Finite Group Databasebeta

← C59×#24432 #28436541

Subgroups — C59×#24432 #28436541

Order 15104.

1922 conjugacy classes of subgroups.

The subgroup lattice has 996 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D42×C59C211yesmaximal, characteristic
2C2×C59×#465C211yesmaximal, characteristic, complemented
3C2×C59×#450C211yesmaximal, characteristic, complemented
4C2×C59×#450C211yesmaximal, characteristic, complemented
5C22×#102×C59C211yesmaximal, characteristic, complemented
6C59×#2417C211yesmaximal, characteristic, complemented
7C59×#2041C211yesmaximal, characteristic, complemented
8C59×#2034C211yesmaximal, characteristic, complemented
9C59×#2014C211yesmaximal, characteristic, complemented
10C59×#2000C211yesmaximal, characteristic, complemented
11C59×#1877C211yesmaximal, characteristic, complemented
12C59×#1874C211yesmaximal, characteristic, complemented
13C59×#1869C211yesmaximal, characteristic, complemented
14C59×#1864C211yesmaximal, characteristic, complemented
15C59×#1786C211yesmaximal, characteristic, complemented
16C23×D4×C59—21no—
17C23×D4×C59C2211yescharacteristic
18C23×D4×C59C2211yescharacteristic
19C22×SD16×C59C2211yescharacteristic
20C22×SD16×C59C2211yescharacteristic, complemented
21C22×SD16×C59C2211yescharacteristic, complemented
22C23×C8×C59C2211yescharacteristic, complemented
23D42×C59—24no—
24D42×C59—24no—
25C2×#127×C59C2211yescharacteristic
26C2×C22⋊Q8×C59C2211yescharacteristic, complemented
27C2×C22⋊Q8×C59C2211yescharacteristic, complemented
28C2×#121×C59—21no—
29C2×#121×C59C2211yescharacteristic
30C2×#121×C59C2211yescharacteristic
31C2×#120×C59—21no—
32C2×#120×C59—21no—
33C2×C4×D4×C59C2211yescharacteristic
34C2×C4×D4×C59C2211yescharacteristic
35C22×C4⋊C4×C59C2211yescharacteristic, complemented
36C59×#465—24no—
37C59×#450—24no—
38C59×#450—24no—
39C2×#106×C59C2211yescharacteristic, complemented
40C2×#103×C59C2211yescharacteristic, complemented
41C2×#102×C59—24no—
42C2×#102×C59C2211yescharacteristic
43C2×#102×C59C2211yescharacteristic
44C2×#102×C59C2211yescharacteristic
45C2×#102×C59C2211yescharacteristic, complemented
46C2×#102×C59C2211yescharacteristic, complemented
47C2×#102×C59C2211yescharacteristic, complemented
48C2×#102×C59C2211yescharacteristic, complemented
49C2×#102×C59C2211yescharacteristic, complemented
50C2×#102×C59C2211yescharacteristic, complemented
51C2×C22⋊C8×C59C2211yescharacteristic, complemented
52C2×C22⋊C8×C59C2211yescharacteristic, complemented
53C2×C22⋊C8×C59C2211yescharacteristic, complemented
54C59×#398—21no—
55C59×#396—21no—
56C59×#391C2211yescharacteristic, complemented
57C59×#389C2211yescharacteristic, complemented
58C59×#386—21no—
59C59×#380—21no—
60C59×#380C2211yescharacteristic, complemented
61C59×#340C2211yescharacteristic, complemented
62C59×#340C2211yescharacteristic, complemented
63C59×#336C2211yescharacteristic, complemented
64C59×#336C2211yescharacteristic, complemented
65C25×C59—21no—
66C25×C59—21no—
67C22×Q8×C59C2311yescharacteristic
68C22×D4×C59—22no—
69C22×D4×C59—22no—
70C22×D4×C59—28no—
71C22×D4×C59—21no—
72C22×D4×C59—21no—
73C22×D4×C59—22no—
74C22×D4×C59—22no—
75C22×D4×C59—22no—
76C22×D4×C59—22no—
77C22×D4×C59—21no—
78C22×D4×C59—21no—
79C22×D4×C59—21no—
80C22×D4×C59—22no—
81C22×D4×C59—21no—
82C22×D4×C59—41no—
83C22×D4×C59—41no—
84C22×D4×C59—41no—
85C22×D4×C59—41no—
86C22×D4×C59—44no—
87C22×D4×C59—44no—
88C22×D4×C59D411yescharacteristic
89C22×D4×C59D414yes—
90C22×D4×C59C2311yescharacteristic
91C22×D4×C59C2311yescharacteristic
92C22×D4×C59C2311yescharacteristic
93C23×C4×C59—21no—
94C23×C4×C59—21no—
95C23×C4×C59C2311yescharacteristic
96C23×C4×C59C2311yescharacteristic
97C2×SD16×C59—22no—
98C2×SD16×C59—22no—
99C2×SD16×C59—22no—
100C2×SD16×C59—22no—
101C2×SD16×C59—22no—
102C2×SD16×C59—22no—
103C2×SD16×C59—41no—
104C2×SD16×C59—41no—
105C2×SD16×C59—41no—
106C22×C8×C59—22no—
107C22×C8×C59—22no—
108C22×C8×C59—41no—
109C22×C8×C59C2311yescharacteristic
110C22×C8×C59C2311yescharacteristic
111C22×C8×C59C2311yescharacteristic
112C22×C8×C59C2311yescharacteristic
113#127×C59—22no—
114#127×C59—22no—
115C22⋊Q8×C59—22no—
116C22⋊Q8×C59—22no—
117C22⋊Q8×C59—22no—
118C22⋊Q8×C59—41no—
119#121×C59—28no—
120#121×C59—22no—
121#121×C59—22no—
122#121×C59—22no—
123#121×C59D414yes—
124#120×C59—28no—
125#120×C59—28no—
126C4×D4×C59—22no—
127C4×D4×C59—22no—
128C4×D4×C59—22no—
129C4×D4×C59—22no—
130C2×C4⋊C4×C59—22no—
131C2×C4⋊C4×C59—21no—
132C2×C4⋊C4×C59—21no—
133C2×C4⋊C4×C59—21no—
134C2×C4⋊C4×C59—21no—
135C2×C4⋊C4×C59—41no—
136C2×C4⋊C4×C59D411yescharacteristic
137C2×C4⋊C4×C59C2311yescharacteristic
138C2×C4⋊C4×C59C2311yescharacteristic
139C2×C4⋊C4×C59C2311yescharacteristic
140C2×C4⋊C4×C59C2311yescharacteristic
141C2×C22⋊C4×C59—21no—
142C2×C22⋊C4×C59—21no—
143C2×C22⋊C4×C59—21no—
144C2×C22⋊C4×C59—21no—
145C2×C22⋊C4×C59—21no—
146C2×C22⋊C4×C59—21no—
147C2×C22⋊C4×C59D411yescharacteristic
148C2×C22⋊C4×C59D411yescharacteristic
149C2×C42×C59C2311yescharacteristic
150#106×C59—22no—
151#103×C59—22no—
152#102×C59—22no—
153#102×C59—22no—
154#102×C59—22no—
155#102×C59—22no—
156#102×C59—22no—
157#102×C59—22no—
158#102×C59—22no—
159#102×C59—41no—
160#102×C59D414yescomplemented
161C22⋊C8×C59—22no—
162C22⋊C8×C59—22no—
163C22⋊C8×C59—41no—
164#95×C59—21no—
165#95×C59—21no—
166#95×C59—21no—
167#95×C59—21no—
168C24×C59—21no—
169C24×C59—24no—
170C24×C59—21no—
171C24×C59—21no—
172C24×C59—24no—
173C24×C59—42no—
174C24×C59—42no—
175C24×C59—42no—
176C24×C59—42no—
177C24×C59—42no—
178C24×C59—42no—
179C24×C59—42no—
180C24×C59—42no—
181C24×C59—81no—
182C24×C59—81no—
183C24×C59—81no—
184C24×C59—81no—
185C24×C59C2×D411yescharacteristic
186C24×C59C2×D411yescharacteristic
187C2×Q8×C59—21no—
188C2×Q8×C59—21no—
189C2×Q8×C59—21no—
190C2×Q8×C59—21no—
191C2×Q8×C59—21no—
192C2×Q8×C59—21no—
193C2×D4×C59—22no—
194C2×D4×C59—22no—
195C2×D4×C59—28no—
196C2×D4×C59—24no—
197C2×D4×C59—24no—
198C2×D4×C59—24no—
199C2×D4×C59—24no—
200C2×D4×C59—24no—
201C2×D4×C59—24no—
202C2×D4×C59—21no—
203C2×D4×C59—21no—
204C2×D4×C59—21no—
205C2×D4×C59—21no—
206C2×D4×C59—21no—
207C2×D4×C59—21no—
208C2×D4×C59—21no—
209C2×D4×C59—21no—
210C2×D4×C59—21no—
211C2×D4×C59—21no—
212C2×D4×C59—21no—
213C2×D4×C59—21no—
214C2×D4×C59—21no—
215C2×D4×C59—44no—
216C2×D4×C59—44no—
217C2×D4×C59—44no—
218C2×D4×C59—42no—
219C2×D4×C59—42no—
220C2×D4×C59—42no—
221C2×D4×C59—42no—
222C2×D4×C59—42no—
223C2×D4×C59—44no—
224C2×D4×C59—44no—
225C2×D4×C59—432no—
226C2×D4×C59—44no—
227C2×D4×C59—42no—
228C2×D4×C59—42no—
229C2×D4×C59—42no—
230C2×D4×C59—42no—
231C2×D4×C59—44no—
232C2×D4×C59—42no—
233C2×D4×C59—81no—
234C2×D4×C59—81no—
235C2×D4×C59SD1614yescomplemented
236C2×D4×C59C2×D412yes—
237C2×D4×C59C2×D412yes—
238C2×D4×C59C2×D412yes—
239C2×D4×C59C2×D412yes—
240C2×D4×C59#4112yes—
241C22×C4×C59—21no—
242C22×C4×C59—21no—
243C22×C4×C59—21no—
244C22×C4×C59—21no—
245C22×C4×C59—24no—
246C22×C4×C59—21no—
247C22×C4×C59—21no—
248C22×C4×C59—21no—
249C22×C4×C59—21no—
250C22×C4×C59—21no—
251C22×C4×C59—21no—
252C22×C4×C59—21no—
253C22×C4×C59—21no—
254C22×C4×C59—21no—
255C22×C4×C59—21no—
256C22×C4×C59—21no—
257C22×C4×C59—42no—
258C22×C4×C59—42no—
259C22×C4×C59—42no—
260C22×C4×C59—42no—
261C22×C4×C59—81no—
262C22×C4×C59C2×D411yescharacteristic
263C22×C4×C59C2×D411yescharacteristic
264C22×C4×C59C2×D411yescharacteristic
265C22×C4×C59C2×D412yes—
266C22×C4×C59C2×D412yes—
267C22×C4×C59C2×D411yescharacteristic
268C22×C4×C59C2411yescharacteristic
269SD16×C59—44no—
270SD16×C59—44no—
271SD16×C59—44no—
272C2×C8×C59—21no—
273C2×C8×C59—21no—
274C2×C8×C59—21no—
275C2×C8×C59—21no—
276C2×C8×C59—21no—
277C2×C8×C59—21no—
278C2×C8×C59—21no—
279C2×C8×C59—21no—
280C2×C8×C59—21no—
281C2×C8×C59—21no—
282C2×C8×C59—21no—
283C2×C8×C59—44no—
284C2×C8×C59C2×D412yescomplemented
285C4⋊C4×C59—22no—
286C4⋊C4×C59—21no—
287C4⋊C4×C59—21no—
288C4⋊C4×C59—21no—
289C4⋊C4×C59—21no—
290C4⋊C4×C59—21no—
291C4⋊C4×C59—21no—
292C4⋊C4×C59—42no—
293C4⋊C4×C59—42no—
294C4⋊C4×C59—42no—
295C4⋊C4×C59—81no—
296C4⋊C4×C59C2×D412yes—
297C4⋊C4×C59C2×D412yescomplemented
298C22⋊C4×C59—24no—
299C22⋊C4×C59—24no—
300C22⋊C4×C59—22no—
301C22⋊C4×C59—24no—
302C22⋊C4×C59—22no—
303C22⋊C4×C59—42no—
304C22⋊C4×C59—42no—
305C22⋊C4×C59—81no—
306C42×C59—21no—
307C42×C59—21no—
308C23×C59—21no—
309C23×C59—21no—
310C23×C59—21no—
311C23×C59—21no—
312C23×C59—21no—
313C23×C59—22no—
314C23×C59—21no—
315C23×C59—22no—
316C23×C59—21no—
317C23×C59—22no—
318C23×C59—21no—
319C23×C59—21no—
320C23×C59—21no—
321C23×C59—22no—
322C23×C59—22no—
323C23×C59—48no—
324C23×C59—48no—
325C23×C59—48no—
326C23×C59—41no—
327C23×C59—41no—
328C23×C59—41no—
329C23×C59—41no—
330C23×C59—41no—
331C23×C59—41no—
332C23×C59—41no—
333C23×C59—41no—
334C23×C59—41no—
335C23×C59—41no—
336C23×C59—41no—
337C23×C59—41no—
338C23×C59—41no—
339C23×C59—41no—
340C23×C59—41no—
341C23×C59—41no—
342C23×C59—48no—
343C23×C59—84no—
344C23×C59—84no—
345C23×C59—84no—
346C23×C59—84no—
347C23×C59—84no—
348C23×C59—84no—
349C23×C59—84no—
350C23×C59—84no—
351C23×C59—84no—
352C23×C59—84no—
353C23×C59#12012yes—
354C23×C59C2×SD1612yes—
355C23×C59C2×SD1612yes—
356C23×C59AGL(1,ℤ/8)12yes—
357C23×C59C22×D411yescharacteristic
358Q8×C59—41no—
359Q8×C59—41no—
360Q8×C59—41no—
361Q8×C59—41no—
362D4×C59—28no—
363D4×C59—22no—
364D4×C59—22no—
365D4×C59—22no—
366D4×C59—22no—
367D4×C59—22no—
368D4×C59—22no—
369D4×C59—22no—
370D4×C59—48no—
371D4×C59—48no—
372D4×C59—48no—
373D4×C59—48no—
374D4×C59—48no—
375D4×C59—41no—
376D4×C59—41no—
377D4×C59—41no—
378D4×C59—41no—
379D4×C59—84no—
380D4×C59#12114yes—
381C2×C4×C59—21no—
382C2×C4×C59—21no—
383C2×C4×C59—21no—
384C2×C4×C59—21no—
385C2×C4×C59—22no—
386C2×C4×C59—22no—
387C2×C4×C59—22no—
388C2×C4×C59—22no—
389C2×C4×C59—21no—
390C2×C4×C59—21no—
391C2×C4×C59—22no—
392C2×C4×C59—22no—
393C2×C4×C59—21no—
394C2×C4×C59—21no—
395C2×C4×C59—21no—
396C2×C4×C59—21no—
397C2×C4×C59—48no—
398C2×C4×C59—41no—
399C2×C4×C59—41no—
400C2×C4×C59—41no—
401C2×C4×C59—41no—
402C2×C4×C59—41no—
403C2×C4×C59—41no—
404C2×C4×C59—41no—
405C2×C4×C59—41no—
406C2×C4×C59—41no—
407C2×C4×C59—41no—
408C2×C4×C59—41no—
409C2×C4×C59—41no—
410C2×C4×C59—41no—
411C2×C4×C59—41no—
412C2×C4×C59—41no—
413C2×C4×C59—41no—
414C2×C4×C59—41no—
415C2×C4×C59—84no—
416C2×C4×C59#12012yes—
417C2×C4×C59C2×SD1612yes—
418C2×C4×C59C22×D411yescharacteristic
419C2×C4×C59C22×D411yescharacteristic
420C2×C4×C59C22×D411yescharacteristic
421C2×C4×C59C2×#4111yescharacteristic
422C2×C4×C59H(5,𝔽2)11yescharacteristic
423C2×C4×C59H(5,𝔽2)11yescharacteristic
424C8×C59—22no—
425C8×C59—41no—
426C8×C59—41no—
427C8×C59—41no—
428#24432C5911yesmaximal, characteristic, direct product factor, Sylow
429C22×C59—22no—
430C22×C59—22no—
431C22×C59—22no—
432C22×C59—22no—
433C22×C59—22no—
434C22×C59—22no—
435C22×C59—24no—
436C22×C59—22no—
437C22×C59—22no—
438C22×C59—22no—
439C22×C59—41no—
440C22×C59—42no—
441C22×C59—41no—
442C22×C59—42no—
443C22×C59—41no—
444C22×C59—42no—
445C22×C59—42no—
446C22×C59—42no—
447C22×C59—41no—
448C22×C59—42no—
449C22×C59—42no—
450C22×C59—42no—
451C22×C59—42no—
452C22×C59—42no—
453C22×C59—42no—
454C22×C59—42no—
455C22×C59—816no—
456C22×C59—816no—
457C22×C59—81no—
458C22×C59—81no—
459C22×C59—81no—
460C22×C59—81no—
461C22×C59—81no—
462C22×C59—81no—
463C22×C59—81no—
464C22×C59—81no—
465C22×C59#45014yescomplemented
466C22×C59C2×#12011yescharacteristic
467C22×C59D4211yescharacteristic
468C22×C59#54611yescharacteristic
469C22×C59C22×SD1611yescharacteristic
470C22×C59C2×AGL(1,ℤ/8)11yescharacteristic
471C22×C59#57611yescharacteristic
472C22×C59#57711yescharacteristic
473C4×C59—22no—
474C4×C59—22no—
475C4×C59—41no—
476C4×C59—42no—
477C4×C59—42no—
478C4×C59—41no—
479C4×C59—81no—
480C4×C59—81no—
481C4×C59—81no—
482C4×C59C2×#12111yescharacteristic
483C4×C59#53411yescharacteristic
484C4×C59D4211yescharacteristic
485C4×C59#54611yescharacteristic
486C2×D42C2×C5911yescharacteristic
487C2×#465C2×C5911yescharacteristic, complemented
488C2×#450C2×C5911yescharacteristic, complemented
489C2×#450C2×C5911yescharacteristic, complemented
490C22×#102C2×C5911yescharacteristic, complemented
491#2417C2×C5911yescharacteristic, complemented
492#2041C2×C5911yescharacteristic, complemented
493#2034C2×C5911yescharacteristic, complemented
494#2014C2×C5911yescharacteristic, complemented
495#2000C2×C5911yescharacteristic, complemented
496#1877C2×C5911yescharacteristic, complemented
497#1874C2×C5911yescharacteristic, complemented
498#1869C2×C5911yescharacteristic, complemented
499#1864C2×C5911yescharacteristic, complemented
500#1786C2×C5911yescharacteristic, complemented
501C2×C59—24no—
502C2×C59—42no—
503C2×C59—44no—
504C2×C59—82no—
505C2×C59—82no—
506C2×C59#241011yescharacteristic
507C2×C59C2×#45011yescharacteristic
508C2×C59#301211yescharacteristic
509C2×C59#326411yescharacteristic
510C2×C59D4×SD1611yescharacteristic
511C2×C59#329511yescharacteristic
512C2×C59#331011yescharacteristic
513C23×D4—21no—
514C23×D4C22×C5911yescharacteristic
515C23×D4C22×C5911yescharacteristic
516C22×SD16C22×C5911yescharacteristic
517C22×SD16C22×C5911yescharacteristic, complemented
518C22×SD16C22×C5911yescharacteristic, complemented
519C23×C8C22×C5911yescharacteristic, complemented
520D42—24no—
521D42—24no—
522C2×#127C22×C5911yescharacteristic
523C2×C22⋊Q8C22×C5911yescharacteristic, complemented
524C2×C22⋊Q8C22×C5911yescharacteristic, complemented
525C2×#121—21no—
526C2×#121C22×C5911yescharacteristic
527C2×#121C22×C5911yescharacteristic
528C2×#120—21no—
529C2×#120—21no—
530C2×C4×D4C22×C5911yescharacteristic
531C2×C4×D4C22×C5911yescharacteristic
532C22×C4⋊C4C22×C5911yescharacteristic, complemented
533#465—24no—
534#450—24no—
535#450—24no—
536C2×#106C22×C5911yescharacteristic, complemented
537C2×#103C22×C5911yescharacteristic, complemented
538C2×#102—24no—
539C2×#102C22×C5911yescharacteristic
540C2×#102C22×C5911yescharacteristic
541C2×#102C22×C5911yescharacteristic
542C2×#102C22×C5911yescharacteristic, complemented
543C2×#102C22×C5911yescharacteristic, complemented
544C2×#102C22×C5911yescharacteristic, complemented
545C2×#102C22×C5911yescharacteristic, complemented
546C2×#102C22×C5911yescharacteristic, complemented
547C2×#102C22×C5911yescharacteristic, complemented
548C2×C22⋊C8C22×C5911yescharacteristic, complemented
549C2×C22⋊C8C22×C5911yescharacteristic, complemented
550C2×C22⋊C8C22×C5911yescharacteristic, complemented
551#398—21no—
552#396—21no—
553#391C22×C5911yescharacteristic, complemented
554#389C22×C5911yescharacteristic, complemented
555#386—21no—
556#380—21no—
557#380C22×C5911yescharacteristic, complemented
558#340C22×C5911yescharacteristic, complemented
559#340C22×C5911yescharacteristic, complemented
560#336C22×C5911yescharacteristic, complemented
561#336C22×C5911yescharacteristic, complemented
562C59#2443211yescharacteristic, direct product factor, Sylow
563C25—21no—
564C25—21no—
565C22×Q8C23×C5911yescharacteristic
566C22×D4—22no—
567C22×D4—22no—
568C22×D4—28no—
569C22×D4—21no—
570C22×D4—21no—
571C22×D4—22no—
572C22×D4—22no—
573C22×D4—22no—
574C22×D4—22no—
575C22×D4—21no—
576C22×D4—21no—
577C22×D4—21no—
578C22×D4—22no—
579C22×D4—21no—
580C22×D4—41no—
581C22×D4—41no—
582C22×D4—41no—
583C22×D4—41no—
584C22×D4—44no—
585C22×D4—44no—
586C22×D4D4×C5911yescharacteristic
587C22×D4D4×C5914yes—
588C22×D4C23×C5911yescharacteristic
589C22×D4C23×C5911yescharacteristic
590C22×D4C23×C5911yescharacteristic
591C23×C4—21no—
592C23×C4—21no—
593C23×C4C23×C5911yescharacteristic
594C23×C4C23×C5911yescharacteristic
595C2×SD16—22no—
596C2×SD16—22no—
597C2×SD16—22no—
598C2×SD16—22no—
599C2×SD16—22no—
600C2×SD16—22no—
601C2×SD16—41no—
602C2×SD16—41no—
603C2×SD16—41no—
604C22×C8—22no—
605C22×C8—22no—
606C22×C8—41no—
607C22×C8C23×C5911yescharacteristic
608C22×C8C23×C5911yescharacteristic
609C22×C8C23×C5911yescharacteristic
610C22×C8C23×C5911yescharacteristic
611#127—22no—
612#127—22no—
613C22⋊Q8—22no—
614C22⋊Q8—22no—
615C22⋊Q8—22no—
616C22⋊Q8—41no—
617#121—28no—
618#121—22no—
619#121—22no—
620#121—22no—
621#121D4×C5914yes—
622#120—28no—
623#120—28no—
624C4×D4—22no—
625C4×D4—22no—
626C4×D4—22no—
627C4×D4—22no—
628C2×C4⋊C4—22no—
629C2×C4⋊C4—21no—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—21no—
632C2×C4⋊C4—21no—
633C2×C4⋊C4—41no—
634C2×C4⋊C4D4×C5911yescharacteristic
635C2×C4⋊C4C23×C5911yescharacteristic
636C2×C4⋊C4C23×C5911yescharacteristic
637C2×C4⋊C4C23×C5911yescharacteristic
638C2×C4⋊C4C23×C5911yescharacteristic
639C2×C22⋊C4—21no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4—21no—
642C2×C22⋊C4—21no—
643C2×C22⋊C4—21no—
644C2×C22⋊C4—21no—
645C2×C22⋊C4D4×C5911yescharacteristic
646C2×C22⋊C4D4×C5911yescharacteristic
647C2×C42C23×C5911yescharacteristic
648#106—22no—
649#103—22no—
650#102—22no—
651#102—22no—
652#102—22no—
653#102—22no—
654#102—22no—
655#102—22no—
656#102—22no—
657#102—41no—
658#102D4×C5914yescomplemented
659C22⋊C8—22no—
660C22⋊C8—22no—
661C22⋊C8—41no—
662#95—21no—
663#95—21no—
664#95—21no—
665#95—21no—
666C24—21no—
667C24—24no—
668C24—21no—
669C24—21no—
670C24—24no—
671C24—42no—
672C24—42no—
673C24—42no—
674C24—42no—
675C24—42no—
676C24—42no—
677C24—42no—
678C24—42no—
679C24—81no—
680C24—81no—
681C24—81no—
682C24—81no—
683C24C2×D4×C5911yescharacteristic
684C24C2×D4×C5911yescharacteristic
685C2×Q8—21no—
686C2×Q8—21no—
687C2×Q8—21no—
688C2×Q8—21no—
689C2×Q8—21no—
690C2×Q8—21no—
691C2×D4—22no—
692C2×D4—22no—
693C2×D4—28no—
694C2×D4—24no—
695C2×D4—24no—
696C2×D4—24no—
697C2×D4—24no—
698C2×D4—24no—
699C2×D4—24no—
700C2×D4—21no—
701C2×D4—21no—
702C2×D4—21no—
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—21no—
706C2×D4—21no—
707C2×D4—21no—
708C2×D4—21no—
709C2×D4—21no—
710C2×D4—21no—
711C2×D4—21no—
712C2×D4—21no—
713C2×D4—44no—
714C2×D4—44no—
715C2×D4—44no—
716C2×D4—42no—
717C2×D4—42no—
718C2×D4—42no—
719C2×D4—42no—
720C2×D4—42no—
721C2×D4—44no—
722C2×D4—44no—
723C2×D4—432no—
724C2×D4—44no—
725C2×D4—42no—
726C2×D4—42no—
727C2×D4—42no—
728C2×D4—42no—
729C2×D4—44no—
730C2×D4—42no—
731C2×D4—81no—
732C2×D4—81no—
733C2×D4SD16×C5914yescomplemented
734C2×D4C2×D4×C5912yes—
735C2×D4C2×D4×C5912yes—
736C2×D4C2×D4×C5912yes—
737C2×D4C2×D4×C5912yes—
738C2×D4#41×C5912yes—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—24no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—42no—
756C22×C4—42no—
757C22×C4—42no—
758C22×C4—42no—
759C22×C4—81no—
760C22×C4C2×D4×C5911yescharacteristic
761C22×C4C2×D4×C5911yescharacteristic
762C22×C4C2×D4×C5911yescharacteristic
763C22×C4C2×D4×C5912yes—
764C22×C4C2×D4×C5912yes—
765C22×C4C2×D4×C5911yescharacteristic
766C22×C4C24×C5911yescharacteristic
767SD16—44no—
768SD16—44no—
769SD16—44no—
770C2×C8—21no—
771C2×C8—21no—
772C2×C8—21no—
773C2×C8—21no—
774C2×C8—21no—
775C2×C8—21no—
776C2×C8—21no—
777C2×C8—21no—
778C2×C8—21no—
779C2×C8—21no—
780C2×C8—21no—
781C2×C8—44no—
782C2×C8C2×D4×C5912yescomplemented
783C4⋊C4—22no—
784C4⋊C4—21no—
785C4⋊C4—21no—
786C4⋊C4—21no—
787C4⋊C4—21no—
788C4⋊C4—21no—
789C4⋊C4—21no—
790C4⋊C4—42no—
791C4⋊C4—42no—
792C4⋊C4—42no—
793C4⋊C4—81no—
794C4⋊C4C2×D4×C5912yes—
795C4⋊C4C2×D4×C5912yescomplemented
796C22⋊C4—24no—
797C22⋊C4—24no—
798C22⋊C4—22no—
799C22⋊C4—24no—
800C22⋊C4—22no—
801C22⋊C4—42no—
802C22⋊C4—42no—
803C22⋊C4—81no—
804C42—21no—
805C42—21no—
806C23—21no—
807C23—21no—
808C23—21no—
809C23—21no—
810C23—21no—
811C23—22no—
812C23—21no—
813C23—22no—
814C23—21no—
815C23—22no—
816C23—21no—
817C23—21no—
818C23—21no—
819C23—22no—
820C23—22no—
821C23—48no—
822C23—48no—
823C23—48no—
824C23—41no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23—48no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23—41no—
833C23—41no—
834C23—41no—
835C23—41no—
836C23—41no—
837C23—41no—
838C23—41no—
839C23—41no—
840C23—41no—
841C23—84no—
842C23—84no—
843C23—84no—
844C23—84no—
845C23—84no—
846C23—84no—
847C23—84no—
848C23—84no—
849C23—84no—
850C23—84no—
851C23#120×C5912yes—
852C23C2×SD16×C5912yes—
853C23C2×SD16×C5912yes—
854C23AGL(1,ℤ/8)×C5912yes—
855C23C22×D4×C5911yescharacteristic
856Q8—41no—
857Q8—41no—
858Q8—41no—
859Q8—41no—
860D4—28no—
861D4—22no—
862D4—22no—
863D4—22no—
864D4—22no—
865D4—22no—
866D4—22no—
867D4—22no—
868D4—48no—
869D4—48no—
870D4—48no—
871D4—48no—
872D4—48no—
873D4—41no—
874D4—41no—
875D4—41no—
876D4—41no—
877D4—84no—
878D4#121×C5914yes—
879C2×C4—21no—
880C2×C4—21no—
881C2×C4—21no—
882C2×C4—21no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—21no—
888C2×C4—21no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—21no—
892C2×C4—21no—
893C2×C4—21no—
894C2×C4—21no—
895C2×C4—48no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—84no—
914C2×C4#120×C5912yes—
915C2×C4C2×SD16×C5912yes—
916C2×C4C22×D4×C5911yescharacteristic
917C2×C4C22×D4×C5911yescharacteristic
918C2×C4C22×D4×C5911yescharacteristic
919C2×C4C2×#41×C5911yescharacteristic
920C2×C4H(5,𝔽2)×C5911yescharacteristic
921C2×C4H(5,𝔽2)×C5911yescharacteristic
922C8—22no—
923C8—41no—
924C8—41no—
925C8—41no—
926C22—22no—
927C22—22no—
928C22—22no—
929C22—22no—
930C22—22no—
931C22—22no—
932C22—22no—
933C22—22no—
934C22—22no—
935C22—24no—
936C22—42no—
937C22—41no—
938C22—42no—
939C22—41no—
940C22—42no—
941C22—42no—
942C22—42no—
943C22—41no—
944C22—42no—
945C22—41no—
946C22—42no—
947C22—42no—
948C22—42no—
949C22—42no—
950C22—42no—
951C22—42no—
952C22—816no—
953C22—816no—
954C22—81no—
955C22—81no—
956C22—81no—
957C22—81no—
958C22—81no—
959C22—81no—
960C22—81no—
961C22—81no—
962C22C59×#45014yescomplemented
963C22C2×#120×C5911yescharacteristic
964C22D42×C5911yescharacteristic
965C22C59×#54611yescharacteristic
966C22C22×SD16×C5911yescharacteristic
967C22C2×AGL(1,ℤ/8)×C5911yescharacteristic
968C22C59×#57611yescharacteristic
969C22C59×#57711yescharacteristic
970C4—22no—
971C4—22no—
972C4—42no—
973C4—42no—
974C4—41no—
975C4—41no—
976C4—81no—
977C4—81no—
978C4—81no—
979C4C2×#121×C5911yescharacteristic
980C4C59×#53411yescharacteristic
981C4D42×C5911yescharacteristic
982C4C59×#54611yescharacteristic
983C2—24no—
984C2—42no—
985C2—44no—
986C2—82no—
987C2—82no—
988C2C59×#241011yescharacteristic
989C2C2×C59×#45011yescharacteristic
990C2C59×#301211yescharacteristic
991C2C59×#326411yescharacteristic
992C2D4×SD16×C5911yescharacteristic
993C2C59×#329511yescharacteristic
994C2C59×#331011yescharacteristic
subgroupG/H
center, socleC23×C59C22×D4
commutator, Frattini, cosocleC22×C4C24×C59
prime radicalC2×D42×C59C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C59 ◁ C2×C4×D4×C59 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×C59×#465C2semidirect
3. C2×C59×#450C2semidirect
4. C2×C59×#450C2semidirect
5. C22×#102×C59C2semidirect
6. C59×#2417C2semidirect
7. C59×#2041C2semidirect
8. C59×#2034C2semidirect
9. C59×#2014C2semidirect
10. C59×#2000C2semidirect
11. C59×#1877C2semidirect
12. C59×#1874C2semidirect
13. C59×#1869C2semidirect
14. C59×#1864C2semidirect
15. C59×#1786C2semidirect
20. C22×SD16×C59C22semidirect
21. C22×SD16×C59C22semidirect
22. C23×C8×C59C22semidirect
26. C2×C22⋊Q8×C59C22semidirect
27. C2×C22⋊Q8×C59C22semidirect
35. C22×C4⋊C4×C59C22semidirect
39. C2×#106×C59C22semidirect
40. C2×#103×C59C22semidirect
45. C2×#102×C59C22semidirect
46. C2×#102×C59C22semidirect
47. C2×#102×C59C22semidirect
48. C2×#102×C59C22semidirect
49. C2×#102×C59C22semidirect
50. C2×#102×C59C22semidirect
51. C2×C22⋊C8×C59C22semidirect
52. C2×C22⋊C8×C59C22semidirect
53. C2×C22⋊C8×C59C22semidirect
56. C59×#391C22semidirect
57. C59×#389C22semidirect
60. C59×#380C22semidirect
61. C59×#340C22semidirect
62. C59×#340C22semidirect
63. C59×#336C22semidirect
64. C59×#336C22semidirect
160. #102×C59D4semidirect
235. C2×D4×C59SD16semidirect
284. C2×C8×C59C2×D4semidirect
297. C4⋊C4×C59C2×D4semidirect
428. #24432C59direct (N × H)
465. C22×C59#450semidirect
487. C2×#465C2×C59semidirect
488. C2×#450C2×C59semidirect
489. C2×#450C2×C59semidirect
490. C22×#102C2×C59semidirect
491. #2417C2×C59semidirect
492. #2041C2×C59semidirect
493. #2034C2×C59semidirect
494. #2014C2×C59semidirect
495. #2000C2×C59semidirect
496. #1877C2×C59semidirect
497. #1874C2×C59semidirect
498. #1869C2×C59semidirect
499. #1864C2×C59semidirect
500. #1786C2×C59semidirect
517. C22×SD16C22×C59semidirect
518. C22×SD16C22×C59semidirect
519. C23×C8C22×C59semidirect
523. C2×C22⋊Q8C22×C59semidirect
524. C2×C22⋊Q8C22×C59semidirect
532. C22×C4⋊C4C22×C59semidirect
536. C2×#106C22×C59semidirect
537. C2×#103C22×C59semidirect
542. C2×#102C22×C59semidirect
543. C2×#102C22×C59semidirect
544. C2×#102C22×C59semidirect
545. C2×#102C22×C59semidirect
546. C2×#102C22×C59semidirect
547. C2×#102C22×C59semidirect
548. C2×C22⋊C8C22×C59semidirect
549. C2×C22⋊C8C22×C59semidirect
550. C2×C22⋊C8C22×C59semidirect
553. #391C22×C59semidirect
554. #389C22×C59semidirect
557. #380C22×C59semidirect
558. #340C22×C59semidirect
559. #340C22×C59semidirect
560. #336C22×C59semidirect
561. #336C22×C59semidirect
562. C59#24432direct (N × H)
658. #102D4×C59semidirect
733. C2×D4SD16×C59semidirect
782. C2×C8C2×D4×C59semidirect
795. C4⋊C4C2×D4×C59semidirect
962. C22C59×#450semidirect

Maximal subgroups

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

subgroupindex
C2×D42×C592
C2×C59×#4652
C2×C59×#4502
C22×#102×C592
C59×#24172
C59×#20412
C59×#20342
C59×#20142
C59×#20002
C59×#18772
C59×#18742
C59×#18692
C59×#18642
C59×#17862
#2443259