Finite Group Databasebeta

← C59×#18414 #28430523

Subgroups — C59×#18414 #28430523

Order 15104.

1042 conjugacy classes of subgroups.

The subgroup lattice has 1010 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C59×#3534C211yesmaximal, characteristic, complemented
2C59×#3194C211yesmaximal, characteristic, complemented
3C59×#3186C211yesmaximal, characteristic, complemented
4C59×#2661C211yesmaximal, characteristic, complemented
5C59×#1612C211yesmaximal, characteristic, complemented
6C59×#1610C211yesmaximal, characteristic, complemented
7C59×#1609C211yesmaximal, characteristic, complemented
8C59×#1607C211yesmaximal, characteristic, complemented
9C59×#1600C211yesmaximal, characteristic, complemented
10C59×#1598C211yesmaximal, characteristic, complemented
11C59×#1597C211yesmaximal, characteristic, complemented
12C59×#1595C211yesmaximal, 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×#121×C59C2211yescharacteristic
35C2×#121×C59C2211yescharacteristic, complemented
36C59×#483C2211yescharacteristic, complemented
37C59×#482—21no—
38C59×#480—21no—
39C59×#480C2211yescharacteristic
40C59×#480C2211yescharacteristic, complemented
41C59×#480C2211yescharacteristic, complemented
42C59×#469—21no—
43C59×#468—21no—
44C59×#466—21no—
45C59×#466—21no—
46C59×#450C2211yescharacteristic, complemented
47C59×#449—21no—
48C59×#447—21no—
49C59×#447C2211yescharacteristic
50C59×#447C2211yescharacteristic, complemented
51C59×#447C2211yescharacteristic, complemented
52C59×#407C2211yescharacteristic, complemented
53C2×C22⋊C8×C59C2211yescharacteristic, complemented
54C59×#398C2211yescharacteristic, complemented
55C59×#397C2211yescharacteristic, complemented
56C59×#394—21no—
57C59×#394C2211yescharacteristic, complemented
58C59×#392—21no—
59C59×#392C2211yescharacteristic, complemented
60C59×#390—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, complemented
77C22×D4×C59—21no—
78C22×D4×C59—21no—
79C22×D4×C59—21no—
80C22×D4×C59—21no—
81C22×D4×C59—21no—
82C22×D4×C59D411yescharacteristic
83C22×D4×C59D411yescharacteristic, complemented
84C22×D4×C59C2311yescharacteristic
85C23×C4×C59C2311yescharacteristic
86C2×SD16×C59—21no—
87C2×D8×C59—21no—
88C2×D8×C59—21no—
89C2×D8×C59—21no—
90C2×M16×C59—21no—
91C22×C8×C59—21no—
92#127×C59—21no—
93#126×C59—21no—
94#126×C59—21no—
95#126×C59—21no—
96#126×C59—21no—
97#125×C59—21no—
98#125×C59—21no—
99#124×C59—21no—
100#124×C59—21no—
101#124×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—
114#123×C59—21no—
115#123×C59—21no—
116C22⋊Q8×C59—21no—
117C22⋊Q8×C59—21no—
118C22⋊Q8×C59—21no—
119C22⋊Q8×C59—21no—
120C22⋊Q8×C59—21no—
121C22⋊Q8×C59D411yescharacteristic, complemented
122C22⋊Q8×C59C2311yescharacteristic
123#121×C59—21no—
124#121×C59—21no—
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×C59—21no—
141#121×C59—21no—
142#121×C59D411yescharacteristic, complemented
143#121×C59D411yescharacteristic, complemented
144#121×C59D411yescharacteristic, complemented
145#121×C59C2311yescharacteristic
146#121×C59C2311yescharacteristic
147#121×C59C2311yescharacteristic
148#120×C59—21no—
149#120×C59—21no—
150#120×C59—21no—
151#120×C59—21no—
152#120×C59—21no—
153#120×C59—21no—
154#120×C59—21no—
155#120×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—
162C4×D4×C59—21no—
163C4×D4×C59—21no—
164#117×C59—21no—
165#117×C59D411yescharacteristic, complemented
166C2×C4⋊C4×C59—21no—
167C2×C4⋊C4×C59D411yescharacteristic
168C2×C4⋊C4×C59D411yescharacteristic, complemented
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×C59—21no—
179C2×C22⋊C4×C59—21no—
180C2×C22⋊C4×C59D411yescharacteristic
181C2×C22⋊C4×C59D411yescharacteristic
182C2×C22⋊C4×C59C2311yescharacteristic
183C2×C42×C59—21no—
184#107×C59—21no—
185#107×C59—21no—
186#107×C59—21no—
187#106×C59—21no—
188#103×C59—21no—
189#102×C59—21no—
190#102×C59—21no—
191#102×C59—21no—
192#102×C59—21no—
193#102×C59—21no—
194#102×C59—21no—
195#102×C59—21no—
196C22⋊C8×C59—21no—
197C22⋊C8×C59—21no—
198C22⋊C8×C59C2311yescharacteristic
199C22⋊C8×C59C2311yescharacteristic
200C22⋊C8×C59C2311yescharacteristic
201C22⋊C8×C59C2311yescharacteristic
202#95×C59—21no—
203#95×C59—21no—
204#95×C59C2311yescharacteristic
205#95×C59C2311yescharacteristic
206C24×C59—21no—
207C24×C59—21no—
208C24×C59—21no—
209C24×C59C2×D411yescharacteristic
210C24×C59C2×D411yescharacteristic
211#41×C59—81no—
212#41×C59—81no—
213#41×C59—81no—
214C2×Q8×C59—21no—
215C2×Q8×C59C2×D411yescharacteristic
216C2×D4×C59—21no—
217C2×D4×C59—21no—
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—42no—
236C2×D4×C59—41no—
237C2×D4×C59—41no—
238C2×D4×C59—81no—
239C2×D4×C59—81no—
240C2×D4×C59—81no—
241C2×D4×C59—81no—
242C2×D4×C59—81no—
243C2×D4×C59—81no—
244C2×D4×C59—81no—
245C2×D4×C59—81no—
246C2×D4×C59—81no—
247C2×D4×C59—81no—
248C2×D4×C59—81no—
249C2×D4×C59—82no—
250C2×D4×C59C2×D411yescharacteristic
251C2×D4×C59C2×D411yescharacteristic
252C2×D4×C59C2×D411yescharacteristic
253C22×C4×C59—21no—
254C22×C4×C59—21no—
255C22×C4×C59—21no—
256C22×C4×C59—21no—
257C22×C4×C59—21no—
258C22×C4×C59—21no—
259C22×C4×C59—21no—
260C22×C4×C59—21no—
261C22×C4×C59—21no—
262C22×C4×C59—21no—
263C22×C4×C59—81no—
264C22×C4×C59C2×D411yescharacteristic
265C22×C4×C59C2×D411yescharacteristic
266C22×C4×C59C2×D411yescharacteristic
267C22×C4×C59C2×D411yescharacteristic
268C22×C4×C59C2×D411yescharacteristic
269C22×C4×C59C2×D411yescharacteristic
270C22×C4×C59C2×D411yescharacteristic
271C22×C4×C59C2×D411yescharacteristic
272C22×C4×C59C2411yescharacteristic
273SD16×C59—81no—
274D8×C59—81no—
275D8×C59—81no—
276D8×C59—81no—
277M16×C59—81no—
278C2×C8×C59—21no—
279C2×C8×C59—21no—
280C2×C8×C59—21no—
281C2×C8×C59—21no—
282C2×C8×C59—81no—
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—21no—
292C4⋊C4×C59—21no—
293C4⋊C4×C59—21no—
294C4⋊C4×C59—21no—
295C4⋊C4×C59—21no—
296C4⋊C4×C59—21no—
297C4⋊C4×C59—21no—
298C4⋊C4×C59—81no—
299C4⋊C4×C59C2×D411yescharacteristic
300C4⋊C4×C59C2×D411yescharacteristic
301C4⋊C4×C59C2×D411yescharacteristic
302C4⋊C4×C59C2×D411yescharacteristic
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—21no—
325C22⋊C4×C59—21no—
326C22⋊C4×C59—21no—
327C22⋊C4×C59—21no—
328C22⋊C4×C59—42no—
329C22⋊C4×C59—42no—
330C22⋊C4×C59—41no—
331C22⋊C4×C59—41no—
332C22⋊C4×C59—81no—
333C22⋊C4×C59—81no—
334C22⋊C4×C59—81no—
335C42×C59—21no—
336C42×C59—21no—
337C42×C59—21no—
338C42×C59—81no—
339C23×C59—21no—
340C23×C59—21no—
341C23×C59—21no—
342C23×C59—21no—
343C23×C59—21no—
344C23×C59—21no—
345C23×C59—21no—
346C23×C59—21no—
347C23×C59—41no—
348C23×C59—41no—
349C23×C59—42no—
350C23×C59—41no—
351C23×C59—41no—
352C23×C59—41no—
353C23×C59—41no—
354C23×C59—41no—
355C23×C59—41no—
356C23×C59—41no—
357C23×C59—41no—
358C23×C59—41no—
359C23×C59—81no—
360C23×C59—81no—
361C23×C59—81no—
362C23×C59—81no—
363C23×C59—81no—
364C23×C59#12011yescharacteristic
365C23×C59#12011yescharacteristic
366C23×C59C22×D411yescharacteristic
367Q8×C59—41no—
368Q8×C59—81no—
369D4×C59—41no—
370D4×C59—41no—
371D4×C59—41no—
372D4×C59—41no—
373D4×C59—41no—
374D4×C59—41no—
375D4×C59—41no—
376D4×C59—42no—
377D4×C59—42no—
378D4×C59—41no—
379D4×C59—41no—
380D4×C59—41no—
381D4×C59—41no—
382D4×C59—41no—
383D4×C59—41no—
384D4×C59—81no—
385D4×C59—81no—
386D4×C59—81no—
387D4×C59—81no—
388D4×C59—81no—
389D4×C59—81no—
390D4×C59—81no—
391D4×C59—81no—
392D4×C59—81no—
393D4×C59—81no—
394D4×C59—81no—
395D4×C59—81no—
396D4×C59—84no—
397D4×C59—82no—
398D4×C59—82no—
399C2×C4×C59—22no—
400C2×C4×C59—21no—
401C2×C4×C59—21no—
402C2×C4×C59—21no—
403C2×C4×C59—21no—
404C2×C4×C59—21no—
405C2×C4×C59—21no—
406C2×C4×C59—21no—
407C2×C4×C59—21no—
408C2×C4×C59—21no—
409C2×C4×C59—21no—
410C2×C4×C59—41no—
411C2×C4×C59—41no—
412C2×C4×C59—41no—
413C2×C4×C59—41no—
414C2×C4×C59—41no—
415C2×C4×C59—41no—
416C2×C4×C59—41no—
417C2×C4×C59—41no—
418C2×C4×C59—41no—
419C2×C4×C59—41no—
420C2×C4×C59—41no—
421C2×C4×C59—41no—
422C2×C4×C59—41no—
423C2×C4×C59—41no—
424C2×C4×C59—41no—
425C2×C4×C59—41no—
426C2×C4×C59—81no—
427C2×C4×C59—81no—
428C2×C4×C59—81no—
429C2×C4×C59—81no—
430C2×C4×C59—81no—
431C2×C4×C59—81no—
432C2×C4×C59—81no—
433C2×C4×C59#12011yescharacteristic
434C2×C4×C59#12011yescharacteristic
435C2×C4×C59C22×D411yescharacteristic
436C2×C4×C59C22×D411yescharacteristic
437C8×C59—41no—
438C8×C59—41no—
439C8×C59—41no—
440C8×C59—41no—
441#18414C5911yesmaximal, characteristic, direct product factor, Sylow
442C22×C59—21no—
443C22×C59—21no—
444C22×C59—21no—
445C22×C59—21no—
446C22×C59—21no—
447C22×C59—21no—
448C22×C59—21no—
449C22×C59—21no—
450C22×C59—41no—
451C22×C59—41no—
452C22×C59—41no—
453C22×C59—41no—
454C22×C59—41no—
455C22×C59—41no—
456C22×C59—41no—
457C22×C59—41no—
458C22×C59—41no—
459C22×C59—41no—
460C22×C59—41no—
461C22×C59—41no—
462C22×C59—81no—
463C22×C59—81no—
464C22×C59—81no—
465C22×C59—81no—
466C22×C59—81no—
467C22×C59—81no—
468C22×C59—81no—
469C22×C59—81no—
470C22×C59—81no—
471C22×C59—81no—
472C22×C59—81no—
473C22×C59—162no—
474C22×C59—162no—
475C22×C59C2×#12011yescharacteristic
476C22×C59#57611yescharacteristic
477C22×C59#57611yescharacteristic
478C4×C59—21no—
479C4×C59—21no—
480C4×C59—21no—
481C4×C59—21no—
482C4×C59—42no—
483C4×C59—41no—
484C4×C59—41no—
485C4×C59—41no—
486C4×C59—41no—
487C4×C59—41no—
488C4×C59—41no—
489C4×C59—41no—
490C4×C59—41no—
491C4×C59—81no—
492C4×C59—81no—
493#3534C2×C5911yescharacteristic, complemented
494#3194C2×C5911yescharacteristic, complemented
495#3186C2×C5911yescharacteristic, complemented
496#2661C2×C5911yescharacteristic, complemented
497#1612C2×C5911yescharacteristic, complemented
498#1610C2×C5911yescharacteristic, complemented
499#1609C2×C5911yescharacteristic, complemented
500#1607C2×C5911yescharacteristic, complemented
501#1600C2×C5911yescharacteristic, complemented
502#1598C2×C5911yescharacteristic, complemented
503#1597C2×C5911yescharacteristic, complemented
504#1595C2×C5911yescharacteristic, complemented
505#1507C2×C5911yescharacteristic, complemented
506#1501C2×C5911yescharacteristic, complemented
507#1468C2×C5911yescharacteristic, complemented
508C2×C59—21no—
509C2×C59—21no—
510C2×C59—41no—
511C2×C59—41no—
512C2×C59—81no—
513C2×C59—81no—
514C2×C59—81no—
515C2×C59—81no—
516C2×C59—161no—
517C2×C59#300811yescharacteristic
518C2×C59#301811yescharacteristic
519C2×C59#302611yescharacteristic
520#562—21no—
521#560—21no—
522#553—21no—
523#551—21no—
524#546—21no—
525#546—21no—
526#546—21no—
527D42—21no—
528#540—21no—
529#539—21no—
530#539C22×C5911yescharacteristic
531#538—21no—
532#538C22×C5911yescharacteristic
533#537C22×C5911yescharacteristic
534#534—21no—
535#534C22×C5911yescharacteristic
536#525C22×C5911yescharacteristic
537C2×#123C22×C5911yescharacteristic
538C2×#121C22×C5911yescharacteristic
539C2×#121C22×C5911yescharacteristic, complemented
540#483C22×C5911yescharacteristic, complemented
541#482—21no—
542#480—21no—
543#480C22×C5911yescharacteristic
544#480C22×C5911yescharacteristic, complemented
545#480C22×C5911yescharacteristic, complemented
546#469—21no—
547#468—21no—
548#466—21no—
549#466—21no—
550#450C22×C5911yescharacteristic, complemented
551#449—21no—
552#447—21no—
553#447C22×C5911yescharacteristic
554#447C22×C5911yescharacteristic, complemented
555#447C22×C5911yescharacteristic, complemented
556#407C22×C5911yescharacteristic, complemented
557C2×C22⋊C8C22×C5911yescharacteristic, complemented
558#398C22×C5911yescharacteristic, complemented
559#397C22×C5911yescharacteristic, complemented
560#394—21no—
561#394C22×C5911yescharacteristic, complemented
562#392—21no—
563#392C22×C5911yescharacteristic, complemented
564#390—21no—
565#388—21no—
566C4×C22⋊C4C22×C5911yescharacteristic, complemented
567#328C22×C5911yescharacteristic, complemented
568#328C22×C5911yescharacteristic, complemented
569#327C22×C5911yescharacteristic
570#327C22×C5911yescharacteristic
571#327C22×C5911yescharacteristic, complemented
572#327C22×C5911yescharacteristic, complemented
573#327C22×C5911yescharacteristic, complemented
574#327C22×C5911yescharacteristic, complemented
575#324C22×C5911yescharacteristic, complemented
576#324C22×C5911yescharacteristic, complemented
577#323C22×C5911yescharacteristic, complemented
578#323C22×C5911yescharacteristic, complemented
579C59#1841411yescharacteristic, direct product factor, Sylow
580C2×#41—21no—
581C2×#41D4×C5911yescharacteristic, complemented
582C22×D4—21no—
583C22×D4—21no—
584C22×D4—21no—
585C22×D4—21no—
586C22×D4—21no—
587C22×D4D4×C5911yescharacteristic
588C22×D4D4×C5911yescharacteristic, complemented
589C22×D4C23×C5911yescharacteristic
590C23×C4C23×C5911yescharacteristic
591C2×SD16—21no—
592C2×D8—21no—
593C2×D8—21no—
594C2×D8—21no—
595C2×M16—21no—
596C22×C8—21no—
597#127—21no—
598#126—21no—
599#126—21no—
600#126—21no—
601#126—21no—
602#125—21no—
603#125—21no—
604#124—21no—
605#124—21no—
606#124—21no—
607#123—21no—
608#123—21no—
609#123—21no—
610#123—21no—
611#123—21no—
612#123—21no—
613#123—21no—
614#123—21no—
615#123—21no—
616#123—21no—
617#123—21no—
618#123—21no—
619#123—21no—
620#123—21no—
621C22⋊Q8—21no—
622C22⋊Q8—21no—
623C22⋊Q8—21no—
624C22⋊Q8—21no—
625C22⋊Q8—21no—
626C22⋊Q8D4×C5911yescharacteristic, complemented
627C22⋊Q8C23×C5911yescharacteristic
628#121—21no—
629#121—21no—
630#121—21no—
631#121—21no—
632#121—21no—
633#121—21no—
634#121—21no—
635#121—21no—
636#121—21no—
637#121—21no—
638#121—21no—
639#121—21no—
640#121—21no—
641#121—21no—
642#121—21no—
643#121—21no—
644#121—21no—
645#121—21no—
646#121—21no—
647#121D4×C5911yescharacteristic, complemented
648#121D4×C5911yescharacteristic, complemented
649#121D4×C5911yescharacteristic, complemented
650#121C23×C5911yescharacteristic
651#121C23×C5911yescharacteristic
652#121C23×C5911yescharacteristic
653#120—21no—
654#120—21no—
655#120—21no—
656#120—21no—
657#120—21no—
658#120—21no—
659#120—21no—
660#120—21no—
661C4×D4—21no—
662C4×D4—21no—
663C4×D4—21no—
664C4×D4—21no—
665C4×D4—21no—
666C4×D4—21no—
667C4×D4—21no—
668C4×D4—21no—
669#117—21no—
670#117D4×C5911yescharacteristic, complemented
671C2×C4⋊C4—21no—
672C2×C4⋊C4D4×C5911yescharacteristic
673C2×C4⋊C4D4×C5911yescharacteristic, complemented
674C2×C4⋊C4C23×C5911yescharacteristic
675C2×C4⋊C4C23×C5911yescharacteristic
676C2×C22⋊C4—21no—
677C2×C22⋊C4—21no—
678C2×C22⋊C4—21no—
679C2×C22⋊C4—21no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4D4×C5911yescharacteristic
686C2×C22⋊C4D4×C5911yescharacteristic
687C2×C22⋊C4C23×C5911yescharacteristic
688C2×C42—21no—
689#107—21no—
690#107—21no—
691#107—21no—
692#106—21no—
693#103—21no—
694#102—21no—
695#102—21no—
696#102—21no—
697#102—21no—
698#102—21no—
699#102—21no—
700#102—21no—
701C22⋊C8—21no—
702C22⋊C8—21no—
703C22⋊C8C23×C5911yescharacteristic
704C22⋊C8C23×C5911yescharacteristic
705C22⋊C8C23×C5911yescharacteristic
706C22⋊C8C23×C5911yescharacteristic
707#95—21no—
708#95—21no—
709#95C23×C5911yescharacteristic
710#95C23×C5911yescharacteristic
711C24—21no—
712C24—21no—
713C24—21no—
714C24C2×D4×C5911yescharacteristic
715C24C2×D4×C5911yescharacteristic
716#41—81no—
717#41—81no—
718#41—81no—
719C2×Q8—21no—
720C2×Q8C2×D4×C5911yescharacteristic
721C2×D4—21no—
722C2×D4—21no—
723C2×D4—21no—
724C2×D4—21no—
725C2×D4—21no—
726C2×D4—21no—
727C2×D4—21no—
728C2×D4—21no—
729C2×D4—21no—
730C2×D4—21no—
731C2×D4—21no—
732C2×D4—21no—
733C2×D4—21no—
734C2×D4—21no—
735C2×D4—21no—
736C2×D4—21no—
737C2×D4—21no—
738C2×D4—21no—
739C2×D4—21no—
740C2×D4—42no—
741C2×D4—41no—
742C2×D4—41no—
743C2×D4—81no—
744C2×D4—81no—
745C2×D4—81no—
746C2×D4—81no—
747C2×D4—81no—
748C2×D4—81no—
749C2×D4—81no—
750C2×D4—81no—
751C2×D4—81no—
752C2×D4—81no—
753C2×D4—81no—
754C2×D4—82no—
755C2×D4C2×D4×C5911yescharacteristic
756C2×D4C2×D4×C5911yescharacteristic
757C2×D4C2×D4×C5911yescharacteristic
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—81no—
769C22×C4C2×D4×C5911yescharacteristic
770C22×C4C2×D4×C5911yescharacteristic
771C22×C4C2×D4×C5911yescharacteristic
772C22×C4C2×D4×C5911yescharacteristic
773C22×C4C2×D4×C5911yescharacteristic
774C22×C4C2×D4×C5911yescharacteristic
775C22×C4C2×D4×C5911yescharacteristic
776C22×C4C2×D4×C5911yescharacteristic
777C22×C4C24×C5911yescharacteristic
778SD16—81no—
779D8—81no—
780D8—81no—
781D8—81no—
782M16—81no—
783C2×C8—21no—
784C2×C8—21no—
785C2×C8—21no—
786C2×C8—21no—
787C2×C8—81no—
788C4⋊C4—21no—
789C4⋊C4—21no—
790C4⋊C4—21no—
791C4⋊C4—21no—
792C4⋊C4—21no—
793C4⋊C4—21no—
794C4⋊C4—21no—
795C4⋊C4—21no—
796C4⋊C4—21no—
797C4⋊C4—21no—
798C4⋊C4—21no—
799C4⋊C4—21no—
800C4⋊C4—21no—
801C4⋊C4—21no—
802C4⋊C4—21no—
803C4⋊C4—81no—
804C4⋊C4C2×D4×C5911yescharacteristic
805C4⋊C4C2×D4×C5911yescharacteristic
806C4⋊C4C2×D4×C5911yescharacteristic
807C4⋊C4C2×D4×C5911yescharacteristic
808C22⋊C4—21no—
809C22⋊C4—21no—
810C22⋊C4—21no—
811C22⋊C4—21no—
812C22⋊C4—21no—
813C22⋊C4—21no—
814C22⋊C4—21no—
815C22⋊C4—21no—
816C22⋊C4—21no—
817C22⋊C4—21no—
818C22⋊C4—21no—
819C22⋊C4—21no—
820C22⋊C4—21no—
821C22⋊C4—21no—
822C22⋊C4—21no—
823C22⋊C4—21no—
824C22⋊C4—21no—
825C22⋊C4—21no—
826C22⋊C4—21no—
827C22⋊C4—21no—
828C22⋊C4—21no—
829C22⋊C4—21no—
830C22⋊C4—21no—
831C22⋊C4—21no—
832C22⋊C4—21no—
833C22⋊C4—42no—
834C22⋊C4—42no—
835C22⋊C4—41no—
836C22⋊C4—41no—
837C22⋊C4—81no—
838C22⋊C4—81no—
839C22⋊C4—81no—
840C42—21no—
841C42—21no—
842C42—21no—
843C42—81no—
844C23—21no—
845C23—21no—
846C23—21no—
847C23—21no—
848C23—21no—
849C23—21no—
850C23—21no—
851C23—21no—
852C23—41no—
853C23—41no—
854C23—42no—
855C23—41no—
856C23—41no—
857C23—41no—
858C23—41no—
859C23—41no—
860C23—41no—
861C23—41no—
862C23—41no—
863C23—41no—
864C23—81no—
865C23—81no—
866C23—81no—
867C23—81no—
868C23—81no—
869C23#120×C5911yescharacteristic
870C23#120×C5911yescharacteristic
871C23C22×D4×C5911yescharacteristic
872Q8—41no—
873Q8—81no—
874D4—41no—
875D4—41no—
876D4—41no—
877D4—41no—
878D4—41no—
879D4—41no—
880D4—41no—
881D4—42no—
882D4—42no—
883D4—41no—
884D4—41no—
885D4—41no—
886D4—41no—
887D4—41no—
888D4—41no—
889D4—81no—
890D4—81no—
891D4—81no—
892D4—81no—
893D4—81no—
894D4—81no—
895D4—81no—
896D4—81no—
897D4—81no—
898D4—81no—
899D4—81no—
900D4—81no—
901D4—84no—
902D4—82no—
903D4—82no—
904C2×C4—22no—
905C2×C4—21no—
906C2×C4—21no—
907C2×C4—21no—
908C2×C4—21no—
909C2×C4—21no—
910C2×C4—21no—
911C2×C4—21no—
912C2×C4—21no—
913C2×C4—21no—
914C2×C4—21no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—81no—
932C2×C4—81no—
933C2×C4—81no—
934C2×C4—81no—
935C2×C4—81no—
936C2×C4—81no—
937C2×C4—81no—
938C2×C4#120×C5911yescharacteristic
939C2×C4#120×C5911yescharacteristic
940C2×C4C22×D4×C5911yescharacteristic
941C2×C4C22×D4×C5911yescharacteristic
942C8—41no—
943C8—41no—
944C8—41no—
945C8—41no—
946C22—21no—
947C22—21no—
948C22—21no—
949C22—21no—
950C22—21no—
951C22—21no—
952C22—21no—
953C22—21no—
954C22—41no—
955C22—41no—
956C22—41no—
957C22—41no—
958C22—41no—
959C22—41no—
960C22—41no—
961C22—41no—
962C22—41no—
963C22—41no—
964C22—41no—
965C22—41no—
966C22—81no—
967C22—81no—
968C22—81no—
969C22—81no—
970C22—81no—
971C22—81no—
972C22—81no—
973C22—81no—
974C22—81no—
975C22—81no—
976C22—81no—
977C22—162no—
978C22—162no—
979C22C2×#120×C5911yescharacteristic
980C22C59×#57611yescharacteristic
981C22C59×#57611yescharacteristic
982C4—21no—
983C4—21no—
984C4—21no—
985C4—21no—
986C4—42no—
987C4—41no—
988C4—41no—
989C4—41no—
990C4—41no—
991C4—41no—
992C4—41no—
993C4—41no—
994C4—41no—
995C4—81no—
996C4—81no—
997C2—21no—
998C2—21no—
999C2—41no—
1000C2—41no—
1001C2—81no—
1002C2—81no—
1003C2—81no—
1004C2—81no—
1005C2—161no—
1006C2C59×#300811yescharacteristic
1007C2C59×#301811yescharacteristic
1008C2C59×#302611yescharacteristic
subgroupG/H
center, socleC22×C59C2×#120
commutator, Frattini, cosocleC22×C4C24×C59
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
1. C59×#3534C2semidirect
2. C59×#3194C2semidirect
3. C59×#3186C2semidirect
4. C59×#2661C2semidirect
5. C59×#1612C2semidirect
6. C59×#1610C2semidirect
7. C59×#1609C2semidirect
8. C59×#1607C2semidirect
9. C59×#1600C2semidirect
10. C59×#1598C2semidirect
11. C59×#1597C2semidirect
12. C59×#1595C2semidirect
13. C59×#1507C2semidirect
14. C59×#1501C2semidirect
15. C59×#1468C2semidirect
35. C2×#121×C59C22semidirect
36. C59×#483C22semidirect
40. C59×#480C22semidirect
41. C59×#480C22semidirect
46. C59×#450C22semidirect
50. C59×#447C22semidirect
51. C59×#447C22semidirect
52. C59×#407C22semidirect
53. C2×C22⋊C8×C59C22semidirect
54. C59×#398C22semidirect
55. C59×#397C22semidirect
57. C59×#394C22semidirect
59. C59×#392C22semidirect
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
76. C2×#41×C59D4semidirect
83. C22×D4×C59D4semidirect
121. C22⋊Q8×C59D4semidirect
142. #121×C59D4semidirect
143. #121×C59D4semidirect
144. #121×C59D4semidirect
165. #117×C59D4semidirect
168. C2×C4⋊C4×C59D4semidirect
441. #18414C59direct (N × H)
493. #3534C2×C59semidirect
494. #3194C2×C59semidirect
495. #3186C2×C59semidirect
496. #2661C2×C59semidirect
497. #1612C2×C59semidirect
498. #1610C2×C59semidirect
499. #1609C2×C59semidirect
500. #1607C2×C59semidirect
501. #1600C2×C59semidirect
502. #1598C2×C59semidirect
503. #1597C2×C59semidirect
504. #1595C2×C59semidirect
505. #1507C2×C59semidirect
506. #1501C2×C59semidirect
507. #1468C2×C59semidirect
539. C2×#121C22×C59semidirect
540. #483C22×C59semidirect
544. #480C22×C59semidirect
545. #480C22×C59semidirect
550. #450C22×C59semidirect
554. #447C22×C59semidirect
555. #447C22×C59semidirect
556. #407C22×C59semidirect
557. C2×C22⋊C8C22×C59semidirect
558. #398C22×C59semidirect
559. #397C22×C59semidirect
561. #394C22×C59semidirect
563. #392C22×C59semidirect
566. C4×C22⋊C4C22×C59semidirect
567. #328C22×C59semidirect
568. #328C22×C59semidirect
571. #327C22×C59semidirect
572. #327C22×C59semidirect
573. #327C22×C59semidirect
574. #327C22×C59semidirect
575. #324C22×C59semidirect
576. #324C22×C59semidirect
577. #323C22×C59semidirect
578. #323C22×C59semidirect
579. C59#18414direct (N × H)
581. C2×#41D4×C59semidirect
588. C22×D4D4×C59semidirect
626. C22⋊Q8D4×C59semidirect
647. #121D4×C59semidirect
648. #121D4×C59semidirect
649. #121D4×C59semidirect
670. #117D4×C59semidirect
673. C2×C4⋊C4D4×C59semidirect

Maximal subgroups

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

subgroupindex
C59×#35342
C59×#31942
C59×#31862
C59×#26612
C59×#16122
C59×#16102
C59×#16092
C59×#16072
C59×#16002
C59×#15982
C59×#15972
C59×#15952
C59×#15072
C59×#15012
C59×#14682
#1841459