Finite Group Databasebeta

← C59×#18415 #28430524

Subgroups — C59×#18415 #28430524

Order 15104.

992 conjugacy classes of subgroups.

The subgroup lattice has 970 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C59×#3534C211yesmaximal, characteristic
2C59×#3196C211yesmaximal, characteristic, complemented
3C59×#3187C211yesmaximal, characteristic, complemented
4C59×#2663C211yesmaximal, characteristic, complemented
5C59×#1618C211yesmaximal, characteristic, complemented
6C59×#1616C211yesmaximal, characteristic, complemented
7C59×#1615C211yesmaximal, characteristic, complemented
8C59×#1613C211yesmaximal, characteristic, complemented
9C59×#1606C211yesmaximal, characteristic, complemented
10C59×#1604C211yesmaximal, characteristic, complemented
11C59×#1603C211yesmaximal, characteristic, complemented
12C59×#1601C211yesmaximal, characteristic, complemented
13C59×#1507C211yesmaximal, characteristic, complemented
14C59×#1501C211yesmaximal, characteristic, complemented
15C59×#1468C211yesmaximal, characteristic, complemented
16C59×#562—21no—
17C59×#560—21no—
18C59×#553—21no—
19C59×#551—21no—
20C59×#546—21no—
21C59×#546—21no—
22C59×#546—21no—
23D42×C59—21no—
24C59×#540—21no—
25C59×#539—21no—
26C59×#539C2211yescharacteristic
27C59×#538—21no—
28C59×#538C2211yescharacteristic
29C59×#537C2211yescharacteristic
30C59×#534—21no—
31C59×#534C2211yescharacteristic
32C59×#525C2211yescharacteristic
33C2×#123×C59C2211yescharacteristic
34C2×C22⋊Q8×C59C2211yescharacteristic, complemented
35C2×#121×C59C2211yescharacteristic
36C59×#485—21no—
37C59×#484C2211yescharacteristic, complemented
38C59×#483—21no—
39C59×#481C2211yescharacteristic
40C59×#481C2211yescharacteristic, complemented
41C59×#481C2211yescharacteristic, complemented
42C59×#470—21no—
43C59×#468—21no—
44C59×#465—21no—
45C59×#465—21no—
46C59×#452—21no—
47C59×#451C2211yescharacteristic, complemented
48C59×#450—21no—
49C59×#448C2211yescharacteristic
50C59×#448C2211yescharacteristic, complemented
51C59×#448C2211yescharacteristic, complemented
52C59×#407C2211yescharacteristic, complemented
53C2×C22⋊C8×C59C2211yescharacteristic, complemented
54C59×#400C2211yescharacteristic, complemented
55C59×#399C2211yescharacteristic, complemented
56C59×#397—21no—
57C59×#395C2211yescharacteristic, complemented
58C59×#394—21no—
59C59×#393C2211yescharacteristic, complemented
60C59×#389—21no—
61C59×#388—21no—
62C4×C22⋊C4×C59C2211yescharacteristic, complemented
63C59×#328C2211yescharacteristic, complemented
64C59×#328C2211yescharacteristic, complemented
65C59×#327C2211yescharacteristic
66C59×#327C2211yescharacteristic
67C59×#327C2211yescharacteristic, complemented
68C59×#327C2211yescharacteristic, complemented
69C59×#327C2211yescharacteristic, complemented
70C59×#327C2211yescharacteristic, complemented
71C59×#324C2211yescharacteristic, complemented
72C59×#324C2211yescharacteristic, complemented
73C59×#323C2211yescharacteristic, complemented
74C59×#323C2211yescharacteristic, complemented
75C2×#41×C59—21no—
76C2×#41×C59D411yescharacteristic
77C22×Q8×C59C2311yescharacteristic
78C22×D4×C59—21no—
79C22×D4×C59—21no—
80C22×D4×C59—21no—
81C22×D4×C59D411yescharacteristic
82C22×D4×C59D411yescharacteristic
83C23×C4×C59C2311yescharacteristic
84C2×Q16×C59—21no—
85C2×SD16×C59—21no—
86C2×SD16×C59—21no—
87C2×SD16×C59—21no—
88C2×M16×C59—21no—
89C22×C8×C59—21no—
90#127×C59—21no—
91#126×C59—21no—
92#126×C59—21no—
93#126×C59—21no—
94#126×C59—21no—
95#125×C59—21no—
96#125×C59—21no—
97#124×C59—21no—
98#124×C59—21no—
99#124×C59—21no—
100#123×C59—21no—
101#123×C59—21no—
102#123×C59—21no—
103#123×C59—21no—
104#123×C59—21no—
105#123×C59—21no—
106#123×C59—21no—
107#123×C59—21no—
108#123×C59—21no—
109#123×C59—21no—
110#123×C59—21no—
111#123×C59—21no—
112#123×C59—21no—
113#123×C59—21no—
114C22⋊Q8×C59—21no—
115C22⋊Q8×C59—21no—
116C22⋊Q8×C59—21no—
117C22⋊Q8×C59—21no—
118C22⋊Q8×C59—21no—
119C22⋊Q8×C59—21no—
120C22⋊Q8×C59—21no—
121C22⋊Q8×C59—21no—
122C22⋊Q8×C59—21no—
123C22⋊Q8×C59D411yescharacteristic
124C22⋊Q8×C59C2311yescharacteristic
125#121×C59—21no—
126#121×C59—21no—
127#121×C59—21no—
128#121×C59—21no—
129#121×C59—21no—
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—21no—
137#121×C59—21no—
138#121×C59—21no—
139#121×C59—21no—
140#121×C59D411yescharacteristic
141#121×C59D411yescharacteristic
142#121×C59D411yescharacteristic
143#121×C59C2311yescharacteristic
144#121×C59C2311yescharacteristic
145#121×C59C2311yescharacteristic
146#120×C59—21no—
147#120×C59—21no—
148#120×C59—21no—
149#120×C59—21no—
150#120×C59—21no—
151#120×C59—21no—
152#120×C59—21no—
153#120×C59—21no—
154C4×D4×C59—21no—
155C4×D4×C59—21no—
156C4×D4×C59—21no—
157C4×D4×C59—21no—
158C4×D4×C59—21no—
159C4×D4×C59—21no—
160C4×D4×C59—21no—
161C4×D4×C59—21no—
162#117×C59—21no—
163#117×C59D411yescharacteristic
164C2×C4⋊C4×C59—21no—
165C2×C4⋊C4×C59—21no—
166C2×C4⋊C4×C59—21no—
167C2×C4⋊C4×C59D411yescharacteristic
168C2×C4⋊C4×C59D411yescharacteristic
169C2×C4⋊C4×C59C2311yescharacteristic
170C2×C4⋊C4×C59C2311yescharacteristic
171C2×C22⋊C4×C59—21no—
172C2×C22⋊C4×C59—21no—
173C2×C22⋊C4×C59—21no—
174C2×C22⋊C4×C59—21no—
175C2×C22⋊C4×C59—21no—
176C2×C22⋊C4×C59—21no—
177C2×C22⋊C4×C59—21no—
178C2×C22⋊C4×C59D411yescharacteristic
179C2×C22⋊C4×C59D411yescharacteristic
180C2×C22⋊C4×C59C2311yescharacteristic
181C2×C42×C59—21no—
182#107×C59—21no—
183#106×C59—21no—
184#106×C59—21no—
185#106×C59—21no—
186#103×C59—21no—
187#103×C59—21no—
188#103×C59—21no—
189#103×C59—21no—
190#103×C59—21no—
191#102×C59—21no—
192#102×C59—21no—
193#102×C59—21no—
194C22⋊C8×C59—21no—
195C22⋊C8×C59—21no—
196C22⋊C8×C59C2311yescharacteristic
197C22⋊C8×C59C2311yescharacteristic
198C22⋊C8×C59C2311yescharacteristic
199C22⋊C8×C59C2311yescharacteristic
200#95×C59—21no—
201#95×C59—21no—
202#95×C59—21no—
203#95×C59—21no—
204#95×C59C2311yescharacteristic
205#95×C59C2311yescharacteristic
206C24×C59—21no—
207C24×C59—21no—
208C24×C59C2×D411yescharacteristic
209C24×C59C2×D411yescharacteristic
210#41×C59—81no—
211#41×C59—81no—
212#41×C59—81no—
213C2×Q8×C59—21no—
214C2×Q8×C59—21no—
215C2×Q8×C59—21no—
216C2×Q8×C59—81no—
217C2×Q8×C59C2×D411yescharacteristic
218C2×D4×C59—21no—
219C2×D4×C59—21no—
220C2×D4×C59—21no—
221C2×D4×C59—21no—
222C2×D4×C59—21no—
223C2×D4×C59—21no—
224C2×D4×C59—21no—
225C2×D4×C59—21no—
226C2×D4×C59—21no—
227C2×D4×C59—21no—
228C2×D4×C59—21no—
229C2×D4×C59—21no—
230C2×D4×C59—21no—
231C2×D4×C59—21no—
232C2×D4×C59—21no—
233C2×D4×C59—21no—
234C2×D4×C59—21no—
235C2×D4×C59—81no—
236C2×D4×C59—81no—
237C2×D4×C59—81no—
238C2×D4×C59—81no—
239C2×D4×C59—81no—
240C2×D4×C59—81no—
241C2×D4×C59—82no—
242C2×D4×C59C2×D411yescharacteristic
243C2×D4×C59C2×D411yescharacteristic
244C2×D4×C59C2×D411yescharacteristic
245C22×C4×C59—21no—
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—81no—
257C22×C4×C59C2×D411yescharacteristic
258C22×C4×C59C2×D411yescharacteristic
259C22×C4×C59C2×D411yescharacteristic
260C22×C4×C59C2×D411yescharacteristic
261C22×C4×C59C2×D411yescharacteristic
262C22×C4×C59C2×D411yescharacteristic
263C22×C4×C59C2×D411yescharacteristic
264C22×C4×C59C2×D411yescharacteristic
265C22×C4×C59C2411yescharacteristic
266Q16×C59—81no—
267SD16×C59—81no—
268SD16×C59—81no—
269SD16×C59—81no—
270M16×C59—81no—
271C2×C8×C59—21no—
272C2×C8×C59—21no—
273C2×C8×C59—21no—
274C2×C8×C59—21no—
275C2×C8×C59—81no—
276C4⋊C4×C59—21no—
277C4⋊C4×C59—21no—
278C4⋊C4×C59—21no—
279C4⋊C4×C59—21no—
280C4⋊C4×C59—21no—
281C4⋊C4×C59—21no—
282C4⋊C4×C59—21no—
283C4⋊C4×C59—21no—
284C4⋊C4×C59—21no—
285C4⋊C4×C59—21no—
286C4⋊C4×C59—21no—
287C4⋊C4×C59—21no—
288C4⋊C4×C59—21no—
289C4⋊C4×C59—21no—
290C4⋊C4×C59—21no—
291C4⋊C4×C59—42no—
292C4⋊C4×C59—41no—
293C4⋊C4×C59—41no—
294C4⋊C4×C59—81no—
295C4⋊C4×C59C2×D411yescharacteristic
296C4⋊C4×C59C2×D411yescharacteristic
297C4⋊C4×C59C2×D411yescharacteristic
298C4⋊C4×C59C2×D411yescharacteristic
299C22⋊C4×C59—21no—
300C22⋊C4×C59—21no—
301C22⋊C4×C59—21no—
302C22⋊C4×C59—21no—
303C22⋊C4×C59—21no—
304C22⋊C4×C59—21no—
305C22⋊C4×C59—21no—
306C22⋊C4×C59—21no—
307C22⋊C4×C59—21no—
308C22⋊C4×C59—21no—
309C22⋊C4×C59—21no—
310C22⋊C4×C59—21no—
311C22⋊C4×C59—21no—
312C22⋊C4×C59—21no—
313C22⋊C4×C59—21no—
314C22⋊C4×C59—21no—
315C22⋊C4×C59—21no—
316C22⋊C4×C59—21no—
317C22⋊C4×C59—21no—
318C22⋊C4×C59—21no—
319C22⋊C4×C59—21no—
320C22⋊C4×C59—21no—
321C22⋊C4×C59—21no—
322C22⋊C4×C59—21no—
323C22⋊C4×C59—21no—
324C22⋊C4×C59—42no—
325C22⋊C4×C59—42no—
326C22⋊C4×C59—41no—
327C22⋊C4×C59—41no—
328C22⋊C4×C59—81no—
329C42×C59—21no—
330C42×C59—21no—
331C42×C59—21no—
332C42×C59—81no—
333C23×C59—21no—
334C23×C59—21no—
335C23×C59—21no—
336C23×C59—21no—
337C23×C59—21no—
338C23×C59—21no—
339C23×C59—21no—
340C23×C59—21no—
341C23×C59—41no—
342C23×C59—41no—
343C23×C59—42no—
344C23×C59—41no—
345C23×C59—41no—
346C23×C59—81no—
347C23×C59—81no—
348C23×C59—81no—
349C23×C59—81no—
350C23×C59—81no—
351C23×C59#12011yescharacteristic
352C23×C59#12011yescharacteristic
353C23×C59C22×D411yescharacteristic
354Q8×C59—41no—
355Q8×C59—41no—
356Q8×C59—41no—
357Q8×C59—41no—
358Q8×C59—41no—
359Q8×C59—81no—
360D4×C59—41no—
361D4×C59—41no—
362D4×C59—41no—
363D4×C59—42no—
364D4×C59—42no—
365D4×C59—41no—
366D4×C59—41no—
367D4×C59—41no—
368D4×C59—41no—
369D4×C59—41no—
370D4×C59—41no—
371D4×C59—81no—
372D4×C59—81no—
373D4×C59—81no—
374D4×C59—81no—
375D4×C59—81no—
376D4×C59—81no—
377D4×C59—81no—
378D4×C59—81no—
379D4×C59—81no—
380D4×C59—81no—
381D4×C59—81no—
382D4×C59—81no—
383C2×C4×C59—22no—
384C2×C4×C59—21no—
385C2×C4×C59—21no—
386C2×C4×C59—21no—
387C2×C4×C59—21no—
388C2×C4×C59—21no—
389C2×C4×C59—21no—
390C2×C4×C59—21no—
391C2×C4×C59—21no—
392C2×C4×C59—21no—
393C2×C4×C59—21no—
394C2×C4×C59—41no—
395C2×C4×C59—41no—
396C2×C4×C59—41no—
397C2×C4×C59—41no—
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—81no—
414C2×C4×C59—81no—
415C2×C4×C59—81no—
416C2×C4×C59—81no—
417C2×C4×C59—81no—
418C2×C4×C59—81no—
419C2×C4×C59—81no—
420C2×C4×C59#12011yescharacteristic
421C2×C4×C59#12011yescharacteristic
422C2×C4×C59C22×D411yescharacteristic
423C2×C4×C59C22×D411yescharacteristic
424C8×C59—41no—
425C8×C59—41no—
426C8×C59—41no—
427C8×C59—41no—
428#18415C5911yesmaximal, characteristic, direct product factor, Sylow
429C22×C59—21no—
430C22×C59—21no—
431C22×C59—21no—
432C22×C59—21no—
433C22×C59—21no—
434C22×C59—21no—
435C22×C59—21no—
436C22×C59—21no—
437C22×C59—41no—
438C22×C59—41no—
439C22×C59—41no—
440C22×C59—41no—
441C22×C59—41no—
442C22×C59—41no—
443C22×C59—41no—
444C22×C59—41no—
445C22×C59—41no—
446C22×C59—41no—
447C22×C59—41no—
448C22×C59—41no—
449C22×C59—81no—
450C22×C59—81no—
451C22×C59—81no—
452C22×C59—81no—
453C22×C59—162no—
454C22×C59—162no—
455C22×C59C2×#12011yescharacteristic
456C22×C59#57711yescharacteristic
457C22×C59#57711yescharacteristic
458C4×C59—21no—
459C4×C59—21no—
460C4×C59—21no—
461C4×C59—21no—
462C4×C59—42no—
463C4×C59—41no—
464C4×C59—41no—
465C4×C59—41no—
466C4×C59—41no—
467C4×C59—41no—
468C4×C59—41no—
469C4×C59—41no—
470C4×C59—41no—
471C4×C59—81no—
472C4×C59—81no—
473C4×C59—81no—
474#3534C2×C5911yescharacteristic
475#3196C2×C5911yescharacteristic, complemented
476#3187C2×C5911yescharacteristic, complemented
477#2663C2×C5911yescharacteristic, complemented
478#1618C2×C5911yescharacteristic, complemented
479#1616C2×C5911yescharacteristic, complemented
480#1615C2×C5911yescharacteristic, complemented
481#1613C2×C5911yescharacteristic, complemented
482#1606C2×C5911yescharacteristic, complemented
483#1604C2×C5911yescharacteristic, complemented
484#1603C2×C5911yescharacteristic, complemented
485#1601C2×C5911yescharacteristic, complemented
486#1507C2×C5911yescharacteristic, complemented
487#1501C2×C5911yescharacteristic, complemented
488#1468C2×C5911yescharacteristic, complemented
489C2×C59—21no—
490C2×C59—21no—
491C2×C59—41no—
492C2×C59—41no—
493C2×C59—81no—
494C2×C59—81no—
495C2×C59—81no—
496C2×C59—81no—
497C2×C59#300911yescharacteristic
498C2×C59#301811yescharacteristic
499C2×C59#302611yescharacteristic
500#562—21no—
501#560—21no—
502#553—21no—
503#551—21no—
504#546—21no—
505#546—21no—
506#546—21no—
507D42—21no—
508#540—21no—
509#539—21no—
510#539C22×C5911yescharacteristic
511#538—21no—
512#538C22×C5911yescharacteristic
513#537C22×C5911yescharacteristic
514#534—21no—
515#534C22×C5911yescharacteristic
516#525C22×C5911yescharacteristic
517C2×#123C22×C5911yescharacteristic
518C2×C22⋊Q8C22×C5911yescharacteristic, complemented
519C2×#121C22×C5911yescharacteristic
520#485—21no—
521#484C22×C5911yescharacteristic, complemented
522#483—21no—
523#481C22×C5911yescharacteristic
524#481C22×C5911yescharacteristic, complemented
525#481C22×C5911yescharacteristic, complemented
526#470—21no—
527#468—21no—
528#465—21no—
529#465—21no—
530#452—21no—
531#451C22×C5911yescharacteristic, complemented
532#450—21no—
533#448C22×C5911yescharacteristic
534#448C22×C5911yescharacteristic, complemented
535#448C22×C5911yescharacteristic, complemented
536#407C22×C5911yescharacteristic, complemented
537C2×C22⋊C8C22×C5911yescharacteristic, complemented
538#400C22×C5911yescharacteristic, complemented
539#399C22×C5911yescharacteristic, complemented
540#397—21no—
541#395C22×C5911yescharacteristic, complemented
542#394—21no—
543#393C22×C5911yescharacteristic, complemented
544#389—21no—
545#388—21no—
546C4×C22⋊C4C22×C5911yescharacteristic, complemented
547#328C22×C5911yescharacteristic, complemented
548#328C22×C5911yescharacteristic, complemented
549#327C22×C5911yescharacteristic
550#327C22×C5911yescharacteristic
551#327C22×C5911yescharacteristic, complemented
552#327C22×C5911yescharacteristic, complemented
553#327C22×C5911yescharacteristic, complemented
554#327C22×C5911yescharacteristic, complemented
555#324C22×C5911yescharacteristic, complemented
556#324C22×C5911yescharacteristic, complemented
557#323C22×C5911yescharacteristic, complemented
558#323C22×C5911yescharacteristic, complemented
559C59#1841511yescharacteristic, direct product factor, Sylow
560C2×#41—21no—
561C2×#41D4×C5911yescharacteristic
562C22×Q8C23×C5911yescharacteristic
563C22×D4—21no—
564C22×D4—21no—
565C22×D4—21no—
566C22×D4D4×C5911yescharacteristic
567C22×D4D4×C5911yescharacteristic
568C23×C4C23×C5911yescharacteristic
569C2×Q16—21no—
570C2×SD16—21no—
571C2×SD16—21no—
572C2×SD16—21no—
573C2×M16—21no—
574C22×C8—21no—
575#127—21no—
576#126—21no—
577#126—21no—
578#126—21no—
579#126—21no—
580#125—21no—
581#125—21no—
582#124—21no—
583#124—21no—
584#124—21no—
585#123—21no—
586#123—21no—
587#123—21no—
588#123—21no—
589#123—21no—
590#123—21no—
591#123—21no—
592#123—21no—
593#123—21no—
594#123—21no—
595#123—21no—
596#123—21no—
597#123—21no—
598#123—21no—
599C22⋊Q8—21no—
600C22⋊Q8—21no—
601C22⋊Q8—21no—
602C22⋊Q8—21no—
603C22⋊Q8—21no—
604C22⋊Q8—21no—
605C22⋊Q8—21no—
606C22⋊Q8—21no—
607C22⋊Q8—21no—
608C22⋊Q8D4×C5911yescharacteristic
609C22⋊Q8C23×C5911yescharacteristic
610#121—21no—
611#121—21no—
612#121—21no—
613#121—21no—
614#121—21no—
615#121—21no—
616#121—21no—
617#121—21no—
618#121—21no—
619#121—21no—
620#121—21no—
621#121—21no—
622#121—21no—
623#121—21no—
624#121—21no—
625#121D4×C5911yescharacteristic
626#121D4×C5911yescharacteristic
627#121D4×C5911yescharacteristic
628#121C23×C5911yescharacteristic
629#121C23×C5911yescharacteristic
630#121C23×C5911yescharacteristic
631#120—21no—
632#120—21no—
633#120—21no—
634#120—21no—
635#120—21no—
636#120—21no—
637#120—21no—
638#120—21no—
639C4×D4—21no—
640C4×D4—21no—
641C4×D4—21no—
642C4×D4—21no—
643C4×D4—21no—
644C4×D4—21no—
645C4×D4—21no—
646C4×D4—21no—
647#117—21no—
648#117D4×C5911yescharacteristic
649C2×C4⋊C4—21no—
650C2×C4⋊C4—21no—
651C2×C4⋊C4—21no—
652C2×C4⋊C4D4×C5911yescharacteristic
653C2×C4⋊C4D4×C5911yescharacteristic
654C2×C4⋊C4C23×C5911yescharacteristic
655C2×C4⋊C4C23×C5911yescharacteristic
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4D4×C5911yescharacteristic
664C2×C22⋊C4D4×C5911yescharacteristic
665C2×C22⋊C4C23×C5911yescharacteristic
666C2×C42—21no—
667#107—21no—
668#106—21no—
669#106—21no—
670#106—21no—
671#103—21no—
672#103—21no—
673#103—21no—
674#103—21no—
675#103—21no—
676#102—21no—
677#102—21no—
678#102—21no—
679C22⋊C8—21no—
680C22⋊C8—21no—
681C22⋊C8C23×C5911yescharacteristic
682C22⋊C8C23×C5911yescharacteristic
683C22⋊C8C23×C5911yescharacteristic
684C22⋊C8C23×C5911yescharacteristic
685#95—21no—
686#95—21no—
687#95—21no—
688#95—21no—
689#95C23×C5911yescharacteristic
690#95C23×C5911yescharacteristic
691C24—21no—
692C24—21no—
693C24C2×D4×C5911yescharacteristic
694C24C2×D4×C5911yescharacteristic
695#41—81no—
696#41—81no—
697#41—81no—
698C2×Q8—21no—
699C2×Q8—21no—
700C2×Q8—21no—
701C2×Q8—81no—
702C2×Q8C2×D4×C5911yescharacteristic
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—21no—
714C2×D4—21no—
715C2×D4—21no—
716C2×D4—21no—
717C2×D4—21no—
718C2×D4—21no—
719C2×D4—21no—
720C2×D4—81no—
721C2×D4—81no—
722C2×D4—81no—
723C2×D4—81no—
724C2×D4—81no—
725C2×D4—81no—
726C2×D4—82no—
727C2×D4C2×D4×C5911yescharacteristic
728C2×D4C2×D4×C5911yescharacteristic
729C2×D4C2×D4×C5911yescharacteristic
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—81no—
742C22×C4C2×D4×C5911yescharacteristic
743C22×C4C2×D4×C5911yescharacteristic
744C22×C4C2×D4×C5911yescharacteristic
745C22×C4C2×D4×C5911yescharacteristic
746C22×C4C2×D4×C5911yescharacteristic
747C22×C4C2×D4×C5911yescharacteristic
748C22×C4C2×D4×C5911yescharacteristic
749C22×C4C2×D4×C5911yescharacteristic
750C22×C4C24×C5911yescharacteristic
751Q16—81no—
752SD16—81no—
753SD16—81no—
754SD16—81no—
755M16—81no—
756C2×C8—21no—
757C2×C8—21no—
758C2×C8—21no—
759C2×C8—21no—
760C2×C8—81no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—21no—
766C4⋊C4—21no—
767C4⋊C4—21no—
768C4⋊C4—21no—
769C4⋊C4—21no—
770C4⋊C4—21no—
771C4⋊C4—21no—
772C4⋊C4—21no—
773C4⋊C4—21no—
774C4⋊C4—21no—
775C4⋊C4—21no—
776C4⋊C4—42no—
777C4⋊C4—41no—
778C4⋊C4—41no—
779C4⋊C4—81no—
780C4⋊C4C2×D4×C5911yescharacteristic
781C4⋊C4C2×D4×C5911yescharacteristic
782C4⋊C4C2×D4×C5911yescharacteristic
783C4⋊C4C2×D4×C5911yescharacteristic
784C22⋊C4—21no—
785C22⋊C4—21no—
786C22⋊C4—21no—
787C22⋊C4—21no—
788C22⋊C4—21no—
789C22⋊C4—21no—
790C22⋊C4—21no—
791C22⋊C4—21no—
792C22⋊C4—21no—
793C22⋊C4—21no—
794C22⋊C4—21no—
795C22⋊C4—21no—
796C22⋊C4—21no—
797C22⋊C4—21no—
798C22⋊C4—21no—
799C22⋊C4—21no—
800C22⋊C4—21no—
801C22⋊C4—21no—
802C22⋊C4—21no—
803C22⋊C4—21no—
804C22⋊C4—21no—
805C22⋊C4—21no—
806C22⋊C4—21no—
807C22⋊C4—21no—
808C22⋊C4—21no—
809C22⋊C4—42no—
810C22⋊C4—42no—
811C22⋊C4—41no—
812C22⋊C4—41no—
813C22⋊C4—81no—
814C42—21no—
815C42—21no—
816C42—21no—
817C42—81no—
818C23—21no—
819C23—21no—
820C23—21no—
821C23—21no—
822C23—21no—
823C23—21no—
824C23—21no—
825C23—21no—
826C23—41no—
827C23—41no—
828C23—42no—
829C23—41no—
830C23—41no—
831C23—81no—
832C23—81no—
833C23—81no—
834C23—81no—
835C23—81no—
836C23#120×C5911yescharacteristic
837C23#120×C5911yescharacteristic
838C23C22×D4×C5911yescharacteristic
839Q8—41no—
840Q8—41no—
841Q8—41no—
842Q8—41no—
843Q8—41no—
844Q8—81no—
845D4—41no—
846D4—41no—
847D4—41no—
848D4—42no—
849D4—42no—
850D4—41no—
851D4—41no—
852D4—41no—
853D4—41no—
854D4—41no—
855D4—41no—
856D4—81no—
857D4—81no—
858D4—81no—
859D4—81no—
860D4—81no—
861D4—81no—
862D4—81no—
863D4—81no—
864D4—81no—
865D4—81no—
866D4—81no—
867D4—81no—
868C2×C4—22no—
869C2×C4—21no—
870C2×C4—21no—
871C2×C4—21no—
872C2×C4—21no—
873C2×C4—21no—
874C2×C4—21no—
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—21no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—81no—
899C2×C4—81no—
900C2×C4—81no—
901C2×C4—81no—
902C2×C4—81no—
903C2×C4—81no—
904C2×C4—81no—
905C2×C4#120×C5911yescharacteristic
906C2×C4#120×C5911yescharacteristic
907C2×C4C22×D4×C5911yescharacteristic
908C2×C4C22×D4×C5911yescharacteristic
909C8—41no—
910C8—41no—
911C8—41no—
912C8—41no—
913C22—21no—
914C22—21no—
915C22—21no—
916C22—21no—
917C22—21no—
918C22—21no—
919C22—21no—
920C22—21no—
921C22—41no—
922C22—41no—
923C22—41no—
924C22—41no—
925C22—41no—
926C22—41no—
927C22—41no—
928C22—41no—
929C22—41no—
930C22—41no—
931C22—41no—
932C22—41no—
933C22—81no—
934C22—81no—
935C22—81no—
936C22—81no—
937C22—162no—
938C22—162no—
939C22C2×#120×C5911yescharacteristic
940C22C59×#57711yescharacteristic
941C22C59×#57711yescharacteristic
942C4—21no—
943C4—21no—
944C4—21no—
945C4—21no—
946C4—42no—
947C4—41no—
948C4—41no—
949C4—41no—
950C4—41no—
951C4—41no—
952C4—41no—
953C4—41no—
954C4—41no—
955C4—81no—
956C4—81no—
957C4—81no—
958C2—21no—
959C2—21no—
960C2—41no—
961C2—41no—
962C2—81no—
963C2—81no—
964C2—81no—
965C2—81no—
966C2C59×#300911yescharacteristic
967C2C59×#301811yescharacteristic
968C2C59×#302611yescharacteristic
subgroupG/H
center, socleC22×C59C2×#120
commutator, Frattini, cosocleC22×C4C24×C59
prime radicalC59×#3534C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C59 ◁ C23×C4×C59 ◁ G

Complements

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

NH ≅ G/Ntype
2. C59×#3196C2semidirect
3. C59×#3187C2semidirect
4. C59×#2663C2semidirect
5. C59×#1618C2semidirect
6. C59×#1616C2semidirect
7. C59×#1615C2semidirect
8. C59×#1613C2semidirect
9. C59×#1606C2semidirect
10. C59×#1604C2semidirect
11. C59×#1603C2semidirect
12. C59×#1601C2semidirect
13. C59×#1507C2semidirect
14. C59×#1501C2semidirect
15. C59×#1468C2semidirect
34. C2×C22⋊Q8×C59C22semidirect
37. C59×#484C22semidirect
40. C59×#481C22semidirect
41. C59×#481C22semidirect
47. C59×#451C22semidirect
50. C59×#448C22semidirect
51. C59×#448C22semidirect
52. C59×#407C22semidirect
53. C2×C22⋊C8×C59C22semidirect
54. C59×#400C22semidirect
55. C59×#399C22semidirect
57. C59×#395C22semidirect
59. C59×#393C22semidirect
62. C4×C22⋊C4×C59C22semidirect
63. C59×#328C22semidirect
64. C59×#328C22semidirect
67. C59×#327C22semidirect
68. C59×#327C22semidirect
69. C59×#327C22semidirect
70. C59×#327C22semidirect
71. C59×#324C22semidirect
72. C59×#324C22semidirect
73. C59×#323C22semidirect
74. C59×#323C22semidirect
428. #18415C59direct (N × H)
475. #3196C2×C59semidirect
476. #3187C2×C59semidirect
477. #2663C2×C59semidirect
478. #1618C2×C59semidirect
479. #1616C2×C59semidirect
480. #1615C2×C59semidirect
481. #1613C2×C59semidirect
482. #1606C2×C59semidirect
483. #1604C2×C59semidirect
484. #1603C2×C59semidirect
485. #1601C2×C59semidirect
486. #1507C2×C59semidirect
487. #1501C2×C59semidirect
488. #1468C2×C59semidirect
518. C2×C22⋊Q8C22×C59semidirect
521. #484C22×C59semidirect
524. #481C22×C59semidirect
525. #481C22×C59semidirect
531. #451C22×C59semidirect
534. #448C22×C59semidirect
535. #448C22×C59semidirect
536. #407C22×C59semidirect
537. C2×C22⋊C8C22×C59semidirect
538. #400C22×C59semidirect
539. #399C22×C59semidirect
541. #395C22×C59semidirect
543. #393C22×C59semidirect
546. C4×C22⋊C4C22×C59semidirect
547. #328C22×C59semidirect
548. #328C22×C59semidirect
551. #327C22×C59semidirect
552. #327C22×C59semidirect
553. #327C22×C59semidirect
554. #327C22×C59semidirect
555. #324C22×C59semidirect
556. #324C22×C59semidirect
557. #323C22×C59semidirect
558. #323C22×C59semidirect
559. C59#18415direct (N × H)

Maximal subgroups

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

subgroupindex
C59×#35342
C59×#31962
C59×#31872
C59×#26632
C59×#16182
C59×#16162
C59×#16152
C59×#16132
C59×#16062
C59×#16042
C59×#16032
C59×#16012
C59×#15072
C59×#15012
C59×#14682
#1841559