Finite Group Databasebeta

← C59×#18445 #28430554

Subgroups — C59×#18445 #28430554

Order 15104.

848 conjugacy classes of subgroups.

The subgroup lattice has 838 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C59×#3564C211yesmaximal, characteristic
2C59×#3236C211yesmaximal, characteristic, complemented
3C59×#3232C211yesmaximal, characteristic, complemented
4C59×#2664C211yesmaximal, characteristic, complemented
5C59×#1618C211yesmaximal, characteristic
6C59×#1617C211yesmaximal, characteristic, complemented
7C59×#1615C211yesmaximal, characteristic, complemented
8C59×#1614C211yesmaximal, characteristic, complemented
9C59×#1612C211yesmaximal, characteristic
10C59×#1611C211yesmaximal, characteristic, complemented
11C59×#1609C211yesmaximal, characteristic, complemented
12C59×#1608C211yesmaximal, characteristic, complemented
13C59×#1509C211yesmaximal, characteristic, complemented
14C59×#1503C211yesmaximal, characteristic, complemented
15C59×#1473C211yesmaximal, characteristic, complemented
16C59×#563—21no—
17C59×#563—21no—
18C59×#556—21no—
19C59×#554—21no—
20C59×#552—21no—
21C59×#552—21no—
22C59×#551—21no—
23C59×#551—21no—
24C59×#544C2211yescharacteristic
25C59×#543C2211yescharacteristic
26C59×#542—21no—
27C59×#541—21no—
28C59×#541—21no—
29C59×#539—21no—
30C59×#539C2211yescharacteristic
31C59×#538C2211yescharacteristic
32C59×#533C2211yescharacteristic
33C59×#529C2211yescharacteristic
34C2×#126×C59C2211yescharacteristic
35C2×#125×C59C2211yescharacteristic
36C59×#501—21no—
37C59×#499—21no—
38C59×#491—21no—
39C59×#488—21no—
40C59×#484C2211yescharacteristic
41C59×#484C2211yescharacteristic
42C59×#484C2211yescharacteristic
43C59×#483C2211yescharacteristic
44C59×#483C2211yescharacteristic
45C59×#483C2211yescharacteristic
46C59×#481C2211yescharacteristic
47C59×#480C2211yescharacteristic
48C59×#479—21no—
49C59×#479—21no—
50C59×#479—21no—
51C59×#478—21no—
52C59×#432C2211yescharacteristic
53C59×#431C2211yescharacteristic
54C59×#400C2211yescharacteristic
55C59×#399C2211yescharacteristic
56C59×#398—21no—
57C59×#398C2211yescharacteristic
58C59×#397C2211yescharacteristic
59C59×#396—21no—
60C59×#389—21no—
61C59×#388—21no—
62C4×C4⋊C4×C59C2211yescharacteristic
63C59×#328C2211yescharacteristic
64C59×#328C2211yescharacteristic
65C59×#328C2211yescharacteristic
66C59×#328C2211yescharacteristic
67C59×#328C2211yescharacteristic
68C59×#328C2211yescharacteristic
69C59×#327C2211yescharacteristic
70C59×#327C2211yescharacteristic
71C59×#324C2211yescharacteristic
72C59×#324C2211yescharacteristic
73C59×#323C2211yescharacteristic
74C59×#323C2211yescharacteristic
75C4⋊Q8×C59—21no—
76C4⋊Q8×C59—21no—
77C4⋊Q8×C59—21no—
78C4⋊Q8×C59D411yescharacteristic
79C4⋊Q8×C59D411yescharacteristic
80#126×C59—21no—
81#126×C59—21no—
82#126×C59—21no—
83#126×C59—21no—
84#126×C59—21no—
85#126×C59—21no—
86#126×C59—21no—
87#126×C59—21no—
88#126×C59—21no—
89#126×C59—21no—
90#126×C59—21no—
91#126×C59—21no—
92#126×C59—21no—
93#125×C59—21no—
94#125×C59—21no—
95#125×C59—21no—
96#125×C59—21no—
97#125×C59—21no—
98#125×C59—21no—
99#125×C59—21no—
100#125×C59—21no—
101#125×C59—21no—
102#125×C59—21no—
103#125×C59—21no—
104#125×C59—21no—
105#125×C59—21no—
106#125×C59D411yescharacteristic
107#124×C59—21no—
108#124×C59—21no—
109#124×C59—21no—
110#124×C59D411yescharacteristic
111#123×C59—21no—
112#123×C59—21no—
113#123×C59—21no—
114#123×C59—21no—
115#123×C59—21no—
116#123×C59—21no—
117#123×C59—21no—
118#123×C59—21no—
119C22⋊Q8×C59—21no—
120C22⋊Q8×C59—21no—
121C22⋊Q8×C59—21no—
122C22⋊Q8×C59—21no—
123C22⋊Q8×C59—21no—
124C22⋊Q8×C59—21no—
125C22⋊Q8×C59—21no—
126C22⋊Q8×C59—21no—
127C22⋊Q8×C59—21no—
128C22⋊Q8×C59—21no—
129C22⋊Q8×C59—21no—
130C22⋊Q8×C59—21no—
131C22⋊Q8×C59—21no—
132C22⋊Q8×C59—21no—
133C22⋊Q8×C59C2311yescharacteristic
134C22⋊Q8×C59C2311yescharacteristic
135C22⋊Q8×C59C2311yescharacteristic
136#121×C59—21no—
137#121×C59C2311yescharacteristic
138#120×C59—21no—
139C4×Q8×C59—21no—
140C4×Q8×C59—21no—
141C4×Q8×C59—21no—
142C4×Q8×C59D411yescharacteristic
143C4×Q8×C59D411yescharacteristic
144C4×Q8×C59D411yescharacteristic
145C4×D4×C59—21no—
146C4×D4×C59—21no—
147C4×D4×C59—21no—
148C4×D4×C59—21no—
149C4×D4×C59—21no—
150C4×D4×C59D411yescharacteristic
151#117×C59—21no—
152#117×C59—21no—
153#117×C59—21no—
154#117×C59—21no—
155#117×C59—21no—
156#117×C59—21no—
157C2×C4⋊C4×C59—21no—
158C2×C4⋊C4×C59—21no—
159C2×C4⋊C4×C59—21no—
160C2×C4⋊C4×C59—21no—
161C2×C4⋊C4×C59—21no—
162C2×C4⋊C4×C59—21no—
163C2×C4⋊C4×C59D411yescharacteristic
164C2×C4⋊C4×C59D411yescharacteristic
165C2×C4⋊C4×C59C2311yescharacteristic
166C2×C4⋊C4×C59C2311yescharacteristic
167C2×C4⋊C4×C59C2311yescharacteristic
168C2×C22⋊C4×C59—21no—
169C2×C22⋊C4×C59—21no—
170C2×C22⋊C4×C59—21no—
171C2×C22⋊C4×C59D411yescharacteristic
172C2×C22⋊C4×C59D411yescharacteristic
173C2×C22⋊C4×C59C2311yescharacteristic
174C2×C42×C59—21no—
175C2×C42×C59C2311yescharacteristic
176#107×C59—21no—
177#107×C59—21no—
178#107×C59—21no—
179#107×C59—21no—
180#106×C59—21no—
181#106×C59—21no—
182#106×C59—21no—
183#106×C59—21no—
184C4⋊C8×C59—21no—
185C4⋊C8×C59—21no—
186#103×C59—21no—
187#103×C59—21no—
188#103×C59—21no—
189#103×C59—21no—
190#103×C59—21no—
191#103×C59—21no—
192#102×C59—21no—
193#102×C59—21no—
194C22⋊C8×C59C2311yescharacteristic
195C22⋊C8×C59C2311yescharacteristic
196C22⋊C8×C59C2311yescharacteristic
197C22⋊C8×C59C2311yescharacteristic
198#97×C59—21no—
199C4×C8×C59—21no—
200#95×C59—21no—
201#95×C59—21no—
202#95×C59—21no—
203#95×C59—21no—
204#95×C59C2311yescharacteristic
205#95×C59C2311yescharacteristic
206C24×C59C2×D411yescharacteristic
207C2×Q8×C59—21no—
208C2×Q8×C59—21no—
209C2×Q8×C59—21no—
210C2×Q8×C59C2×D411yescharacteristic
211C2×Q8×C59C2×D411yescharacteristic
212C2×Q8×C59C2×D411yescharacteristic
213C2×D4×C59—21no—
214C2×D4×C59—21no—
215C2×D4×C59—21no—
216C2×D4×C59C2×D411yescharacteristic
217C22×C4×C59—21no—
218C22×C4×C59—21no—
219C22×C4×C59—21no—
220C22×C4×C59—21no—
221C22×C4×C59—21no—
222C22×C4×C59—21no—
223C22×C4×C59—21no—
224C22×C4×C59—21no—
225C22×C4×C59—21no—
226C22×C4×C59C2×D411yescharacteristic
227C22×C4×C59C2×D411yescharacteristic
228C22×C4×C59C2×D411yescharacteristic
229C22×C4×C59C2×D411yescharacteristic
230C22×C4×C59C2×D411yescharacteristic
231C22×C4×C59C2411yescharacteristic
232C2×C8×C59—21no—
233C2×C8×C59—21no—
234C2×C8×C59—21no—
235C2×C8×C59—21no—
236C4⋊C4×C59—21no—
237C4⋊C4×C59—21no—
238C4⋊C4×C59—21no—
239C4⋊C4×C59—21no—
240C4⋊C4×C59—21no—
241C4⋊C4×C59—21no—
242C4⋊C4×C59—21no—
243C4⋊C4×C59—21no—
244C4⋊C4×C59—21no—
245C4⋊C4×C59—21no—
246C4⋊C4×C59—21no—
247C4⋊C4×C59—21no—
248C4⋊C4×C59—21no—
249C4⋊C4×C59—21no—
250C4⋊C4×C59—21no—
251C4⋊C4×C59—21no—
252C4⋊C4×C59—21no—
253C4⋊C4×C59—21no—
254C4⋊C4×C59—21no—
255C4⋊C4×C59—21no—
256C4⋊C4×C59—21no—
257C4⋊C4×C59—21no—
258C4⋊C4×C59—21no—
259C4⋊C4×C59—21no—
260C4⋊C4×C59—21no—
261C4⋊C4×C59—21no—
262C4⋊C4×C59—21no—
263C4⋊C4×C59—21no—
264C4⋊C4×C59—21no—
265C4⋊C4×C59—21no—
266C4⋊C4×C59—21no—
267C4⋊C4×C59—21no—
268C4⋊C4×C59—21no—
269C4⋊C4×C59—42no—
270C4⋊C4×C59—42no—
271C4⋊C4×C59—41no—
272C4⋊C4×C59—41no—
273C4⋊C4×C59—41no—
274C4⋊C4×C59—41no—
275C4⋊C4×C59—81no—
276C4⋊C4×C59C2×D411yescharacteristic
277C4⋊C4×C59C2×D411yescharacteristic
278C4⋊C4×C59C2×D411yescharacteristic
279C4⋊C4×C59C2×D411yescharacteristic
280C22⋊C4×C59—21no—
281C22⋊C4×C59—21no—
282C22⋊C4×C59—21no—
283C22⋊C4×C59—21no—
284C22⋊C4×C59—21no—
285C22⋊C4×C59—21no—
286C22⋊C4×C59—21no—
287C22⋊C4×C59—21no—
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—21no—
295C22⋊C4×C59—21no—
296C22⋊C4×C59—21no—
297C22⋊C4×C59—21no—
298C22⋊C4×C59—21no—
299C22⋊C4×C59—21no—
300C22⋊C4×C59—21no—
301C22⋊C4×C59—42no—
302C22⋊C4×C59—81no—
303C42×C59—21no—
304C42×C59—21no—
305C42×C59—21no—
306C42×C59—21no—
307C42×C59—21no—
308C42×C59—21no—
309C42×C59—21no—
310C42×C59—81no—
311C42×C59C2×D411yescharacteristic
312C42×C59C2×D411yescharacteristic
313C42×C59C2×D411yescharacteristic
314C42×C59C2×D411yescharacteristic
315C23×C59—21no—
316C23×C59—21no—
317C23×C59—21no—
318C23×C59—21no—
319C23×C59—41no—
320C23×C59—41no—
321C23×C59C22×D411yescharacteristic
322Q8×C59—41no—
323Q8×C59—41no—
324Q8×C59—41no—
325Q8×C59—81no—
326Q8×C59—81no—
327Q8×C59—81no—
328D4×C59—41no—
329D4×C59—41no—
330D4×C59—41no—
331D4×C59—81no—
332D4×C59—81no—
333C2×C4×C59—21no—
334C2×C4×C59—21no—
335C2×C4×C59—22no—
336C2×C4×C59—21no—
337C2×C4×C59—21no—
338C2×C4×C59—21no—
339C2×C4×C59—21no—
340C2×C4×C59—21no—
341C2×C4×C59—21no—
342C2×C4×C59—21no—
343C2×C4×C59—21no—
344C2×C4×C59—21no—
345C2×C4×C59—21no—
346C2×C4×C59—21no—
347C2×C4×C59—21no—
348C2×C4×C59—41no—
349C2×C4×C59—41no—
350C2×C4×C59—41no—
351C2×C4×C59—41no—
352C2×C4×C59—41no—
353C2×C4×C59—41no—
354C2×C4×C59—41no—
355C2×C4×C59—41no—
356C2×C4×C59—41no—
357C2×C4×C59—41no—
358C2×C4×C59—41no—
359C2×C4×C59—41no—
360C2×C4×C59—41no—
361C2×C4×C59—41no—
362C2×C4×C59—41no—
363C2×C4×C59—81no—
364C2×C4×C59—81no—
365C2×C4×C59—81no—
366C2×C4×C59—81no—
367C2×C4×C59—81no—
368C2×C4×C59#12011yescharacteristic
369C2×C4×C59#12011yescharacteristic
370C2×C4×C59#12011yescharacteristic
371C2×C4×C59#12011yescharacteristic
372C2×C4×C59C22×D411yescharacteristic
373C2×C4×C59C22×D411yescharacteristic
374C8×C59—41no—
375C8×C59—41no—
376C8×C59—41no—
377C8×C59—41no—
378#18445C5911yesmaximal, characteristic, direct product factor, Sylow
379C22×C59—21no—
380C22×C59—21no—
381C22×C59—41no—
382C22×C59—41no—
383C22×C59—41no—
384C22×C59—41no—
385C22×C59—41no—
386C22×C59—41no—
387C22×C59—81no—
388C22×C59—81no—
389C22×C59C2×#12011yescharacteristic
390C22×C59#57711yescharacteristic
391C22×C59#57811yescharacteristic
392C4×C59—21no—
393C4×C59—21no—
394C4×C59—21no—
395C4×C59—21no—
396C4×C59—21no—
397C4×C59—21no—
398C4×C59—42no—
399C4×C59—41no—
400C4×C59—41no—
401C4×C59—41no—
402C4×C59—41no—
403C4×C59—41no—
404C4×C59—41no—
405C4×C59—41no—
406C4×C59—41no—
407C4×C59—41no—
408C4×C59—41no—
409C4×C59—81no—
410C4×C59—81no—
411C4×C59—81no—
412#3564C2×C5911yescharacteristic
413#3236C2×C5911yescharacteristic, complemented
414#3232C2×C5911yescharacteristic, complemented
415#2664C2×C5911yescharacteristic, complemented
416#1618C2×C5911yescharacteristic
417#1617C2×C5911yescharacteristic, complemented
418#1615C2×C5911yescharacteristic, complemented
419#1614C2×C5911yescharacteristic, complemented
420#1612C2×C5911yescharacteristic
421#1611C2×C5911yescharacteristic, complemented
422#1609C2×C5911yescharacteristic, complemented
423#1608C2×C5911yescharacteristic, complemented
424#1509C2×C5911yescharacteristic, complemented
425#1503C2×C5911yescharacteristic, complemented
426#1473C2×C5911yescharacteristic, complemented
427C2×C59—21no—
428C2×C59—21no—
429C2×C59—81no—
430C2×C59—81no—
431C2×C59#301311yescharacteristic
432C2×C59#301811yescharacteristic
433C2×C59#302811yescharacteristic
434#563—21no—
435#563—21no—
436#556—21no—
437#554—21no—
438#552—21no—
439#552—21no—
440#551—21no—
441#551—21no—
442#544C22×C5911yescharacteristic
443#543C22×C5911yescharacteristic
444#542—21no—
445#541—21no—
446#541—21no—
447#539—21no—
448#539C22×C5911yescharacteristic
449#538C22×C5911yescharacteristic
450#533C22×C5911yescharacteristic
451#529C22×C5911yescharacteristic
452C2×#126C22×C5911yescharacteristic
453C2×#125C22×C5911yescharacteristic
454#501—21no—
455#499—21no—
456#491—21no—
457#488—21no—
458#484C22×C5911yescharacteristic
459#484C22×C5911yescharacteristic
460#484C22×C5911yescharacteristic
461#483C22×C5911yescharacteristic
462#483C22×C5911yescharacteristic
463#483C22×C5911yescharacteristic
464#481C22×C5911yescharacteristic
465#480C22×C5911yescharacteristic
466#479—21no—
467#479—21no—
468#479—21no—
469#478—21no—
470#432C22×C5911yescharacteristic
471#431C22×C5911yescharacteristic
472#400C22×C5911yescharacteristic
473#399C22×C5911yescharacteristic
474#398—21no—
475#398C22×C5911yescharacteristic
476#397C22×C5911yescharacteristic
477#396—21no—
478#389—21no—
479#388—21no—
480C4×C4⋊C4C22×C5911yescharacteristic
481#328C22×C5911yescharacteristic
482#328C22×C5911yescharacteristic
483#328C22×C5911yescharacteristic
484#328C22×C5911yescharacteristic
485#328C22×C5911yescharacteristic
486#328C22×C5911yescharacteristic
487#327C22×C5911yescharacteristic
488#327C22×C5911yescharacteristic
489#324C22×C5911yescharacteristic
490#324C22×C5911yescharacteristic
491#323C22×C5911yescharacteristic
492#323C22×C5911yescharacteristic
493C59#1844511yescharacteristic, direct product factor, Sylow
494C4⋊Q8—21no—
495C4⋊Q8—21no—
496C4⋊Q8—21no—
497C4⋊Q8D4×C5911yescharacteristic
498C4⋊Q8D4×C5911yescharacteristic
499#126—21no—
500#126—21no—
501#126—21no—
502#126—21no—
503#126—21no—
504#126—21no—
505#126—21no—
506#126—21no—
507#126—21no—
508#126—21no—
509#126—21no—
510#126—21no—
511#126—21no—
512#125—21no—
513#125—21no—
514#125—21no—
515#125—21no—
516#125—21no—
517#125—21no—
518#125—21no—
519#125—21no—
520#125—21no—
521#125—21no—
522#125—21no—
523#125—21no—
524#125—21no—
525#125D4×C5911yescharacteristic
526#124—21no—
527#124—21no—
528#124—21no—
529#124D4×C5911yescharacteristic
530#123—21no—
531#123—21no—
532#123—21no—
533#123—21no—
534#123—21no—
535#123—21no—
536#123—21no—
537#123—21no—
538C22⋊Q8—21no—
539C22⋊Q8—21no—
540C22⋊Q8—21no—
541C22⋊Q8—21no—
542C22⋊Q8—21no—
543C22⋊Q8—21no—
544C22⋊Q8—21no—
545C22⋊Q8—21no—
546C22⋊Q8—21no—
547C22⋊Q8—21no—
548C22⋊Q8—21no—
549C22⋊Q8—21no—
550C22⋊Q8—21no—
551C22⋊Q8—21no—
552C22⋊Q8C23×C5911yescharacteristic
553C22⋊Q8C23×C5911yescharacteristic
554C22⋊Q8C23×C5911yescharacteristic
555#121—21no—
556#121C23×C5911yescharacteristic
557#120—21no—
558C4×Q8—21no—
559C4×Q8—21no—
560C4×Q8—21no—
561C4×Q8D4×C5911yescharacteristic
562C4×Q8D4×C5911yescharacteristic
563C4×Q8D4×C5911yescharacteristic
564C4×D4—21no—
565C4×D4—21no—
566C4×D4—21no—
567C4×D4—21no—
568C4×D4—21no—
569C4×D4D4×C5911yescharacteristic
570#117—21no—
571#117—21no—
572#117—21no—
573#117—21no—
574#117—21no—
575#117—21no—
576C2×C4⋊C4—21no—
577C2×C4⋊C4—21no—
578C2×C4⋊C4—21no—
579C2×C4⋊C4—21no—
580C2×C4⋊C4—21no—
581C2×C4⋊C4—21no—
582C2×C4⋊C4D4×C5911yescharacteristic
583C2×C4⋊C4D4×C5911yescharacteristic
584C2×C4⋊C4C23×C5911yescharacteristic
585C2×C4⋊C4C23×C5911yescharacteristic
586C2×C4⋊C4C23×C5911yescharacteristic
587C2×C22⋊C4—21no—
588C2×C22⋊C4—21no—
589C2×C22⋊C4—21no—
590C2×C22⋊C4D4×C5911yescharacteristic
591C2×C22⋊C4D4×C5911yescharacteristic
592C2×C22⋊C4C23×C5911yescharacteristic
593C2×C42—21no—
594C2×C42C23×C5911yescharacteristic
595#107—21no—
596#107—21no—
597#107—21no—
598#107—21no—
599#106—21no—
600#106—21no—
601#106—21no—
602#106—21no—
603C4⋊C8—21no—
604C4⋊C8—21no—
605#103—21no—
606#103—21no—
607#103—21no—
608#103—21no—
609#103—21no—
610#103—21no—
611#102—21no—
612#102—21no—
613C22⋊C8C23×C5911yescharacteristic
614C22⋊C8C23×C5911yescharacteristic
615C22⋊C8C23×C5911yescharacteristic
616C22⋊C8C23×C5911yescharacteristic
617#97—21no—
618C4×C8—21no—
619#95—21no—
620#95—21no—
621#95—21no—
622#95—21no—
623#95C23×C5911yescharacteristic
624#95C23×C5911yescharacteristic
625C24C2×D4×C5911yescharacteristic
626C2×Q8—21no—
627C2×Q8—21no—
628C2×Q8—21no—
629C2×Q8C2×D4×C5911yescharacteristic
630C2×Q8C2×D4×C5911yescharacteristic
631C2×Q8C2×D4×C5911yescharacteristic
632C2×D4—21no—
633C2×D4—21no—
634C2×D4—21no—
635C2×D4C2×D4×C5911yescharacteristic
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4C2×D4×C5911yescharacteristic
646C22×C4C2×D4×C5911yescharacteristic
647C22×C4C2×D4×C5911yescharacteristic
648C22×C4C2×D4×C5911yescharacteristic
649C22×C4C2×D4×C5911yescharacteristic
650C22×C4C24×C5911yescharacteristic
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—21no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—21no—
673C4⋊C4—21no—
674C4⋊C4—21no—
675C4⋊C4—21no—
676C4⋊C4—21no—
677C4⋊C4—21no—
678C4⋊C4—21no—
679C4⋊C4—21no—
680C4⋊C4—21no—
681C4⋊C4—21no—
682C4⋊C4—21no—
683C4⋊C4—21no—
684C4⋊C4—21no—
685C4⋊C4—21no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—42no—
689C4⋊C4—42no—
690C4⋊C4—41no—
691C4⋊C4—41no—
692C4⋊C4—41no—
693C4⋊C4—41no—
694C4⋊C4—81no—
695C4⋊C4C2×D4×C5911yescharacteristic
696C4⋊C4C2×D4×C5911yescharacteristic
697C4⋊C4C2×D4×C5911yescharacteristic
698C4⋊C4C2×D4×C5911yescharacteristic
699C22⋊C4—21no—
700C22⋊C4—21no—
701C22⋊C4—21no—
702C22⋊C4—21no—
703C22⋊C4—21no—
704C22⋊C4—21no—
705C22⋊C4—21no—
706C22⋊C4—21no—
707C22⋊C4—21no—
708C22⋊C4—21no—
709C22⋊C4—21no—
710C22⋊C4—21no—
711C22⋊C4—21no—
712C22⋊C4—21no—
713C22⋊C4—21no—
714C22⋊C4—21no—
715C22⋊C4—21no—
716C22⋊C4—21no—
717C22⋊C4—21no—
718C22⋊C4—21no—
719C22⋊C4—21no—
720C22⋊C4—42no—
721C22⋊C4—81no—
722C42—21no—
723C42—21no—
724C42—21no—
725C42—21no—
726C42—21no—
727C42—21no—
728C42—21no—
729C42—81no—
730C42C2×D4×C5911yescharacteristic
731C42C2×D4×C5911yescharacteristic
732C42C2×D4×C5911yescharacteristic
733C42C2×D4×C5911yescharacteristic
734C23—21no—
735C23—21no—
736C23—21no—
737C23—21no—
738C23—41no—
739C23—41no—
740C23C22×D4×C5911yescharacteristic
741Q8—41no—
742Q8—41no—
743Q8—41no—
744Q8—81no—
745Q8—81no—
746Q8—81no—
747D4—41no—
748D4—41no—
749D4—41no—
750D4—81no—
751D4—81no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—22no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—81no—
783C2×C4—81no—
784C2×C4—81no—
785C2×C4—81no—
786C2×C4—81no—
787C2×C4#120×C5911yescharacteristic
788C2×C4#120×C5911yescharacteristic
789C2×C4#120×C5911yescharacteristic
790C2×C4#120×C5911yescharacteristic
791C2×C4C22×D4×C5911yescharacteristic
792C2×C4C22×D4×C5911yescharacteristic
793C8—41no—
794C8—41no—
795C8—41no—
796C8—41no—
797C22—21no—
798C22—21no—
799C22—41no—
800C22—41no—
801C22—41no—
802C22—41no—
803C22—41no—
804C22—41no—
805C22—81no—
806C22—81no—
807C22C2×#120×C5911yescharacteristic
808C22C59×#57711yescharacteristic
809C22C59×#57811yescharacteristic
810C4—21no—
811C4—21no—
812C4—21no—
813C4—21no—
814C4—21no—
815C4—21no—
816C4—42no—
817C4—41no—
818C4—41no—
819C4—41no—
820C4—41no—
821C4—41no—
822C4—41no—
823C4—41no—
824C4—41no—
825C4—41no—
826C4—41no—
827C4—81no—
828C4—81no—
829C4—81no—
830C2—21no—
831C2—21no—
832C2—81no—
833C2—81no—
834C2C59×#301311yescharacteristic
835C2C59×#301811yescharacteristic
836C2C59×#302811yescharacteristic
subgroupG/H
center, socleC22×C59C2×#120
commutator, Frattini, cosocleC22×C4C24×C59
prime radicalC59×#538C22
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C59 ◁ C2×C42×C59 ◁ G

Complements

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

NH ≅ G/Ntype
2. C59×#3236C2semidirect
3. C59×#3232C2semidirect
4. C59×#2664C2semidirect
6. C59×#1617C2semidirect
7. C59×#1615C2semidirect
8. C59×#1614C2semidirect
10. C59×#1611C2semidirect
11. C59×#1609C2semidirect
12. C59×#1608C2semidirect
13. C59×#1509C2semidirect
14. C59×#1503C2semidirect
15. C59×#1473C2semidirect
378. #18445C59direct (N × H)
413. #3236C2×C59semidirect
414. #3232C2×C59semidirect
415. #2664C2×C59semidirect
417. #1617C2×C59semidirect
418. #1615C2×C59semidirect
419. #1614C2×C59semidirect
421. #1611C2×C59semidirect
422. #1609C2×C59semidirect
423. #1608C2×C59semidirect
424. #1509C2×C59semidirect
425. #1503C2×C59semidirect
426. #1473C2×C59semidirect
493. C59#18445direct (N × H)

Maximal subgroups

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

subgroupindex
C59×#35642
C59×#32362
C59×#32322
C59×#26642
C59×#16182
C59×#16172
C59×#16152
C59×#16142
C59×#16122
C59×#16112
C59×#16092
C59×#16082
C59×#15092
C59×#15032
C59×#14732
#1844559