Finite Group Databasebeta

← C59×#23876 #28435985

Subgroups — C59×#23876 #28435985

Order 15104.

2012 conjugacy classes of subgroups.

The subgroup lattice has 938 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×AGL(1,ℤ/8)×C59C211yesmaximal, characteristic, complemented
2C59×#3488C211yesmaximal, characteristic, complemented
3C2×C59×#453C212yesmaximal, complemented
4C59×#3003C211yesmaximal, characteristic, complemented
5C59×#2433C211yesmaximal, characteristic, complemented
6C59×#2006C212yesmaximal, complemented
7C59×#2002C212yesmaximal, complemented
8C59×#1900C211yesmaximal, characteristic, complemented
9C59×#1883C212yesmaximal, complemented
10C59×#1871C211yesmaximal, characteristic, complemented
11C59×#1789C211yesmaximal, characteristic, complemented
12C2×H(5,𝔽2)×C59C2211yescharacteristic, complemented
13C22×#41×C59C2211yescharacteristic
14C23×D4×C59C2211yescharacteristic, complemented
15C2×AGL(1,ℤ/8)×C59—21no—
16C2×AGL(1,ℤ/8)×C59—21no—
17C2×AGL(1,ℤ/8)×C59—28no—
18C2×AGL(1,ℤ/8)×C59C2212yes—
19C2×AGL(1,ℤ/8)×C59C2212yescomplemented
20C2×AGL(1,ℤ/8)×C59C2212yescomplemented
21C22×SD16×C59—21no—
22C22×D8×C59—21no—
23C22×M16×C59C2211yescharacteristic, complemented
24C59×#550—21no—
25C59×#548—21no—
26C59×#546—21no—
27C59×#546—22no—
28D42×C59—22no—
29D42×C59—21no—
30C59×#537—21no—
31C59×#537C2211yescharacteristic, complemented
32C59×#535—21no—
33C59×#535C2211yescharacteristic, complemented
34C2×#127×C59C2212yescomplemented
35C59×#525—21no—
36C59×#525C2211yescharacteristic
37C2×#121×C59—21no—
38C2×#121×C59C2211yescharacteristic
39C2×#120×C59—22no—
40C59×#520C2211yescharacteristic, complemented
41C59×#453—28no—
42C59×#450—21no—
43C59×#450—21no—
44C59×#447—21no—
45C59×#447—21no—
46C2×#104×C59C2212yescomplemented
47C2×#104×C59C2212yescomplemented
48C2×#104×C59C2212yescomplemented
49C59×#418C2212yescomplemented
50C2×#100×C59C2212yescomplemented
51C59×#407C2211yescharacteristic, complemented
52C59×#392—22no—
53C59×#390C2212yescomplemented
54C4×C22⋊C4×C59C2211yescharacteristic, complemented
55C59×#343C2212yescomplemented
56C59×#339C2212yescomplemented
57C25×C59—21no—
58H(5,𝔽2)×C59—24no—
59H(5,𝔽2)×C59—42no—
60C2×#41×C59—21no—
61C2×#41×C59—21no—
62C2×#41×C59—21no—
63C2×#41×C59—21no—
64C2×#41×C59—24no—
65C2×#41×C59—42no—
66C2×#41×C59D411yescharacteristic, complemented
67C2×#41×C59D411yescharacteristic, complemented
68C2×#41×C59C2311yescharacteristic
69C2×#41×C59C2311yescharacteristic
70C2×#41×C59C2311yescharacteristic
71C22×Q8×C59D411yescharacteristic, complemented
72C22×D4×C59—24no—
73C22×D4×C59—21no—
74C22×D4×C59—22no—
75C22×D4×C59—22no—
76C22×D4×C59—21no—
77C22×D4×C59—21no—
78C22×D4×C59—24no—
79C22×D4×C59—21no—
80C22×D4×C59—21no—
81C22×D4×C59—21no—
82C22×D4×C59—21no—
83C22×D4×C59—21no—
84C22×D4×C59—42no—
85C22×D4×C59D412yes—
86C22×D4×C59D411yescharacteristic, complemented
87C22×D4×C59C2311yescharacteristic
88C22×D4×C59C2312yes—
89C23×C4×C59—21no—
90C23×C4×C59C2311yescharacteristic
91AGL(1,ℤ/8)×C59—28no—
92AGL(1,ℤ/8)×C59—28no—
93AGL(1,ℤ/8)×C59—24no—
94AGL(1,ℤ/8)×C59—24no—
95AGL(1,ℤ/8)×C59—24no—
96AGL(1,ℤ/8)×C59—24no—
97AGL(1,ℤ/8)×C59—42no—
98AGL(1,ℤ/8)×C59D418yescomplemented
99C2×SD16×C59—28no—
100C2×SD16×C59—22no—
101C2×SD16×C59—22no—
102C2×SD16×C59—22no—
103C2×D8×C59—28no—
104C2×D8×C59—22no—
105C2×D8×C59—22no—
106C2×D8×C59—22no—
107C2×M16×C59—21no—
108C2×M16×C59—24no—
109C2×M16×C59C2312yes—
110C2×M16×C59C2312yes—
111C22×C8×C59—21no—
112#127×C59—22no—
113#127×C59—21no—
114#127×C59—24no—
115#127×C59—42no—
116#124×C59—22no—
117#124×C59—21no—
118#123×C59—22no—
119#123×C59—21no—
120C22⋊Q8×C59—22no—
121C22⋊Q8×C59—21no—
122C22⋊Q8×C59—21no—
123C22⋊Q8×C59D411yescharacteristic, complemented
124C22⋊Q8×C59D411yescharacteristic, complemented
125#121×C59—22no—
126#121×C59—22no—
127#121×C59—22no—
128#121×C59—22no—
129#121×C59—22no—
130#121×C59—21no—
131#121×C59—21no—
132#121×C59—21no—
133#121×C59—21no—
134#121×C59—21no—
135#121×C59—21no—
136#121×C59—22no—
137#121×C59—21no—
138#121×C59—21no—
139#121×C59D411yescharacteristic, complemented
140#121×C59D411yescharacteristic, complemented
141#120×C59—22no—
142#120×C59—22no—
143#120×C59—22no—
144#120×C59—21no—
145#120×C59—22no—
146#120×C59—48no—
147C4×Q8×C59—21no—
148C4×D4×C59—22no—
149C4×D4×C59—22no—
150C4×D4×C59—21no—
151C4×D4×C59—22no—
152C4×D4×C59—21no—
153C4×D4×C59—21no—
154#117×C59—21no—
155#117×C59C2311yescharacteristic
156C2×C4⋊C4×C59—21no—
157C2×C4⋊C4×C59C2311yescharacteristic
158C2×C22⋊C4×C59—22no—
159C2×C22⋊C4×C59—21no—
160C2×C22⋊C4×C59—24no—
161C2×C22⋊C4×C59D412yes—
162C2×C42×C59C2312yes—
163#104×C59—24no—
164#104×C59—24no—
165#104×C59—42no—
166#102×C59—22no—
167#102×C59—22no—
168#100×C59—24no—
169C22⋊C8×C59—21no—
170C22⋊C8×C59—21no—
171#95×C59—21no—
172C24×C59—22no—
173C24×C59—22no—
174C24×C59—21no—
175C24×C59—44no—
176C24×C59—44no—
177C24×C59—41no—
178C24×C59—41no—
179C24×C59—82no—
180C24×C59C2×D411yescharacteristic
181C24×C59C2×D412yes—
182#41×C59—22no—
183#41×C59—22no—
184#41×C59—22no—
185#41×C59—22no—
186#41×C59—22no—
187#41×C59—22no—
188#41×C59—22no—
189#41×C59—44no—
190#41×C59—41no—
191#41×C59—41no—
192#41×C59—44no—
193#41×C59—44no—
194#41×C59—42no—
195#41×C59—42no—
196#41×C59C2×D414yes—
197C2×Q8×C59—21no—
198C2×Q8×C59—22no—
199C2×Q8×C59—41no—
200C2×Q8×C59C2×D411yescharacteristic
201C2×Q8×C59C2×D411yescharacteristic
202C2×Q8×C59C2×D411yescharacteristic
203C2×D4×C59—21no—
204C2×D4×C59—24no—
205C2×D4×C59—24no—
206C2×D4×C59—22no—
207C2×D4×C59—22no—
208C2×D4×C59—22no—
209C2×D4×C59—22no—
210C2×D4×C59—21no—
211C2×D4×C59—21no—
212C2×D4×C59—21no—
213C2×D4×C59—21no—
214C2×D4×C59—21no—
215C2×D4×C59—22no—
216C2×D4×C59—22no—
217C2×D4×C59—22no—
218C2×D4×C59—21no—
219C2×D4×C59—22no—
220C2×D4×C59—21no—
221C2×D4×C59—22no—
222C2×D4×C59—22no—
223C2×D4×C59—22no—
224C2×D4×C59—22no—
225C2×D4×C59—21no—
226C2×D4×C59—21no—
227C2×D4×C59—22no—
228C2×D4×C59—22no—
229C2×D4×C59—22no—
230C2×D4×C59—41no—
231C2×D4×C59—44no—
232C2×D4×C59—44no—
233C2×D4×C59—44no—
234C2×D4×C59—44no—
235C2×D4×C59—42no—
236C2×D4×C59—42no—
237C2×D4×C59—48no—
238C2×D4×C59—44no—
239C2×D4×C59—48no—
240C2×D4×C59—42no—
241C2×D4×C59—42no—
242C2×D4×C59—44no—
243C2×D4×C59—48no—
244C2×D4×C59—41no—
245C2×D4×C59—41no—
246C2×D4×C59—84no—
247C2×D4×C59—84no—
248C2×D4×C59C2×D411yescharacteristic
249C2×D4×C59C2×D411yescharacteristic
250C2×D4×C59C2×D411yescharacteristic
251C2×D4×C59C2×D414yescomplemented
252C22×C4×C59—21no—
253C22×C4×C59—22no—
254C22×C4×C59—22no—
255C22×C4×C59—22no—
256C22×C4×C59—21no—
257C22×C4×C59—22no—
258C22×C4×C59—22no—
259C22×C4×C59—21no—
260C22×C4×C59—21no—
261C22×C4×C59—21no—
262C22×C4×C59—21no—
263C22×C4×C59—44no—
264C22×C4×C59C2×D411yescharacteristic
265C22×C4×C59C2×D411yescharacteristic
266C22×C4×C59C2×D411yescharacteristic
267C22×C4×C59C2×D411yescharacteristic
268C22×C4×C59C2×D411yescharacteristic
269C22×C4×C59C2×D412yes—
270C22×C4×C59C2411yescharacteristic
271SD16×C59—28no—
272SD16×C59—28no—
273SD16×C59—44no—
274D8×C59—28no—
275D8×C59—28no—
276D8×C59—44no—
277M16×C59—24no—
278M16×C59—22no—
279M16×C59—22no—
280M16×C59—22no—
281M16×C59C2×D414yescomplemented
282C2×C8×C59—24no—
283C2×C8×C59—22no—
284C2×C8×C59—22no—
285C4⋊C4×C59—22no—
286C4⋊C4×C59—22no—
287C4⋊C4×C59—21no—
288C4⋊C4×C59—21no—
289C4⋊C4×C59—21no—
290C4⋊C4×C59—21no—
291C4⋊C4×C59C2×D411yescharacteristic
292C4⋊C4×C59C2×D411yescharacteristic
293C22⋊C4×C59—22no—
294C22⋊C4×C59—22no—
295C22⋊C4×C59—24no—
296C22⋊C4×C59—22no—
297C22⋊C4×C59—22no—
298C22⋊C4×C59—22no—
299C22⋊C4×C59—21no—
300C22⋊C4×C59—21no—
301C22⋊C4×C59—21no—
302C22⋊C4×C59—21no—
303C22⋊C4×C59—22no—
304C22⋊C4×C59—22no—
305C22⋊C4×C59—21no—
306C22⋊C4×C59—48no—
307C42×C59—22no—
308C42×C59—21no—
309C42×C59—22no—
310C42×C59—22no—
311C23×C59—21no—
312C23×C59—22no—
313C23×C59—22no—
314C23×C59—22no—
315C23×C59—21no—
316C23×C59—21no—
317C23×C59—24no—
318C23×C59—24no—
319C23×C59—41no—
320C23×C59—42no—
321C23×C59—44no—
322C23×C59—44no—
323C23×C59—44no—
324C23×C59—44no—
325C23×C59—44no—
326C23×C59—42no—
327C23×C59—42no—
328C23×C59—42no—
329C23×C59—42no—
330C23×C59—42no—
331C23×C59—81no—
332C23×C59—82no—
333C23×C59—82no—
334C23×C59—82no—
335C23×C59—82no—
336C23×C59—82no—
337C23×C59—816no—
338C23×C59—82no—
339C23×C59#12011yescharacteristic
340C23×C59#12011yescharacteristic
341C23×C59C22×D411yescharacteristic
342Q8×C59—21no—
343Q8×C59—21no—
344Q8×C59—21no—
345Q8×C59—22no—
346Q8×C59—42no—
347Q8×C59#12012yescomplemented
348D4×C59—24no—
349D4×C59—21no—
350D4×C59—24no—
351D4×C59—21no—
352D4×C59—21no—
353D4×C59—22no—
354D4×C59—24no—
355D4×C59—42no—
356D4×C59—42no—
357D4×C59—44no—
358D4×C59—44no—
359D4×C59—44no—
360D4×C59—42no—
361D4×C59—44no—
362D4×C59—42no—
363D4×C59—42no—
364D4×C59—44no—
365D4×C59—42no—
366D4×C59—41no—
367D4×C59—42no—
368D4×C59—41no—
369D4×C59—42no—
370D4×C59—42no—
371D4×C59—81no—
372D4×C59—82no—
373D4×C59—82no—
374D4×C59—82no—
375D4×C59—82no—
376D4×C59—816no—
377D4×C59#12012yescomplemented
378C2×C4×C59—21no—
379C2×C4×C59—22no—
380C2×C4×C59—21no—
381C2×C4×C59—21no—
382C2×C4×C59—21no—
383C2×C4×C59—21no—
384C2×C4×C59—22no—
385C2×C4×C59—22no—
386C2×C4×C59—24no—
387C2×C4×C59—24no—
388C2×C4×C59—21no—
389C2×C4×C59—22no—
390C2×C4×C59—21no—
391C2×C4×C59—21no—
392C2×C4×C59—21no—
393C2×C4×C59—42no—
394C2×C4×C59—42no—
395C2×C4×C59—42no—
396C2×C4×C59—44no—
397C2×C4×C59—42no—
398C2×C4×C59—42no—
399C2×C4×C59—41no—
400C2×C4×C59—41no—
401C2×C4×C59—42no—
402C2×C4×C59—42no—
403C2×C4×C59—82no—
404C2×C4×C59#12011yescharacteristic
405C2×C4×C59#12011yescharacteristic
406C2×C4×C59C22×D411yescharacteristic
407C2×C4×C59C22×D412yes—
408C2×C4×C59C22×D411yescharacteristic
409C2×C4×C59H(5,𝔽2)12yes—
410C8×C59—24no—
411C8×C59—42no—
412#23876C5911yesmaximal, characteristic, direct product factor, Sylow
413C22×C59—21no—
414C22×C59—21no—
415C22×C59—21no—
416C22×C59—21no—
417C22×C59—21no—
418C22×C59—22no—
419C22×C59—21no—
420C22×C59—21no—
421C22×C59—44no—
422C22×C59—48no—
423C22×C59—41no—
424C22×C59—41no—
425C22×C59—41no—
426C22×C59—41no—
427C22×C59—42no—
428C22×C59—44no—
429C22×C59—42no—
430C22×C59—41no—
431C22×C59—41no—
432C22×C59—41no—
433C22×C59—42no—
434C22×C59—41no—
435C22×C59—84no—
436C22×C59—84no—
437C22×C59—84no—
438C22×C59—88no—
439C22×C59—88no—
440C22×C59—82no—
441C22×C59—82no—
442C22×C59—164no—
443C22×C59#45312yescomplemented
444C22×C59C2×#12011yescharacteristic
445C22×C59D4212yes—
446C4×C59—21no—
447C4×C59—21no—
448C4×C59—22no—
449C4×C59—44no—
450C4×C59—41no—
451C4×C59—41no—
452C4×C59—42no—
453C4×C59—41no—
454C4×C59—41no—
455C4×C59C2×#12011yescharacteristic
456C4×C59#53411yescharacteristic
457C4×C59D4212yes—
458C22×AGL(1,ℤ/8)C2×C5911yescharacteristic, complemented
459#3488C2×C5911yescharacteristic, complemented
460C2×#453C2×C5912yescomplemented
461#3003C2×C5911yescharacteristic, complemented
462#2433C2×C5911yescharacteristic, complemented
463#2006C2×C5912yescomplemented
464#2002C2×C5912yescomplemented
465#1900C2×C5911yescharacteristic, complemented
466#1883C2×C5912yescomplemented
467#1871C2×C5911yescharacteristic, complemented
468#1789C2×C5911yescharacteristic, complemented
469C2×C59—22no—
470C2×C59—22no—
471C2×C59—41no—
472C2×C59—42no—
473C2×C59—81no—
474C2×C59—84no—
475C2×C59—82no—
476C2×C59—81no—
477C2×C59#240311yescharacteristic
478C2×C59C2×#45311yescharacteristic
479C2×C59#302111yescharacteristic
480C2×H(5,𝔽2)C22×C5911yescharacteristic, complemented
481C22×#41C22×C5911yescharacteristic
482C23×D4C22×C5911yescharacteristic, complemented
483C2×AGL(1,ℤ/8)—21no—
484C2×AGL(1,ℤ/8)—21no—
485C2×AGL(1,ℤ/8)—28no—
486C2×AGL(1,ℤ/8)C22×C5912yes—
487C2×AGL(1,ℤ/8)C22×C5912yescomplemented
488C2×AGL(1,ℤ/8)C22×C5912yescomplemented
489C22×SD16—21no—
490C22×D8—21no—
491C22×M16C22×C5911yescharacteristic, complemented
492#550—21no—
493#548—21no—
494#546—21no—
495#546—22no—
496D42—22no—
497D42—21no—
498#537—21no—
499#537C22×C5911yescharacteristic, complemented
500#535—21no—
501#535C22×C5911yescharacteristic, complemented
502C2×#127C22×C5912yescomplemented
503#525—21no—
504#525C22×C5911yescharacteristic
505C2×#121—21no—
506C2×#121C22×C5911yescharacteristic
507C2×#120—22no—
508#520C22×C5911yescharacteristic, complemented
509#453—28no—
510#450—21no—
511#450—21no—
512#447—21no—
513#447—21no—
514C2×#104C22×C5912yescomplemented
515C2×#104C22×C5912yescomplemented
516C2×#104C22×C5912yescomplemented
517#418C22×C5912yescomplemented
518C2×#100C22×C5912yescomplemented
519#407C22×C5911yescharacteristic, complemented
520#392—22no—
521#390C22×C5912yescomplemented
522C4×C22⋊C4C22×C5911yescharacteristic, complemented
523#343C22×C5912yescomplemented
524#339C22×C5912yescomplemented
525C59#2387611yescharacteristic, direct product factor, Sylow
526C25—21no—
527H(5,𝔽2)—24no—
528H(5,𝔽2)—42no—
529C2×#41—21no—
530C2×#41—21no—
531C2×#41—21no—
532C2×#41—21no—
533C2×#41—24no—
534C2×#41—42no—
535C2×#41D4×C5911yescharacteristic, complemented
536C2×#41D4×C5911yescharacteristic, complemented
537C2×#41C23×C5911yescharacteristic
538C2×#41C23×C5911yescharacteristic
539C2×#41C23×C5911yescharacteristic
540C22×Q8D4×C5911yescharacteristic, complemented
541C22×D4—24no—
542C22×D4—21no—
543C22×D4—22no—
544C22×D4—22no—
545C22×D4—21no—
546C22×D4—21no—
547C22×D4—24no—
548C22×D4—21no—
549C22×D4—21no—
550C22×D4—21no—
551C22×D4—21no—
552C22×D4—21no—
553C22×D4—42no—
554C22×D4D4×C5912yes—
555C22×D4D4×C5911yescharacteristic, complemented
556C22×D4C23×C5911yescharacteristic
557C22×D4C23×C5912yes—
558C23×C4—21no—
559C23×C4C23×C5911yescharacteristic
560AGL(1,ℤ/8)—28no—
561AGL(1,ℤ/8)—28no—
562AGL(1,ℤ/8)—24no—
563AGL(1,ℤ/8)—24no—
564AGL(1,ℤ/8)—24no—
565AGL(1,ℤ/8)—24no—
566AGL(1,ℤ/8)—42no—
567AGL(1,ℤ/8)D4×C5918yescomplemented
568C2×SD16—28no—
569C2×SD16—22no—
570C2×SD16—22no—
571C2×SD16—22no—
572C2×D8—28no—
573C2×D8—22no—
574C2×D8—22no—
575C2×D8—22no—
576C2×M16—21no—
577C2×M16—24no—
578C2×M16C23×C5912yes—
579C2×M16C23×C5912yes—
580C22×C8—21no—
581#127—22no—
582#127—21no—
583#127—24no—
584#127—42no—
585#124—22no—
586#124—21no—
587#123—22no—
588#123—21no—
589C22⋊Q8—22no—
590C22⋊Q8—21no—
591C22⋊Q8—21no—
592C22⋊Q8D4×C5911yescharacteristic, complemented
593C22⋊Q8D4×C5911yescharacteristic, complemented
594#121—22no—
595#121—22no—
596#121—22no—
597#121—22no—
598#121—22no—
599#121—21no—
600#121—21no—
601#121—21no—
602#121—21no—
603#121—21no—
604#121—21no—
605#121—22no—
606#121—21no—
607#121—21no—
608#121D4×C5911yescharacteristic, complemented
609#121D4×C5911yescharacteristic, complemented
610#120—22no—
611#120—22no—
612#120—22no—
613#120—21no—
614#120—22no—
615#120—48no—
616C4×Q8—21no—
617C4×D4—22no—
618C4×D4—22no—
619C4×D4—21no—
620C4×D4—22no—
621C4×D4—21no—
622C4×D4—21no—
623#117—21no—
624#117C23×C5911yescharacteristic
625C2×C4⋊C4—21no—
626C2×C4⋊C4C23×C5911yescharacteristic
627C2×C22⋊C4—22no—
628C2×C22⋊C4—21no—
629C2×C22⋊C4—24no—
630C2×C22⋊C4D4×C5912yes—
631C2×C42C23×C5912yes—
632#104—24no—
633#104—24no—
634#104—42no—
635#102—22no—
636#102—22no—
637#100—24no—
638C22⋊C8—21no—
639C22⋊C8—21no—
640#95—21no—
641C24—22no—
642C24—22no—
643C24—21no—
644C24—44no—
645C24—44no—
646C24—41no—
647C24—41no—
648C24—82no—
649C24C2×D4×C5911yescharacteristic
650C24C2×D4×C5912yes—
651#41—22no—
652#41—22no—
653#41—22no—
654#41—22no—
655#41—22no—
656#41—22no—
657#41—22no—
658#41—44no—
659#41—41no—
660#41—41no—
661#41—44no—
662#41—44no—
663#41—42no—
664#41—42no—
665#41C2×D4×C5914yes—
666C2×Q8—21no—
667C2×Q8—22no—
668C2×Q8—41no—
669C2×Q8C2×D4×C5911yescharacteristic
670C2×Q8C2×D4×C5911yescharacteristic
671C2×Q8C2×D4×C5911yescharacteristic
672C2×D4—21no—
673C2×D4—24no—
674C2×D4—24no—
675C2×D4—22no—
676C2×D4—22no—
677C2×D4—22no—
678C2×D4—22no—
679C2×D4—21no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—21no—
684C2×D4—22no—
685C2×D4—22no—
686C2×D4—22no—
687C2×D4—21no—
688C2×D4—22no—
689C2×D4—21no—
690C2×D4—22no—
691C2×D4—22no—
692C2×D4—22no—
693C2×D4—22no—
694C2×D4—21no—
695C2×D4—21no—
696C2×D4—22no—
697C2×D4—22no—
698C2×D4—22no—
699C2×D4—41no—
700C2×D4—44no—
701C2×D4—44no—
702C2×D4—44no—
703C2×D4—44no—
704C2×D4—42no—
705C2×D4—42no—
706C2×D4—48no—
707C2×D4—44no—
708C2×D4—48no—
709C2×D4—42no—
710C2×D4—42no—
711C2×D4—44no—
712C2×D4—48no—
713C2×D4—41no—
714C2×D4—41no—
715C2×D4—84no—
716C2×D4—84no—
717C2×D4C2×D4×C5911yescharacteristic
718C2×D4C2×D4×C5911yescharacteristic
719C2×D4C2×D4×C5911yescharacteristic
720C2×D4C2×D4×C5914yescomplemented
721C22×C4—21no—
722C22×C4—22no—
723C22×C4—22no—
724C22×C4—22no—
725C22×C4—21no—
726C22×C4—22no—
727C22×C4—22no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—44no—
733C22×C4C2×D4×C5911yescharacteristic
734C22×C4C2×D4×C5911yescharacteristic
735C22×C4C2×D4×C5911yescharacteristic
736C22×C4C2×D4×C5911yescharacteristic
737C22×C4C2×D4×C5911yescharacteristic
738C22×C4C2×D4×C5912yes—
739C22×C4C24×C5911yescharacteristic
740SD16—28no—
741SD16—28no—
742SD16—44no—
743D8—28no—
744D8—28no—
745D8—44no—
746M16—24no—
747M16—22no—
748M16—22no—
749M16—22no—
750M16C2×D4×C5914yescomplemented
751C2×C8—24no—
752C2×C8—22no—
753C2×C8—22no—
754C4⋊C4—22no—
755C4⋊C4—22no—
756C4⋊C4—21no—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—21no—
760C4⋊C4C2×D4×C5911yescharacteristic
761C4⋊C4C2×D4×C5911yescharacteristic
762C22⋊C4—22no—
763C22⋊C4—22no—
764C22⋊C4—24no—
765C22⋊C4—22no—
766C22⋊C4—22no—
767C22⋊C4—22no—
768C22⋊C4—21no—
769C22⋊C4—21no—
770C22⋊C4—21no—
771C22⋊C4—21no—
772C22⋊C4—22no—
773C22⋊C4—22no—
774C22⋊C4—21no—
775C22⋊C4—48no—
776C42—22no—
777C42—21no—
778C42—22no—
779C42—22no—
780C23—22no—
781C23—21no—
782C23—22no—
783C23—22no—
784C23—21no—
785C23—21no—
786C23—24no—
787C23—24no—
788C23—41no—
789C23—42no—
790C23—44no—
791C23—44no—
792C23—44no—
793C23—44no—
794C23—44no—
795C23—42no—
796C23—42no—
797C23—42no—
798C23—42no—
799C23—42no—
800C23—81no—
801C23—82no—
802C23—82no—
803C23—82no—
804C23—82no—
805C23—82no—
806C23—816no—
807C23—82no—
808C23#120×C5911yescharacteristic
809C23#120×C5911yescharacteristic
810C23C22×D4×C5911yescharacteristic
811Q8—21no—
812Q8—21no—
813Q8—21no—
814Q8—22no—
815Q8—42no—
816Q8#120×C5912yescomplemented
817D4—24no—
818D4—21no—
819D4—24no—
820D4—21no—
821D4—21no—
822D4—22no—
823D4—24no—
824D4—42no—
825D4—42no—
826D4—44no—
827D4—44no—
828D4—44no—
829D4—42no—
830D4—44no—
831D4—44no—
832D4—42no—
833D4—42no—
834D4—42no—
835D4—41no—
836D4—42no—
837D4—41no—
838D4—42no—
839D4—42no—
840D4—81no—
841D4—82no—
842D4—82no—
843D4—82no—
844D4—82no—
845D4—816no—
846D4#120×C5912yescomplemented
847C2×C4—21no—
848C2×C4—22no—
849C2×C4—21no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—24no—
856C2×C4—24no—
857C2×C4—21no—
858C2×C4—22no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—42no—
863C2×C4—42no—
864C2×C4—42no—
865C2×C4—44no—
866C2×C4—42no—
867C2×C4—42no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—42no—
871C2×C4—42no—
872C2×C4—82no—
873C2×C4#120×C5911yescharacteristic
874C2×C4#120×C5911yescharacteristic
875C2×C4C22×D4×C5911yescharacteristic
876C2×C4C22×D4×C5912yes—
877C2×C4C22×D4×C5911yescharacteristic
878C2×C4H(5,𝔽2)×C5912yes—
879C8—24no—
880C8—42no—
881C22—21no—
882C22—21no—
883C22—21no—
884C22—21no—
885C22—21no—
886C22—21no—
887C22—21no—
888C22—22no—
889C22—44no—
890C22—48no—
891C22—41no—
892C22—41no—
893C22—42no—
894C22—41no—
895C22—41no—
896C22—41no—
897C22—42no—
898C22—41no—
899C22—41no—
900C22—41no—
901C22—42no—
902C22—44no—
903C22—84no—
904C22—84no—
905C22—84no—
906C22—88no—
907C22—88no—
908C22—82no—
909C22—82no—
910C22—164no—
911C22C59×#45312yescomplemented
912C22C2×#120×C5911yescharacteristic
913C22D42×C5912yes—
914C4—21no—
915C4—21no—
916C4—22no—
917C4—44no—
918C4—42no—
919C4—41no—
920C4—41no—
921C4—41no—
922C4—41no—
923C4C2×#120×C5911yescharacteristic
924C4C59×#53411yescharacteristic
925C4D42×C5912yes—
926C2—22no—
927C2—22no—
928C2—41no—
929C2—42no—
930C2—84no—
931C2—81no—
932C2—82no—
933C2—81no—
934C2C59×#240311yescharacteristic
935C2C2×C59×#45311yescharacteristic
936C2C59×#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. C22×AGL(1,ℤ/8)×C59C2semidirect
2. C59×#3488C2semidirect
3. C2×C59×#453C2semidirect
4. C59×#3003C2semidirect
5. C59×#2433C2semidirect
6. C59×#2006C2semidirect
7. C59×#2002C2semidirect
8. C59×#1900C2semidirect
9. C59×#1883C2semidirect
10. C59×#1871C2semidirect
11. C59×#1789C2semidirect
12. C2×H(5,𝔽2)×C59C22semidirect
14. C23×D4×C59C22semidirect
19. C2×AGL(1,ℤ/8)×C59C22semidirect
20. C2×AGL(1,ℤ/8)×C59C22semidirect
23. C22×M16×C59C22semidirect
31. C59×#537C22semidirect
33. C59×#535C22semidirect
34. C2×#127×C59C22semidirect
40. C59×#520C22semidirect
46. C2×#104×C59C22semidirect
47. C2×#104×C59C22semidirect
48. C2×#104×C59C22semidirect
49. C59×#418C22semidirect
50. C2×#100×C59C22semidirect
51. C59×#407C22semidirect
53. C59×#390C22semidirect
54. C4×C22⋊C4×C59C22semidirect
55. C59×#343C22semidirect
56. C59×#339C22semidirect
66. C2×#41×C59D4semidirect
67. C2×#41×C59D4semidirect
71. C22×Q8×C59D4semidirect
86. C22×D4×C59D4semidirect
98. AGL(1,ℤ/8)×C59D4semidirect
123. C22⋊Q8×C59D4semidirect
124. C22⋊Q8×C59D4semidirect
139. #121×C59D4semidirect
140. #121×C59D4semidirect
251. C2×D4×C59C2×D4semidirect
281. M16×C59C2×D4semidirect
347. Q8×C59#120semidirect
377. D4×C59#120semidirect
412. #23876C59direct (N × H)
443. C22×C59#453semidirect
458. C22×AGL(1,ℤ/8)C2×C59semidirect
459. #3488C2×C59semidirect
460. C2×#453C2×C59semidirect
461. #3003C2×C59semidirect
462. #2433C2×C59semidirect
463. #2006C2×C59semidirect
464. #2002C2×C59semidirect
465. #1900C2×C59semidirect
466. #1883C2×C59semidirect
467. #1871C2×C59semidirect
468. #1789C2×C59semidirect
480. C2×H(5,𝔽2)C22×C59semidirect
482. C23×D4C22×C59semidirect
487. C2×AGL(1,ℤ/8)C22×C59semidirect
488. C2×AGL(1,ℤ/8)C22×C59semidirect
491. C22×M16C22×C59semidirect
499. #537C22×C59semidirect
501. #535C22×C59semidirect
502. C2×#127C22×C59semidirect
508. #520C22×C59semidirect
514. C2×#104C22×C59semidirect
515. C2×#104C22×C59semidirect
516. C2×#104C22×C59semidirect
517. #418C22×C59semidirect
518. C2×#100C22×C59semidirect
519. #407C22×C59semidirect
521. #390C22×C59semidirect
522. C4×C22⋊C4C22×C59semidirect
523. #343C22×C59semidirect
524. #339C22×C59semidirect
525. C59#23876direct (N × H)
535. C2×#41D4×C59semidirect
536. C2×#41D4×C59semidirect
540. C22×Q8D4×C59semidirect
555. C22×D4D4×C59semidirect
567. AGL(1,ℤ/8)D4×C59semidirect
592. C22⋊Q8D4×C59semidirect
593. C22⋊Q8D4×C59semidirect
608. #121D4×C59semidirect
609. #121D4×C59semidirect
720. C2×D4C2×D4×C59semidirect
750. M16C2×D4×C59semidirect
816. Q8#120×C59semidirect
846. D4#120×C59semidirect
911. C22C59×#453semidirect

Maximal subgroups

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

subgroupindex
C22×AGL(1,ℤ/8)×C592
C59×#34882
C2×C59×#4532
C59×#30032
C59×#24332
C59×#20062
C59×#20022
C59×#19002
C59×#18832
C59×#18712
C59×#17892
#2387659