C4×C59—21no—
340C4⋊C4×C59—21no—
341C4⋊C4×C59—42no—
342C4⋊C4×C59C2×D411yescharacteristic
343C4⋊C4×C59C2×D411yescharacteristic
344C22⋊C4×C59—22no—
345C22⋊C4×C59—22no—
346C22⋊C4×C59—22no—
347C22⋊C4×C59—22no—
348C22⋊C4×C59—22no—
349C22⋊C4×C59—21no—
350C22⋊C4×C59—21no—
351C22⋊C4×C59—21no—
352C22⋊C4×C59—21no—
353C22⋊C4×C59—22no—
354C22⋊C4×C59—22no—
355C22⋊C4×C59—21no—
356C22⋊C4×C59—42no—
357C22⋊C4×C59—41no—
358C22⋊C4×C59—41no—
359C22⋊C4×C59—82no—
360C22⋊C4×C59—82no—
361C42×C59—22no—
362C42×C59—21no—
363C42×C59—21no—
364C42×C59—21no—
365C42×C59—21no—
366C42×C59C2×D412yescomplemented
367C23×C59—21no—
368C23×C59—21no—
369C23×C59—21no—
370C23×C59—22no—
371C23×C59—21no—
372C23×C59—21no—
373C23×C59—22no—
374C23×C59—22no—
375C23×C59—41no—
376C23×C59—41no—
377C23×C59—42no—
378C23×C59—42no—
379C23×C59—44no—
380C23×C59—42no—
381C23×C59—42no—
382C23×C59—42no—
383C23×C59—42no—
384C23×C59—41no—
385C23×C59—41no—
386C23×C59—41no—
387C23×C59—81no—
388C23×C59—82no—
389C23×C59—82no—
390C23×C59#12011yescharacteristic
391C23×C59#12011yescharacteristic
392C23×C59C22×D411yescharacteristic
393Q8×C59—21no—
394Q8×C59—21no—
395Q8×C59—21no—
396Q8×C59—21no—
397Q8×C59—21no—
398Q8×C59—42no—
399Q8×C59#12112yes—
400D4×C59—22no—
401D4×C59—22no—
402D4×C59—21no—
403D4×C59—21no—
404D4×C59—21no—
405D4×C59—21no—
406D4×C59—21no—
407D4×C59—42no—
408D4×C59—42no—
409D4×C59—44no—
410D4×C59—42no—
411D4×C59—44no—
412D4×C59—44no—
413D4×C59—42no—
414D4×C59—41no—
415D4×C59—41no—
416D4×C59—41no—
417D4×C59—41no—
418D4×C59—41no—
419D4×C59—41no—
420D4×C59—41no—
421D4×C59—41no—
422D4×C59—41no—
423D4×C59—41no—
424D4×C59—41no—
425D4×C59—41no—
426D4×C59—81no—
427D4×C59—82no—
428D4×C59—82no—
429D4×C59—82no—
430D4×C59—82no—
431D4×C59—88no—
432D4×C59—82no—
433D4×C59—82no—
434D4×C59#12112yes—
435C2×C4×C59—21no—
436C2×C4×C59—21no—
437C2×C4×C59—21no—
438C2×C4×C59—21no—
439C2×C4×C59—21no—
440C2×C4×C59—21no—
441C2×C4×C59—21no—
442C2×C4×C59—21no—
443C2×C4×C59—21no—
444C2×C4×C59—22no—
445C2×C4×C59—21no—
446C2×C4×C59—21no—
447C2×C4×C59—22no—
448C2×C4×C59—21no—
449C2×C4×C59—22no—
450C2×C4×C59—21no—
451C2×C4×C59—21no—
452C2×C4×C59—21no—
453C2×C4×C59—22no—
454C2×C4×C59—42no—
455C2×C4×C59—42no—
456C2×C4×C59—42no—
457C2×C4×C59—44no—
458C2×C4×C59—41no—
459C2×C4×C59—41no—
460C2×C4×C59—41no—
461C2×C4×C59—41no—
462C2×C4×C59—41no—
463C2×C4×C59—41no—
464C2×C4×C59—42no—
465C2×C4×C59—41no—
466C2×C4×C59—41no—
467C2×C4×C59—42no—
468C2×C4×C59—41no—
469C2×C4×C59—41no—
470C2×C4×C59—82no—
471C2×C4×C59#12011yescharacteristic
472C2×C4×C59#12011yescharacteristic
473C2×C4×C59C22×D411yescharacteristic
474C2×C4×C59C22×D411yescharacteristic
475C2×C4×C59C22×D411yescharacteristic
476C2×C4×C59C2×#4111yescharacteristic
477C2×C4×C59H(5,𝔽2)11yescharacteristic
478C2×C4×C59H(5,𝔽2)11yescharacteristic
479C8×C59—22no—
480C8×C59—41no—
481C8×C59—41no—
482C8×C59—41no—
483#24468C5911yesmaximal, characteristic, direct product factor, Sylow
484C22×C59—21no—
485C22×C59—21no—
486C22×C59—21no—
487C22×C59—21no—
488C22×C59—22no—
489C22×C59—21no—
490C22×C59—21no—
491C22×C59—21no—
492C22×C59—21no—
493C22×C59—41no—
494C22×C59—41no—
495C22×C59—41no—
496C22×C59—41no—
497C22×C59—42no—
498C22×C59—42no—
499C22×C59—41no—
500C22×C59—41no—
501C22×C59—41no—
502C22×C59—42no—
503C22×C59—41no—
504C22×C59—81no—
505C22×C59—81no—
506C22×C59—82no—
507C22×C59—82no—
508C22×C59—82no—
509C22×C59—82no—
510C22×C59—84no—
511C22×C59—81no—
512C22×C59—81no—
513C22×C59—81no—
514C22×C59—164no—
515C22×C59C2×#12011yescharacteristic
516C22×C59D4211yescharacteristic
517C22×C59#54611yescharacteristic
518C4×C59—21no—
519C4×C59—21no—
520C4×C59—22no—
521C4×C59—42no—
522C4×C59—41no—
523C4×C59—41no—
524C4×C59—42no—
525C4×C59—41no—
526C4×C59—41no—
527C4×C59—81no—
528C4×C59—81no—
529C4×C59C2×#12111yescharacteristic
530C4×C59#53411yescharacteristic
531C4×C59D4211yescharacteristic
532C4×C59#54611yescharacteristic
533#3488C2×C5911yescharacteristic, complemented
534#3055C2×C5911yescharacteristic, complemented
535C2×#453C2×C5911yescharacteristic, complemented
536#3006C2×C5911yescharacteristic, complemented
537C2×#421C2×C5911yescharacteristic, complemented
538#2619C2×C5911yescharacteristic, complemented
539#2040C2×C5911yescharacteristic, complemented
540#2037C2×C5911yescharacteristic, complemented
541#2006C2×C5911yescharacteristic, complemented
542#2002C2×C5911yescharacteristic, complemented
543#1900C2×C5911yescharacteristic, complemented
544#1897C2×C5911yescharacteristic, complemented
545#1883C2×C5911yescharacteristic, complemented
546#1860C2×C5911yescharacteristic, complemented
547#1792C2×C5911yescharacteristic, complemented
548C2×C59—21no—
549C2×C59—21no—
550C2×C59—41no—
551C2×C59—41no—
552C2×C59—42no—
553C2×C59—81no—
554C2×C59—82no—
555C2×C59—81no—
556C2×C59—161no—
557C2×C59#241011yescharacteristic
558C2×C59#301911yescharacteristic
559C2×C59#302111yescharacteristic
560C2×H(5,𝔽2)C22×C5911yescharacteristic
561C22×#41C22×C5911yescharacteristic
562C2×AGL(1,ℤ/8)C22×C5911yescharacteristic
563C2×AGL(1,ℤ/8)C22×C5911yescharacteristic, complemented
564C2×AGL(1,ℤ/8)C22×C5911yescharacteristic, complemented
565C22×M16C22×C5911yescharacteristic, complemented
566#550—21no—
567#548—21no—
568#546—21no—
569#546—22no—
570D42—22no—
571D42—21no—
572#537—21no—
573#537C22×C5911yescharacteristic
574#535—21no—
575#535C22×C5911yescharacteristic
576C2×#127C22×C5911yescharacteristic, complemented
577#525—21no—
578#525C22×C5911yescharacteristic
579C2×#121—21no—
580C2×#121C22×C5911yescharacteristic
581C2×#121C22×C5911yescharacteristic, complemented
582#520C22×C5911yescharacteristic
583C2×#117C22×C5911yescharacteristic, complemented
584#469—21no—
585#468—21no—
586#466—21no—
587#465—21no—
588#453—24no—
589#449—21no—
590#449—21no—
591#448—21no—
592#447—21no—
593#428C22×C5911yescharacteristic, complemented
594#421—24no—
595C2×#104C22×C5911yescharacteristic
596C2×#104C22×C5911yescharacteristic
597C2×#104C22×C5911yescharacteristic, complemented
598C2×#104C22×C5911yescharacteristic, complemented
599C2×#104C22×C5911yescharacteristic, complemented
600C2×#104C22×C5911yescharacteristic, complemented
601#418C22×C5911yescharacteristic, complemented
602#417C22×C5911yescharacteristic
603#417C22×C5911yescharacteristic, complemented
604#417C22×C5911yescharacteristic, complemented
605C2×#100C22×C5911yescharacteristic, complemented
606C2×#100C22×C5911yescharacteristic, complemented
607#407C22×C5911yescharacteristic, complemented
608#394—22no—
609#392—22no—
610#390C22×C5911yescharacteristic, complemented
611#390C22×C5911yescharacteristic, complemented
612#382C22×C5911yescharacteristic, complemented
613#343C22×C5911yescharacteristic, complemented
614#343C22×C5911yescharacteristic, complemented
615#339C22×C5911yescharacteristic, complemented
616#339C22×C5911yescharacteristic, complemented
617C59#2446811yescharacteristic, direct product factor, Sylow
618H(5,𝔽2)—22no—
619H(5,𝔽2)—22no—
620H(5,𝔽2)—41no—
621H(5,𝔽2)—41no—
622C2×#41—21no—
623C2×#41—21no—
624C2×#41—21no—
625C2×#41—21no—
626C2×#41—22no—
627C2×#41—22no—
628C2×#41—41no—
629C2×#41—41no—
630C2×#41D4×C5911yescharacteristic, complemented
631C2×#41D4×C5911yescharacteristic, complemented
632C2×#41C23×C5911yescharacteristic
633C2×#41C23×C5911yescharacteristic
634C2×#41C23×C5911yescharacteristic
635C22×Q8D4×C5911yescharacteristic, complemented
636C22×D4—21no—
637C22×D4—22no—
638C22×D4—22no—
639C22×D4—21no—
640C22×D4—21no—
641C22×D4—21no—
642C22×D4—22no—
643C22×D4D4×C5912yes—
644C22×D4D4×C5911yescharacteristic, complemented
645C22×D4C23×C5911yescharacteristic
646C22×D4C23×C5911yescharacteristic
647C23×C4—21no—
648C23×C4C23×C5911yescharacteristic
649AGL(1,ℤ/8)—22no—
650AGL(1,ℤ/8)—22no—
651AGL(1,ℤ/8)—22no—
652AGL(1,ℤ/8)—41no—
653AGL(1,ℤ/8)—41no—
654AGL(1,ℤ/8)—41no—
655C2×SD16—21no—
656C2×SD16—21no—
657C2×SD16—21no—
658C2×D8—21no—
659C2×D8—21no—
660C2×D8—21no—
661C2×M16—21no—
662C2×M16—22no—
663C2×M16—41no—
664C2×M16C23×C5911yescharacteristic
665C2×M16C23×C5911yescharacteristic
666C2×M16C23×C5911yescharacteristic
667C2×M16C23×C5911yescharacteristic
668C22×C8—21no—
669#127—22no—
670#127—21no—
671#127—22no—
672#127—41no—
673#124—22no—
674#124—21no—
675#123—22no—
676#123—21no—
677C22⋊Q8—22no—
678C22⋊Q8—21no—
679C22⋊Q8—21no—
680C22⋊Q8D4×C5911yescharacteristic, complemented
681C22⋊Q8D4×C5911yescharacteristic, complemented
682#121—22no—
683#121—22no—
684#121—22no—
685#121—22no—
686#121—22no—
687#121—21no—
688#121—21no—
689#121—21no—
690#121—21no—
691#121—21no—
692#121—21no—
693#121—22no—
694#121—21no—
695#121—21no—
696#121—21no—
697#121—21no—
698#121—21no—
699#121—21no—
700#121D4×C5911yescharacteristic, complemented
701#121D4×C5911yescharacteristic, complemented
702#120—22no—
703#120—22no—
704#120—22no—
705#120—21no—
706#120—22no—
707C4×Q8—21no—
708C4×D4—22no—
709C4×D4—22no—
710C4×D4—21no—
711C4×D4—22no—
712C4×D4—21no—
713C4×D4—21no—
714#117—21no—
715#117—22no—
716#117—41no—
717#117C23×C5911yescharacteristic
718C2×C4⋊C4—21no—
719C2×C4⋊C4—21no—
720C2×C4⋊C4C23×C5911yescharacteristic
721C2×C4⋊C4C23×C5911yescharacteristic
722C2×C22⋊C4—22no—
723C2×C22⋊C4—21no—
724C2×C22⋊C4—21no—
725C2×C22⋊C4—22no—
726C2×C22⋊C4—22no—
727C2×C22⋊C4D4×C5912yes—
728C2×C42C23×C5911yescharacteristic
729C2×C42C23×C5911yescharacteristic
730#107—21no—
731#106—21no—
732#104—22no—
733#104—22no—
734#104—22no—
735#104—22no—
736#104—41no—
737#104D4×C5914yescomplemented
738#103—21no—
739#103—21no—
740#103—21no—
741#102—21no—
742#102—21no—
743#102—21no—
744#102—21no—
745#102—21no—
746#100—22no—
747#100—41no—
748C22⋊C8—21no—
749C22⋊C8—21no—
750#95—22no—
751C24—22no—
752C24—21no—
753C24—21no—
754C24C2×D4×C5912yes—
755C24C2×D4×C5911yescharacteristic
756#41—21no—
757#41—21no—
758#41—22no—
759#41—22no—
760#41—21no—
761#41—21no—
762#41—21no—
763#41—21no—
764#41—21no—
765#41—21no—
766#41—21no—
767#41—21no—
768#41—42no—
769#41—42no—
770#41—41no—
771#41—41no—
772#41—42no—
773#41—42no—
774#41—42no—
775#41—42no—
776#41—42no—
777#41—42no—
778#41C2×D4×C5912yes—
779#41#41×C5912yes—
780C2×Q8—21no—
781C2×Q8—22no—
782C2×Q8—41no—
783C2×Q8C2×D4×C5911yescharacteristic
784C2×Q8C2×D4×C5911yescharacteristic
785C2×Q8C2×D4×C5911yescharacteristic
786C2×D4—21no—
787C2×D4—22no—
788C2×D4—22no—
789C2×D4—22no—
790C2×D4—22no—
791C2×D4—21no—
792C2×D4—21no—
793C2×D4—21no—
794C2×D4—21no—
795C2×D4—21no—
796C2×D4—22no—
797C2×D4—22no—
798C2×D4—22no—
799C2×D4—21no—
800C2×D4—22no—
801C2×D4—21no—
802C2×D4—21no—
803C2×D4—21no—
804C2×D4—21no—
805C2×D4—21no—
806C2×D4—21no—
807C2×D4—21no—
808C2×D4—21no—
809C2×D4—21no—
810C2×D4—21no—
811C2×D4—21no—
812C2×D4—21no—
813C2×D4—21no—
814C2×D4—41no—
815C2×D4—42no—
816C2×D4—42no—
817C2×D4—44no—
818C2×D4—42no—
819C2×D4—42no—
820C2×D4—44no—
821C2×D4—44no—
822C2×D4—42no—
823C2×D4—42no—
824C2×D4—41no—
825C2×D4—41no—
826C2×D4—82no—
827C2×D4—82no—
828C2×D4—82no—
829C2×D4—82no—
830C2×D4—84no—
831C2×D4C2×D4×C5911yescharacteristic
832C2×D4C2×D4×C5911yescharacteristic
833C2×D4C2×D4×C5911yescharacteristic
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—22no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—22no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—42no—
850C22×C4—42no—
851C22×C4C2×D4×C5911yescharacteristic
852C22×C4C2×D4×C5911yescharacteristic
853C22×C4C2×D4×C5911yescharacteristic
854C22×C4C2×D4×C5911yescharacteristic
855C22×C4C2×D4×C5911yescharacteristic
856C22×C4C2×D4×C5912yes—
857C22×C4C24×C5911yescharacteristic
858SD16—42no—
859SD16—42no—
860SD16—42no—
861D8—42no—
862D8—42no—
863D8—42no—
864M16—21no—
865M16—21no—
866M16—21no—
867M16—21no—
868M16—21no—
869M16—21no—
870M16—21no—
871M16—42no—
872M16C2×D4×C5912yescomplemented
873C2×C8—21no—
874C2×C8—21no—
875C2×C8—21no—
876C2×C8—21no—
877C2×C8—42no—
878C4⋊C4—22no—
879C4⋊C4—22no—
880C4⋊C4—21no—
881C4⋊C4—21no—
882C4⋊C4—21no—
883C4⋊C4—21no—
884C4⋊C4—21no—
885C4⋊C4—21no—
886C4⋊C4—42no—
887C4⋊C4C2×D4×C5911yescharacteristic
888C4⋊C4C2×D4×C5911yescharacteristic
889C22⋊C4—22no—
890C22⋊C4—22no—
891C22⋊C4—22no—
892C22⋊C4—22no—
893C22⋊C4—22no—
894C22⋊C4—21no—
895C22⋊C4—21no—
896C22⋊C4—21no—
897C22⋊C4—21no—
898C22⋊C4—22no—
899C22⋊C4—22no—
900C22⋊C4—21no—
901C22⋊C4—42no—
902C22⋊C4—41no—
903C22⋊C4—41no—
904C22⋊C4—82no—
905C22⋊C4—82no—
906C42—22no—
907C42—21no—
908C42—21no—
909C42—21no—
910C42—21no—
911C42C2×D4×C5912yescomplemented
912C23—21no—
913C23—21no—
914C23—21no—
915C23—22no—
916C23—21no—
917C23—21no—
918C23—22no—
919C23—22no—
920C23—41no—
921C23—41no—
922C23—42no—
923C23—42no—
924C23—44no—
925C23—42no—
926C23—42no—
927C23—42no—
928C23—42no—
929C23—41no—
930C23—41no—
931C23—41no—
932C23—81no—
933C23—82no—
934C23—82no—
935C23#120×C5911yescharacteristic
936C23#120×C5911yescharacteristic
937C23C22×D4×C5911yescharacteristic
938Q8—21no—
939Q8—21no—
940Q8—21no—
941Q8—21no—
942Q8—21no—
943Q8—42no—
944Q8#121×C5912yes—
945D4—22no—
946D4—22no—
947D4—21no—
948D4—21no—
949D4—21no—
950D4—21no—
951D4—21no—
952D4—42no—
953D4—42no—
954D4—44no—
955D4—42no—
956D4—44no—
957D4—44no—
958D4—42no—
959D4—41no—
960D4—41no—
961D4—41no—
962D4—41no—
963D4—41no—
964D4—41no—
965D4—41no—
966D4—41no—
967D4—41no—
968D4—41no—
969D4—41no—
970D4—41no—
971D4—81no—
972D4—82no—
973D4—82no—
974D4—82no—
975D4—82no—
976D4—88no—
977D4—82no—
978D4—82no—
979D4#121×C5912yes—
980C2×C4—21no—
981C2×C4—21no—
982C2×C4—21no—
983C2×C4—21no—
984C2×C4—21no—
985C2×C4—21no—
986C2×C4—21no—
987C2×C4—21no—
988C2×C4—21no—
989C2×C4—22no—
990C2×C4—21no—
991C2×C4—21no—
992C2×C4—22no—
993C2×C4—21no—
994C2×C4—22no—
995C2×C4—21no—
996C2×C4—21no—
997C2×C4—21no—
998C2×C4—22no—
999C2×C4—42no—
1000C2×C4—42no—
1001C2×C4—42no—
1002C2×C4—44no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—42no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—42no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—82no—
1016C2×C4#120×C5911yescharacteristic
1017C2×C4#120×C5911yescharacteristic
1018C2×C4C22×D4×C5911yescharacteristic
1019C2×C4C22×D4×C5911yescharacteristic
1020C2×C4C22×D4×C5911yescharacteristic
1021C2×C4C2×#41×C5911yescharacteristic
1022C2×C4H(5,𝔽2)×C5911yescharacteristic
1023C2×C4H(5,𝔽2)×C5911yescharacteristic
1024C8—22no—
1025C8—41no—
1026C8—41no—
1027C8—41no—
1028C22—21no—
1029C22—21no—
1030C22—21no—
1031C22—21no—
1032C22—21no—
1033C22—21no—
1034C22—21no—
1035C22—21no—
1036C22—22no—
1037C22—41no—
1038C22—41no—
1039C22—42no—
1040C22—41no—
1041C22—41no—
1042C22—41no—
1043C22—42no—
1044C22—41no—
1045C22—41no—
1046C22—41no—
1047C22—42no—
1048C22—81no—
1049C22—81no—
1050C22—82no—
1051C22—82no—
1052C22—82no—
1053C22—82no—
1054C22—84no—
1055C22—81no—
1056C22—81no—
1057C22—81no—
1058C22—164no—
1059C22C2×#120×C5911yescharacteristic
1060C22D42×C5911yescharacteristic
1061C22C59×#54611yescharacteristic
1062C4—21no—
1063C4—21no—
1064C4—22no—
1065C4—42no—
1066C4—42no—
1067C4—41no—
1068C4—41no—
1069C4—41no—
1070C4—41no—
1071C4—81no—
1072C4—81no—
1073C4C2×#121×C5911yescharacteristic
1074C4C59×#53411yescharacteristic
1075C4D42×C5911yescharacteristic
1076C4C59×#54611yescharacteristic
1077C2—21no—
1078C2—21no—
1079C2—41no—
1080C2—41no—
1081C2—42no—
1082C2—81no—
1083C2—82no—
1084C2—81no—
1085C2—161no—
1086C2C59×#241011yescharacteristic
1087C2C59×#301911yescharacteristic
1088C2C59×#302111yescharacteristic
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. C2×C59×#421C2semidirect
6. C59×#2619C2semidirect
7. C59×#2040C2semidirect
8. C59×#2037C2semidirect
9. C59×#2006C2semidirect
10. C59×#2002C2semidirect
11. C59×#1900C2semidirect
12. C59×#1897C2semidirect
13. C59×#1883C2semidirect
14. C59×#1860C2semidirect
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
37. C2×#121×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×#418C22semidirect
59. C59×#417C22semidirect
60. C59×#417C22semidirect
61. C2×#100×C59C22semidirect
62. C2×#100×C59C22semidirect
63. C59×#407C22semidirect
66. C59×#390C22semidirect
67. C59×#390C22semidirect
68. C59×#382C22semidirect
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
135. C22⋊Q8×C59D4semidirect
136. C22⋊Q8×C59D4semidirect
155. #121×C59D4semidirect
156. #121×C59D4semidirect
192. #104×C59D4semidirect
327. M16×C59C2×D4semidirect
366. C42×C59C2×D4semidirect
483. #24468C59direct (N × H)
533. #3488C2×C59semidirect
534. #3055C2×C59semidirect
535. C2×#453C2×C59semidirect
536. #3006C2×C59semidirect
537. C2×#421C2×C59semidirect
538. #2619C2×C59semidirect
539. #2040C2×C59semidirect
540. #2037C2×C59semidirect
541. #2006C2×C59semidirect
542. #2002C2×C59semidirect
543. #1900C2×C59semidirect
544. #1897C2×C59semidirect
545. #1883C2×C59semidirect
546. #1860C2×C59semidirect
547. #1792C2×C59semidirect
563. C2×AGL(1,ℤ/8)C22×C59semidirect
564. C2×AGL(1,ℤ/8)C22×C59semidirect
565. C22×M16C22×C59semidirect
576. C2×#127C22×C59semidirect
581. C2×#121C22×C59semidirect
583. C2×#117C22×C59semidirect
593. #428C22×C59semidirect
597. C2×#104C22×C59semidirect
598. C2×#104C22×C59semidirect
599. C2×#104C22×C59semidirect
600. C2×#104C22×C59semidirect
601. #418C22×C59semidirect
603. #417C22×C59semidirect
604. #417C22×C59semidirect
605. C2×#100C22×C59semidirect
606. C2×#100C22×C59semidirect
607. #407C22×C59semidirect
610. #390C22×C59semidirect
611. #390C22×C59semidirect
612. #382C22×C59semidirect
613. #343C22×C59semidirect
614. #343C22×C59semidirect
615. #339C22×C59semidirect
616. #339C22×C59semidirect
617. C59#24468direct (N × H)
630. C2×#41D4×C59semidirect
631. C2×#41D4×C59semidirect
635. C22×Q8D4×C59semidirect
644. C22×D4D4×C59semidirect
680. C22⋊Q8D4×C59semidirect
681. C22⋊Q8D4×C59semidirect
700. #121D4×C59semidirect
701. #121D4×C59semidirect
737. #104D4×C59semidirect
872. M16C2×D4×C59semidirect
911. 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×#30552
C2×C59×#4532
C59×#30062
C2×C59×#4212
C59×#26192
C59×#20402
C59×#20372
C59×#20062
C59×#20022
C59×#19002
C59×#18972
C59×#18832
C59×#18602
C59×#17922
#2446859