Finite Group Databasebeta

← C59×#24469 #28436578

Subgroups — C59×#24469 #28436578

Order 15104.

1402 conjugacy classes of subgroups.

The subgroup lattice has 1052 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C59×#3489C211yesmaximal, characteristic, complemented
2C59×#3055C211yesmaximal, characteristic, complemented
3C2×C59×#454C211yesmaximal, characteristic, complemented
4C59×#3006C211yesmaximal, characteristic, complemented
5C2×C59×#421C211yesmaximal, characteristic, complemented
6C59×#2620C211yesmaximal, characteristic, complemented
7C59×#2039C211yesmaximal, characteristic, complemented
8C59×#2038C211yesmaximal, characteristic, complemented
9C59×#2006C211yesmaximal, characteristic, complemented
10C59×#2003C211yesmaximal, characteristic, complemented
11C59×#1901C211yesmaximal, characteristic, complemented
12C59×#1897C211yesmaximal, characteristic, complemented
13C59×#1883C211yesmaximal, characteristic, complemented
14C59×#1859C211yesmaximal, characteristic, complemented
15C59×#1793C211yesmaximal, characteristic, complemented
16C2×2−1+4×C59C2211yescharacteristic
17C22×#41×C59C2211yescharacteristic
18C2×AGL(1,ℤ/8)×C59C2211yescharacteristic
19C2×AGL(1,ℤ/8)×C59C2211yescharacteristic
20C2×AGL(1,ℤ/8)×C59C2211yescharacteristic, complemented
21C22×M16×C59C2211yescharacteristic
22D4×Q8×C59—21no—
23C59×#548—21no—
24C59×#547—21no—
25C59×#547—22no—
26C59×#546—21no—
27C59×#546—22no—
28C59×#537—21no—
29C59×#537C2211yescharacteristic
30C59×#536—21no—
31C59×#536C2211yescharacteristic
32C2×#124×C59C2211yescharacteristic, complemented
33C59×#525—21no—
34C59×#525C2211yescharacteristic
35C2×C22⋊Q8×C59—21no—
36C2×C22⋊Q8×C59C2211yescharacteristic
37C2×#121×C59C2211yescharacteristic
38C59×#520C2211yescharacteristic
39C2×#117×C59C2211yescharacteristic
40C59×#469—21no—
41C59×#468—21no—
42C59×#466—21no—
43C59×#465—21no—
44C59×#454—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
54C2×#104×C59C2211yescharacteristic
55C2×#104×C59C2211yescharacteristic, complemented
56C2×#104×C59C2211yescharacteristic, complemented
57C59×#418C2211yescharacteristic, complemented
58C59×#417C2211yescharacteristic
59C59×#417C2211yescharacteristic
60C59×#417C2211yescharacteristic, complemented
61C2×#101×C59C2211yescharacteristic, complemented
62C2×#101×C59C2211yescharacteristic, complemented
63C59×#407C2211yescharacteristic
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
732−1+4×C59—22no—
742−1+4×C59—22no—
752−1+4×C59—41no—
762−1+4×C59—41no—
77C2×#41×C59—21no—
78C2×#41×C59—21no—
79C2×#41×C59—21no—
80C2×#41×C59—22no—
81C2×#41×C59—21no—
82C2×#41×C59—22no—
83C2×#41×C59—22no—
84C2×#41×C59—41no—
85C2×#41×C59—41no—
86C2×#41×C59D411yescharacteristic
87C2×#41×C59D411yescharacteristic
88C2×#41×C59C2311yescharacteristic
89C2×#41×C59C2311yescharacteristic
90C2×#41×C59C2311yescharacteristic
91C22×Q8×C59—21no—
92C22×Q8×C59—21no—
93C22×Q8×C59D411yescharacteristic
94C22×Q8×C59C2311yescharacteristic
95C22×D4×C59—21no—
96C22×D4×C59—21no—
97C22×D4×C59D411yescharacteristic
98C22×D4×C59C2311yescharacteristic
99C23×C4×C59—21no—
100C23×C4×C59C2311yescharacteristic
101AGL(1,ℤ/8)×C59—22no—
102AGL(1,ℤ/8)×C59—22no—
103AGL(1,ℤ/8)×C59—22no—
104AGL(1,ℤ/8)×C59—41no—
105AGL(1,ℤ/8)×C59—41no—
106AGL(1,ℤ/8)×C59—41no—
107C2×SD16×C59—21no—
108C2×SD16×C59—21no—
109C2×SD16×C59—21no—
110C2×D8×C59—21no—
111C2×D8×C59—21no—
112C2×D8×C59—21no—
113C2×M16×C59—21no—
114C2×M16×C59—22no—
115C2×M16×C59—41no—
116C2×M16×C59C2311yescharacteristic
117C2×M16×C59C2311yescharacteristic
118C2×M16×C59C2311yescharacteristic
119C2×M16×C59C2311yescharacteristic
120C22×C8×C59—21no—
121C4⋊Q8×C59—22no—
122C4⋊Q8×C59—21no—
123#124×C59—22no—
124#124×C59—21no—
125#124×C59—22no—
126#124×C59—41no—
127#123×C59—22no—
128#123×C59—22no—
129#123×C59—22no—
130#123×C59—21no—
131#123×C59—22no—
132C22⋊Q8×C59—22no—
133C22⋊Q8×C59—22no—
134C22⋊Q8×C59—22no—
135C22⋊Q8×C59—21no—
136C22⋊Q8×C59—21no—
137C22⋊Q8×C59—21no—
138C22⋊Q8×C59—21no—
139C22⋊Q8×C59—21no—
140C22⋊Q8×C59—21no—
141C22⋊Q8×C59—21no—
142C22⋊Q8×C59—21no—
143C22⋊Q8×C59D411yescharacteristic
144C22⋊Q8×C59D411yescharacteristic
145#121×C59—22no—
146#121×C59—22no—
147#121×C59—22no—
148#121×C59—21no—
149#121×C59—21no—
150#121×C59—22no—
151#121×C59—21no—
152#121×C59—21no—
153#121×C59—21no—
154#121×C59—21no—
155#121×C59D411yescharacteristic
156#121×C59D411yescharacteristic
157#120×C59—22no—
158#120×C59—21no—
159C4×Q8×C59—21no—
160C4×D4×C59—22no—
161C4×D4×C59—22no—
162C4×D4×C59—21no—
163C4×D4×C59—22no—
164C4×D4×C59—21no—
165C4×D4×C59—21no—
166#117×C59—21no—
167#117×C59—22no—
168#117×C59—41no—
169#117×C59C2311yescharacteristic
170C2×C4⋊C4×C59—22no—
171C2×C4⋊C4×C59—21no—
172C2×C4⋊C4×C59—21no—
173C2×C4⋊C4×C59—22no—
174C2×C4⋊C4×C59D412yes—
175C2×C4⋊C4×C59C2311yescharacteristic
176C2×C4⋊C4×C59C2311yescharacteristic
177C2×C22⋊C4×C59—22no—
178C2×C22⋊C4×C59—21no—
179C2×C22⋊C4×C59—22no—
180C2×C22⋊C4×C59—21no—
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#101×C59—22no—
202#101×C59—41no—
203C22⋊C8×C59—21no—
204C22⋊C8×C59—21no—
205#95×C59—22no—
206C24×C59—21no—
207C24×C59—21no—
208C24×C59C2×D411yescharacteristic
209#41×C59—21no—
210#41×C59—21no—
211#41×C59—22no—
212#41×C59—22no—
213#41×C59—21no—
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—42no—
222#41×C59—42no—
223#41×C59—41no—
224#41×C59—41no—
225#41×C59—42no—
226#41×C59—42no—
227#41×C59—42no—
228#41×C59—42no—
229#41×C59—44no—
230#41×C59—44no—
231#41×C59—42no—
232#41×C59—42no—
233#41×C59C2×D412yes—
234#41×C59#4112yes—
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—21no—
243C2×Q8×C59—22no—
244C2×Q8×C59—41no—
245C2×Q8×C59—42no—
246C2×Q8×C59—42no—
247C2×Q8×C59—42no—
248C2×Q8×C59—42no—
249C2×Q8×C59C2×D411yescharacteristic
250C2×Q8×C59C2×D411yescharacteristic
251C2×Q8×C59C2×D411yescharacteristic
252C2×D4×C59—21no—
253C2×D4×C59—22no—
254C2×D4×C59—22no—
255C2×D4×C59—21no—
256C2×D4×C59—21no—
257C2×D4×C59—21no—
258C2×D4×C59—21no—
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—21no—
269C2×D4×C59—41no—
270C2×D4×C59—42no—
271C2×D4×C59—42no—
272C2×D4×C59—41no—
273C2×D4×C59—41no—
274C2×D4×C59—82no—
275C2×D4×C59C2×D411yescharacteristic
276C2×D4×C59C2×D411yescharacteristic
277C2×D4×C59C2×D411yescharacteristic
278C22×C4×C59—21no—
279C22×C4×C59—21no—
280C22×C4×C59—21no—
281C22×C4×C59—21no—
282C22×C4×C59—21no—
283C22×C4×C59—22no—
284C22×C4×C59—22no—
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—21no—
292C22×C4×C59—21no—
293C22×C4×C59—21no—
294C22×C4×C59—42no—
295C22×C4×C59—42no—
296C22×C4×C59C2×D412yes—
297C22×C4×C59C2×D411yescharacteristic
298C22×C4×C59C2×D411yescharacteristic
299C22×C4×C59C2×D411yescharacteristic
300C22×C4×C59C2×D411yescharacteristic
301C22×C4×C59C2×D411yescharacteristic
302C22×C4×C59C2×D412yes—
303C22×C4×C59C2411yescharacteristic
304SD16×C59—42no—
305SD16×C59—42no—
306SD16×C59—42no—
307D8×C59—42no—
308D8×C59—42no—
309D8×C59—42no—
310M16×C59—21no—
311M16×C59—21no—
312M16×C59—21no—
313M16×C59—21no—
314M16×C59—21no—
315M16×C59—21no—
316M16×C59—21no—
317M16×C59—42no—
318M16×C59C2×D412yes—
319C2×C8×C59—21no—
320C2×C8×C59—21no—
321C2×C8×C59—21no—
322C2×C8×C59—21no—
323C2×C8×C59—42no—
324C4⋊C4×C59—22no—
325C4⋊C4×C59—22no—
326C4⋊C4×C59—22no—
327C4⋊C4×C59—22no—
328C4⋊C4×C59—21no—
329C4⋊C4×C59—22no—
330C4⋊C4×C59—22no—
331C4⋊C4×C59—21no—
332C4⋊C4×C59—21no—
333C4⋊C4×C59—21no—
334C4⋊C4×C59—21no—
335C4⋊C4×C59—21no—
336C4⋊C4×C59—42no—
337C4⋊C4×C59—82no—
338C4⋊C4×C59C2×D411yescharacteristic
339C4⋊C4×C59C2×D411yescharacteristic
340C22⋊C4×C59—22no—
341C22⋊C4×C59—22no—
342C22⋊C4×C59—22no—
343C22⋊C4×C59—22no—
344C22⋊C4×C59—22no—
345C22⋊C4×C59—21no—
346C22⋊C4×C59—22no—
347C22⋊C4×C59—22no—
348C22⋊C4×C59—21no—
349C22⋊C4×C59—21no—
350C22⋊C4×C59—21no—
351C22⋊C4×C59—21no—
352C22⋊C4×C59—44no—
353C22⋊C4×C59—42no—
354C22⋊C4×C59—41no—
355C22⋊C4×C59—41no—
356C22⋊C4×C59—82no—
357C42×C59—22no—
358C42×C59—21no—
359C42×C59—21no—
360C42×C59—21no—
361C42×C59—21no—
362C42×C59C2×D412yes—
363C23×C59—21no—
364C23×C59—21no—
365C23×C59—21no—
366C23×C59—21no—
367C23×C59—21no—
368C23×C59—41no—
369C23×C59—41no—
370C23×C59—42no—
371C23×C59—42no—
372C23×C59—42no—
373C23×C59—42no—
374C23×C59—41no—
375C23×C59—41no—
376C23×C59—41no—
377C23×C59—81no—
378C23×C59#12011yescharacteristic
379C23×C59#12011yescharacteristic
380C23×C59C22×D411yescharacteristic
381Q8×C59—21no—
382Q8×C59—21no—
383Q8×C59—21no—
384Q8×C59—21no—
385Q8×C59—21no—
386Q8×C59—42no—
387Q8×C59—44no—
388Q8×C59—41no—
389Q8×C59—41no—
390Q8×C59—41no—
391Q8×C59—41no—
392Q8×C59#12112yes—
393D4×C59—22no—
394D4×C59—22no—
395D4×C59—21no—
396D4×C59—21no—
397D4×C59—21no—
398D4×C59—21no—
399D4×C59—21no—
400D4×C59—42no—
401D4×C59—42no—
402D4×C59—42no—
403D4×C59—42no—
404D4×C59—44no—
405D4×C59—41no—
406D4×C59—41no—
407D4×C59—41no—
408D4×C59—41no—
409D4×C59—41no—
410D4×C59—41no—
411D4×C59—41no—
412D4×C59—41no—
413D4×C59—81no—
414D4×C59—82no—
415D4×C59—82no—
416D4×C59—82no—
417D4×C59#12112yes—
418C2×C4×C59—21no—
419C2×C4×C59—21no—
420C2×C4×C59—21no—
421C2×C4×C59—21no—
422C2×C4×C59—21no—
423C2×C4×C59—21no—
424C2×C4×C59—21no—
425C2×C4×C59—21no—
426C2×C4×C59—21no—
427C2×C4×C59—22no—
428C2×C4×C59—21no—
429C2×C4×C59—21no—
430C2×C4×C59—22no—
431C2×C4×C59—21no—
432C2×C4×C59—22no—
433C2×C4×C59—21no—
434C2×C4×C59—21no—
435C2×C4×C59—22no—
436C2×C4×C59—21no—
437C2×C4×C59—22no—
438C2×C4×C59—22no—
439C2×C4×C59—22no—
440C2×C4×C59—42no—
441C2×C4×C59—42no—
442C2×C4×C59—42no—
443C2×C4×C59—44no—
444C2×C4×C59—41no—
445C2×C4×C59—41no—
446C2×C4×C59—44no—
447C2×C4×C59—41no—
448C2×C4×C59—41no—
449C2×C4×C59—41no—
450C2×C4×C59—41no—
451C2×C4×C59—42no—
452C2×C4×C59—41no—
453C2×C4×C59—42no—
454C2×C4×C59—41no—
455C2×C4×C59—41no—
456C2×C4×C59—41no—
457C2×C4×C59—82no—
458C2×C4×C59#12011yescharacteristic
459C2×C4×C59#12011yescharacteristic
460C2×C4×C59C22×D411yescharacteristic
461C2×C4×C59C22×D411yescharacteristic
462C2×C4×C59C22×D411yescharacteristic
463C2×C4×C59C2×#4111yescharacteristic
464C2×C4×C59H(5,𝔽2)11yescharacteristic
465C2×C4×C59H(5,𝔽2)11yescharacteristic
466C8×C59—22no—
467C8×C59—41no—
468C8×C59—41no—
469C8×C59—41no—
470#24469C5911yesmaximal, characteristic, direct product factor, Sylow
471C22×C59—21no—
472C22×C59—21no—
473C22×C59—21no—
474C22×C59—21no—
475C22×C59—22no—
476C22×C59—21no—
477C22×C59—21no—
478C22×C59—21no—
479C22×C59—21no—
480C22×C59—41no—
481C22×C59—41no—
482C22×C59—41no—
483C22×C59—41no—
484C22×C59—41no—
485C22×C59—41no—
486C22×C59—41no—
487C22×C59—41no—
488C22×C59—81no—
489C22×C59—81no—
490C22×C59—82no—
491C22×C59—82no—
492C22×C59—84no—
493C22×C59—81no—
494C22×C59—81no—
495C22×C59—81no—
496C22×C59C2×#12011yescharacteristic
497C22×C59D4211yescharacteristic
498C22×C59#54611yescharacteristic
499C4×C59—21no—
500C4×C59—21no—
501C4×C59—22no—
502C4×C59—42no—
503C4×C59—42no—
504C4×C59—41no—
505C4×C59—41no—
506C4×C59—41no—
507C4×C59—42no—
508C4×C59—41no—
509C4×C59—81no—
510C4×C59—81no—
511C4×C59C2×#12111yescharacteristic
512C4×C59#53411yescharacteristic
513C4×C59D4211yescharacteristic
514C4×C59#54611yescharacteristic
515#3489C2×C5911yescharacteristic, complemented
516#3055C2×C5911yescharacteristic, complemented
517C2×#454C2×C5911yescharacteristic, complemented
518#3006C2×C5911yescharacteristic, complemented
519C2×#421C2×C5911yescharacteristic, complemented
520#2620C2×C5911yescharacteristic, complemented
521#2039C2×C5911yescharacteristic, complemented
522#2038C2×C5911yescharacteristic, complemented
523#2006C2×C5911yescharacteristic, complemented
524#2003C2×C5911yescharacteristic, complemented
525#1901C2×C5911yescharacteristic, complemented
526#1897C2×C5911yescharacteristic, complemented
527#1883C2×C5911yescharacteristic, complemented
528#1859C2×C5911yescharacteristic, complemented
529#1793C2×C5911yescharacteristic, complemented
530C2×C59—21no—
531C2×C59—21no—
532C2×C59—41no—
533C2×C59—41no—
534C2×C59—42no—
535C2×C59—81no—
536C2×C59—81no—
537C2×C59—161no—
538C2×C59#241011yescharacteristic
539C2×C59#302011yescharacteristic
540C2×C59#302111yescharacteristic
541C2×2−1+4C22×C5911yescharacteristic
542C22×#41C22×C5911yescharacteristic
543C2×AGL(1,ℤ/8)C22×C5911yescharacteristic
544C2×AGL(1,ℤ/8)C22×C5911yescharacteristic
545C2×AGL(1,ℤ/8)C22×C5911yescharacteristic, complemented
546C22×M16C22×C5911yescharacteristic
547D4×Q8—21no—
548#548—21no—
549#547—21no—
550#547—22no—
551#546—21no—
552#546—22no—
553#537—21no—
554#537C22×C5911yescharacteristic
555#536—21no—
556#536C22×C5911yescharacteristic
557C2×#124C22×C5911yescharacteristic, complemented
558#525—21no—
559#525C22×C5911yescharacteristic
560C2×C22⋊Q8—21no—
561C2×C22⋊Q8C22×C5911yescharacteristic
562C2×#121C22×C5911yescharacteristic
563#520C22×C5911yescharacteristic
564C2×#117C22×C5911yescharacteristic
565#469—21no—
566#468—21no—
567#466—21no—
568#465—21no—
569#454—24no—
570#449—21no—
571#449—21no—
572#448—21no—
573#447—21no—
574#428C22×C5911yescharacteristic, complemented
575#421—24no—
576C2×#104C22×C5911yescharacteristic
577C2×#104C22×C5911yescharacteristic
578C2×#104C22×C5911yescharacteristic
579C2×#104C22×C5911yescharacteristic
580C2×#104C22×C5911yescharacteristic, complemented
581C2×#104C22×C5911yescharacteristic, complemented
582#418C22×C5911yescharacteristic, complemented
583#417C22×C5911yescharacteristic
584#417C22×C5911yescharacteristic
585#417C22×C5911yescharacteristic, complemented
586C2×#101C22×C5911yescharacteristic, complemented
587C2×#101C22×C5911yescharacteristic, complemented
588#407C22×C5911yescharacteristic
589#396—22no—
590#394—22no—
591#391C22×C5911yescharacteristic, complemented
592#390C22×C5911yescharacteristic, complemented
593#384C22×C5911yescharacteristic, complemented
594#343C22×C5911yescharacteristic, complemented
595#343C22×C5911yescharacteristic, complemented
596#339C22×C5911yescharacteristic, complemented
597#339C22×C5911yescharacteristic, complemented
598C59#2446911yescharacteristic, direct product factor, Sylow
5992−1+4—22no—
6002−1+4—22no—
6012−1+4—41no—
6022−1+4—41no—
603C2×#41—21no—
604C2×#41—21no—
605C2×#41—21no—
606C2×#41—22no—
607C2×#41—21no—
608C2×#41—22no—
609C2×#41—22no—
610C2×#41—41no—
611C2×#41—41no—
612C2×#41D4×C5911yescharacteristic
613C2×#41D4×C5911yescharacteristic
614C2×#41C23×C5911yescharacteristic
615C2×#41C23×C5911yescharacteristic
616C2×#41C23×C5911yescharacteristic
617C22×Q8—21no—
618C22×Q8—21no—
619C22×Q8D4×C5911yescharacteristic
620C22×Q8C23×C5911yescharacteristic
621C22×D4—21no—
622C22×D4—21no—
623C22×D4D4×C5911yescharacteristic
624C22×D4C23×C5911yescharacteristic
625C23×C4—21no—
626C23×C4C23×C5911yescharacteristic
627AGL(1,ℤ/8)—22no—
628AGL(1,ℤ/8)—22no—
629AGL(1,ℤ/8)—22no—
630AGL(1,ℤ/8)—41no—
631AGL(1,ℤ/8)—41no—
632AGL(1,ℤ/8)—41no—
633C2×SD16—21no—
634C2×SD16—21no—
635C2×SD16—21no—
636C2×D8—21no—
637C2×D8—21no—
638C2×D8—21no—
639C2×M16—21no—
640C2×M16—22no—
641C2×M16—41no—
642C2×M16C23×C5911yescharacteristic
643C2×M16C23×C5911yescharacteristic
644C2×M16C23×C5911yescharacteristic
645C2×M16C23×C5911yescharacteristic
646C22×C8—21no—
647C4⋊Q8—22no—
648C4⋊Q8—21no—
649#124—22no—
650#124—21no—
651#124—22no—
652#124—41no—
653#123—22no—
654#123—22no—
655#123—22no—
656#123—21no—
657#123—22no—
658C22⋊Q8—22no—
659C22⋊Q8—22no—
660C22⋊Q8—22no—
661C22⋊Q8—21no—
662C22⋊Q8—21no—
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—21no—
675#121—21no—
676#121—22no—
677#121—21no—
678#121—21no—
679#121—21no—
680#121—21no—
681#121D4×C5911yescharacteristic
682#121D4×C5911yescharacteristic
683#120—22no—
684#120—21no—
685C4×Q8—21no—
686C4×D4—22no—
687C4×D4—22no—
688C4×D4—21no—
689C4×D4—22no—
690C4×D4—21no—
691C4×D4—21no—
692#117—21no—
693#117—22no—
694#117—41no—
695#117C23×C5911yescharacteristic
696C2×C4⋊C4—22no—
697C2×C4⋊C4—21no—
698C2×C4⋊C4—21no—
699C2×C4⋊C4—22no—
700C2×C4⋊C4D4×C5912yes—
701C2×C4⋊C4C23×C5911yescharacteristic
702C2×C4⋊C4C23×C5911yescharacteristic
703C2×C22⋊C4—22no—
704C2×C22⋊C4—21no—
705C2×C22⋊C4—21no—
706C2×C22⋊C4—22no—
707C2×C22⋊C4—22no—
708C2×C22⋊C4D4×C5912yes—
709C2×C42C23×C5911yescharacteristic
710C2×C42C23×C5911yescharacteristic
711#107—21no—
712#106—21no—
713#104—22no—
714#104—22no—
715#104—22no—
716#104—22no—
717#104—41no—
718#104D4×C5914yescomplemented
719#103—21no—
720#103—21no—
721#103—21no—
722#102—21no—
723#102—21no—
724#102—21no—
725#102—21no—
726#102—21no—
727#101—22no—
728#101—41no—
729C22⋊C8—21no—
730C22⋊C8—21no—
731#95—22no—
732C24—21no—
733C24—21no—
734C24C2×D4×C5911yescharacteristic
735#41—21no—
736#41—21no—
737#41—22no—
738#41—22no—
739#41—21no—
740#41—21no—
741#41—21no—
742#41—21no—
743#41—21no—
744#41—21no—
745#41—21no—
746#41—21no—
747#41—42no—
748#41—42no—
749#41—41no—
750#41—41no—
751#41—42no—
752#41—42no—
753#41—42no—
754#41—42no—
755#41—44no—
756#41—44no—
757#41—42no—
758#41—42no—
759#41C2×D4×C5912yes—
760#41#41×C5912yes—
761C2×Q8—22no—
762C2×Q8—21no—
763C2×Q8—21no—
764C2×Q8—21no—
765C2×Q8—21no—
766C2×Q8—21no—
767C2×Q8—21no—
768C2×Q8—21no—
769C2×Q8—22no—
770C2×Q8—41no—
771C2×Q8—42no—
772C2×Q8—42no—
773C2×Q8—42no—
774C2×Q8—42no—
775C2×Q8C2×D4×C5911yescharacteristic
776C2×Q8C2×D4×C5911yescharacteristic
777C2×Q8C2×D4×C5911yescharacteristic
778C2×D4—21no—
779C2×D4—22no—
780C2×D4—22no—
781C2×D4—21no—
782C2×D4—21no—
783C2×D4—21no—
784C2×D4—21no—
785C2×D4—21no—
786C2×D4—22no—
787C2×D4—21no—
788C2×D4—21no—
789C2×D4—21no—
790C2×D4—21no—
791C2×D4—21no—
792C2×D4—21no—
793C2×D4—21no—
794C2×D4—21no—
795C2×D4—41no—
796C2×D4—42no—
797C2×D4—42no—
798C2×D4—41no—
799C2×D4—41no—
800C2×D4—82no—
801C2×D4C2×D4×C5911yescharacteristic
802C2×D4C2×D4×C5911yescharacteristic
803C2×D4C2×D4×C5911yescharacteristic
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—22no—
810C22×C4—22no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—22no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—42no—
821C22×C4—42no—
822C22×C4C2×D4×C5912yes—
823C22×C4C2×D4×C5911yescharacteristic
824C22×C4C2×D4×C5911yescharacteristic
825C22×C4C2×D4×C5911yescharacteristic
826C22×C4C2×D4×C5911yescharacteristic
827C22×C4C2×D4×C5911yescharacteristic
828C22×C4C2×D4×C5912yes—
829C22×C4C24×C5911yescharacteristic
830SD16—42no—
831SD16—42no—
832SD16—42no—
833D8—42no—
834D8—42no—
835D8—42no—
836M16—21no—
837M16—21no—
838M16—21no—
839M16—21no—
840M16—21no—
841M16—21no—
842M16—21no—
843M16—42no—
844M16C2×D4×C5912yes—
845C2×C8—21no—
846C2×C8—21no—
847C2×C8—21no—
848C2×C8—21no—
849C2×C8—42no—
850C4⋊C4—22no—
851C4⋊C4—22no—
852C4⋊C4—22no—
853C4⋊C4—22no—
854C4⋊C4—21no—
855C4⋊C4—22no—
856C4⋊C4—22no—
857C4⋊C4—21no—
858C4⋊C4—21no—
859C4⋊C4—21no—
860C4⋊C4—21no—
861C4⋊C4—21no—
862C4⋊C4—42no—
863C4⋊C4—82no—
864C4⋊C4C2×D4×C5911yescharacteristic
865C4⋊C4C2×D4×C5911yescharacteristic
866C22⋊C4—22no—
867C22⋊C4—22no—
868C22⋊C4—22no—
869C22⋊C4—22no—
870C22⋊C4—22no—
871C22⋊C4—21no—
872C22⋊C4—22no—
873C22⋊C4—22no—
874C22⋊C4—21no—
875C22⋊C4—21no—
876C22⋊C4—21no—
877C22⋊C4—21no—
878C22⋊C4—44no—
879C22⋊C4—42no—
880C22⋊C4—41no—
881C22⋊C4—41no—
882C22⋊C4—82no—
883C42—22no—
884C42—21no—
885C42—21no—
886C42—21no—
887C42—21no—
888C42C2×D4×C5912yes—
889C23—21no—
890C23—21no—
891C23—21no—
892C23—21no—
893C23—21no—
894C23—41no—
895C23—41no—
896C23—42no—
897C23—42no—
898C23—42no—
899C23—42no—
900C23—41no—
901C23—41no—
902C23—41no—
903C23—81no—
904C23#120×C5911yescharacteristic
905C23#120×C5911yescharacteristic
906C23C22×D4×C5911yescharacteristic
907Q8—21no—
908Q8—21no—
909Q8—21no—
910Q8—21no—
911Q8—21no—
912Q8—42no—
913Q8—44no—
914Q8—41no—
915Q8—41no—
916Q8—41no—
917Q8—41no—
918Q8#121×C5912yes—
919D4—22no—
920D4—22no—
921D4—21no—
922D4—21no—
923D4—21no—
924D4—21no—
925D4—21no—
926D4—42no—
927D4—42no—
928D4—42no—
929D4—42no—
930D4—44no—
931D4—41no—
932D4—41no—
933D4—41no—
934D4—41no—
935D4—41no—
936D4—41no—
937D4—41no—
938D4—41no—
939D4—81no—
940D4—82no—
941D4—82no—
942D4—82no—
943D4#121×C5912yes—
944C2×C4—21no—
945C2×C4—21no—
946C2×C4—21no—
947C2×C4—21no—
948C2×C4—21no—
949C2×C4—21no—
950C2×C4—21no—
951C2×C4—21no—
952C2×C4—21no—
953C2×C4—22no—
954C2×C4—21no—
955C2×C4—21no—
956C2×C4—22no—
957C2×C4—21no—
958C2×C4—22no—
959C2×C4—21no—
960C2×C4—21no—
961C2×C4—22no—
962C2×C4—21no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—42no—
967C2×C4—42no—
968C2×C4—42no—
969C2×C4—44no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—44no—
973C2×C4—41no—
974C2×C4—41no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—42no—
978C2×C4—41no—
979C2×C4—42no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—82no—
984C2×C4#120×C5911yescharacteristic
985C2×C4#120×C5911yescharacteristic
986C2×C4C22×D4×C5911yescharacteristic
987C2×C4C22×D4×C5911yescharacteristic
988C2×C4C22×D4×C5911yescharacteristic
989C2×C4C2×#41×C5911yescharacteristic
990C2×C4H(5,𝔽2)×C5911yescharacteristic
991C2×C4H(5,𝔽2)×C5911yescharacteristic
992C8—22no—
993C8—41no—
994C8—41no—
995C8—41no—
996C22—21no—
997C22—21no—
998C22—21no—
999C22—21no—
1000C22—21no—
1001C22—21no—
1002C22—21no—
1003C22—21no—
1004C22—22no—
1005C22—41no—
1006C22—41no—
1007C22—41no—
1008C22—41no—
1009C22—41no—
1010C22—41no—
1011C22—41no—
1012C22—41no—
1013C22—81no—
1014C22—81no—
1015C22—82no—
1016C22—82no—
1017C22—84no—
1018C22—81no—
1019C22—81no—
1020C22—81no—
1021C22C2×#120×C5911yescharacteristic
1022C22D42×C5911yescharacteristic
1023C22C59×#54611yescharacteristic
1024C4—21no—
1025C4—21no—
1026C4—22no—
1027C4—42no—
1028C4—41no—
1029C4—42no—
1030C4—41no—
1031C4—42no—
1032C4—41no—
1033C4—41no—
1034C4—81no—
1035C4—81no—
1036C4C2×#121×C5911yescharacteristic
1037C4C59×#53411yescharacteristic
1038C4D42×C5911yescharacteristic
1039C4C59×#54611yescharacteristic
1040C2—21no—
1041C2—21no—
1042C2—41no—
1043C2—41no—
1044C2—42no—
1045C2—81no—
1046C2—81no—
1047C2—161no—
1048C2C59×#241011yescharacteristic
1049C2C59×#302011yescharacteristic
1050C2C59×#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×#3489C2semidirect
2. C59×#3055C2semidirect
3. C2×C59×#454C2semidirect
4. C59×#3006C2semidirect
5. C2×C59×#421C2semidirect
6. C59×#2620C2semidirect
7. C59×#2039C2semidirect
8. C59×#2038C2semidirect
9. C59×#2006C2semidirect
10. C59×#2003C2semidirect
11. C59×#1901C2semidirect
12. C59×#1897C2semidirect
13. C59×#1883C2semidirect
14. C59×#1859C2semidirect
15. C59×#1793C2semidirect
20. C2×AGL(1,ℤ/8)×C59C22semidirect
32. C2×#124×C59C22semidirect
49. C59×#428C22semidirect
55. C2×#104×C59C22semidirect
56. C2×#104×C59C22semidirect
57. C59×#418C22semidirect
60. C59×#417C22semidirect
61. C2×#101×C59C22semidirect
62. C2×#101×C59C22semidirect
66. C59×#391C22semidirect
67. C59×#390C22semidirect
68. C59×#384C22semidirect
69. C59×#343C22semidirect
70. C59×#343C22semidirect
71. C59×#339C22semidirect
72. C59×#339C22semidirect
192. #104×C59D4semidirect
470. #24469C59direct (N × H)
515. #3489C2×C59semidirect
516. #3055C2×C59semidirect
517. C2×#454C2×C59semidirect
518. #3006C2×C59semidirect
519. C2×#421C2×C59semidirect
520. #2620C2×C59semidirect
521. #2039C2×C59semidirect
522. #2038C2×C59semidirect
523. #2006C2×C59semidirect
524. #2003C2×C59semidirect
525. #1901C2×C59semidirect
526. #1897C2×C59semidirect
527. #1883C2×C59semidirect
528. #1859C2×C59semidirect
529. #1793C2×C59semidirect
545. C2×AGL(1,ℤ/8)C22×C59semidirect
557. C2×#124C22×C59semidirect
574. #428C22×C59semidirect
580. C2×#104C22×C59semidirect
581. C2×#104C22×C59semidirect
582. #418C22×C59semidirect
585. #417C22×C59semidirect
586. C2×#101C22×C59semidirect
587. C2×#101C22×C59semidirect
591. #391C22×C59semidirect
592. #390C22×C59semidirect
593. #384C22×C59semidirect
594. #343C22×C59semidirect
595. #343C22×C59semidirect
596. #339C22×C59semidirect
597. #339C22×C59semidirect
598. C59#24469direct (N × H)
718. #104D4×C59semidirect

Maximal subgroups

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

subgroupindex
C59×#34892
C59×#30552
C2×C59×#4542
C59×#30062
C2×C59×#4212
C59×#26202
C59×#20392
C59×#20382
C59×#20062
C59×#20032
C59×#19012
C59×#18972
C59×#18832
C59×#18592
C59×#17932
#2446959