Finite Group Databasebeta

← C59×#18262 #28430371

Subgroups — C59×#18262 #28430371

Order 15104.

1012 conjugacy classes of subgroups.

The subgroup lattice has 956 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C59×#3534C211yesmaximal, characteristic
2C59×#3094C211yesmaximal, characteristic, complemented
3C59×#3091C211yesmaximal, characteristic, complemented
4C59×#2498C211yesmaximal, characteristic, complemented
5C59×#1618C211yesmaximal, characteristic, complemented
6C59×#1616C211yesmaximal, characteristic, complemented
7C59×#1615C211yesmaximal, characteristic, complemented
8C59×#1613C211yesmaximal, characteristic, complemented
9C59×#1612C211yesmaximal, characteristic, complemented
10C59×#1610C211yesmaximal, characteristic, complemented
11C59×#1609C211yesmaximal, characteristic, complemented
12C59×#1607C211yesmaximal, characteristic, complemented
13C59×#1504C211yesmaximal, characteristic, complemented
14C2×C59×#327C211yesmaximal, 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×#117×C59C2211yescharacteristic, complemented
36C59×#485—21no—
37C59×#484C2211yescharacteristic, complemented
38C59×#483C2211yescharacteristic, complemented
39C59×#482—21no—
40C59×#482—21no—
41C59×#482—21no—
42C59×#481C2211yescharacteristic
43C59×#481C2211yescharacteristic, complemented
44C59×#481C2211yescharacteristic, complemented
45C59×#480C2211yescharacteristic
46C59×#480C2211yescharacteristic, complemented
47C59×#480C2211yescharacteristic, complemented
48C59×#428—21no—
49C59×#427—21no—
50C59×#418—21no—
51C59×#416—21no—
52C59×#407C2211yescharacteristic, complemented
53C2×C22⋊C8×C59C2211yescharacteristic, complemented
54C59×#400C2211yescharacteristic, complemented
55C59×#399C2211yescharacteristic, complemented
56C59×#398C2211yescharacteristic, complemented
57C59×#397C2211yescharacteristic, complemented
58C59×#388—21no—
59C59×#387—21no—
60C59×#386—21no—
61C59×#380—21no—
62C2×#95×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×D4×C59—21no—
78C22×D4×C59—21no—
79C22×D4×C59—21no—
80C22×D4×C59D411yescharacteristic
81C22×D4×C59D411yescharacteristic
82C23×C4×C59—21no—
83C23×C4×C59C2311yescharacteristic
84C2×M16×C59—21no—
85C22×C8×C59—21no—
86#127×C59—21no—
87#126×C59—21no—
88#126×C59—21no—
89#126×C59—21no—
90#126×C59—21no—
91#125×C59—21no—
92#125×C59—21no—
93#124×C59—21no—
94#124×C59—21no—
95#124×C59—21no—
96#123×C59—21no—
97#123×C59—21no—
98#123×C59—21no—
99#123×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—
110C22⋊Q8×C59—21no—
111C22⋊Q8×C59—21no—
112C22⋊Q8×C59—21no—
113C22⋊Q8×C59—21no—
114C22⋊Q8×C59—21no—
115C22⋊Q8×C59D411yescharacteristic
116C22⋊Q8×C59C2311yescharacteristic
117#121×C59—21no—
118#121×C59—21no—
119#121×C59—21no—
120#121×C59—21no—
121#121×C59—21no—
122#121×C59—21no—
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×C59D411yescharacteristic
133#121×C59D411yescharacteristic
134#121×C59D411yescharacteristic
135#121×C59C2311yescharacteristic
136#121×C59C2311yescharacteristic
137#121×C59C2311yescharacteristic
138#120×C59—21no—
139#120×C59—21no—
140#120×C59—21no—
141#120×C59—21no—
142#120×C59—21no—
143#120×C59—21no—
144#120×C59—21no—
145#120×C59—21no—
146C4×D4×C59—21no—
147C4×D4×C59—21no—
148C4×D4×C59—21no—
149C4×D4×C59—21no—
150C4×D4×C59—21no—
151C4×D4×C59—21no—
152C4×D4×C59—21no—
153C4×D4×C59—21no—
154#117×C59—21no—
155#117×C59—21no—
156#117×C59—21no—
157#117×C59—21no—
158#117×C59—21no—
159#117×C59D411yescharacteristic
160C2×C4⋊C4×C59—21no—
161C2×C4⋊C4×C59—21no—
162C2×C4⋊C4×C59D411yescharacteristic
163C2×C4⋊C4×C59D411yescharacteristic
164C2×C4⋊C4×C59C2311yescharacteristic
165C2×C4⋊C4×C59C2311yescharacteristic
166C2×C4⋊C4×C59C2311yescharacteristic
167C2×C22⋊C4×C59—21no—
168C2×C22⋊C4×C59—21no—
169C2×C22⋊C4×C59—21no—
170C2×C22⋊C4×C59—21no—
171C2×C22⋊C4×C59—21no—
172C2×C22⋊C4×C59—21no—
173C2×C22⋊C4×C59D411yescharacteristic
174C2×C22⋊C4×C59D411yescharacteristic
175C2×C22⋊C4×C59C2311yescharacteristic
176C2×C42×C59—21no—
177#107×C59—21no—
178#107×C59—21no—
179#107×C59—21no—
180#107×C59—21no—
181#106×C59—21no—
182#106×C59—21no—
183#106×C59—21no—
184#106×C59—21no—
185#103×C59—21no—
186#103×C59—21no—
187#102×C59—21no—
188#102×C59—21no—
189#102×C59—21no—
190#102×C59—21no—
191#102×C59—21no—
192#102×C59—21no—
193C22⋊C8×C59—21no—
194C22⋊C8×C59—21no—
195C22⋊C8×C59C2311yescharacteristic
196C22⋊C8×C59C2311yescharacteristic
197C22⋊C8×C59C2311yescharacteristic
198C22⋊C8×C59C2311yescharacteristic
199#95×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×C59—21no—
207C24×C59—21no—
208C24×C59C2×D411yescharacteristic
209C24×C59C2×D411yescharacteristic
210#41×C59—42no—
211#41×C59—81no—
212#41×C59—81no—
213C2×Q8×C59—21no—
214C2×Q8×C59C2×D411yescharacteristic
215C2×D4×C59—21no—
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—42no—
233C2×D4×C59—42no—
234C2×D4×C59—81no—
235C2×D4×C59—81no—
236C2×D4×C59—81no—
237C2×D4×C59—81no—
238C2×D4×C59—82no—
239C2×D4×C59C2×D411yescharacteristic
240C2×D4×C59C2×D411yescharacteristic
241C2×D4×C59C2×D411yescharacteristic
242C22×C4×C59—21no—
243C22×C4×C59—21no—
244C22×C4×C59—21no—
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—42no—
254C22×C4×C59—42no—
255C22×C4×C59—42no—
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
266M16×C59—42no—
267C2×C8×C59—21no—
268C2×C8×C59—21no—
269C2×C8×C59—21no—
270C2×C8×C59—21no—
271C2×C8×C59—42no—
272C4⋊C4×C59—21no—
273C4⋊C4×C59—21no—
274C4⋊C4×C59—21no—
275C4⋊C4×C59—21no—
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—42no—
290C4⋊C4×C59—81no—
291C4⋊C4×C59C2×D411yescharacteristic
292C4⋊C4×C59C2×D411yescharacteristic
293C4⋊C4×C59C2×D411yescharacteristic
294C4⋊C4×C59C2×D411yescharacteristic
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—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—42no—
321C22⋊C4×C59—41no—
322C22⋊C4×C59—41no—
323C22⋊C4×C59—81no—
324C42×C59—21no—
325C42×C59—21no—
326C42×C59—21no—
327C42×C59—41no—
328C42×C59—41no—
329C23×C59—21no—
330C23×C59—21no—
331C23×C59—22no—
332C23×C59—21no—
333C23×C59—21no—
334C23×C59—21no—
335C23×C59—21no—
336C23×C59—21no—
337C23×C59—21no—
338C23×C59—41no—
339C23×C59—41no—
340C23×C59—41no—
341C23×C59—42no—
342C23×C59—81no—
343C23×C59—81no—
344C23×C59—81no—
345C23×C59—81no—
346C23×C59—81no—
347C23×C59#12011yescharacteristic
348C23×C59#12011yescharacteristic
349C23×C59C22×D411yescharacteristic
350Q8×C59—41no—
351Q8×C59—81no—
352D4×C59—41no—
353D4×C59—41no—
354D4×C59—41no—
355D4×C59—41no—
356D4×C59—41no—
357D4×C59—41no—
358D4×C59—41no—
359D4×C59—41no—
360D4×C59—41no—
361D4×C59—42no—
362D4×C59—42no—
363D4×C59—81no—
364D4×C59—81no—
365D4×C59—81no—
366D4×C59—81no—
367D4×C59—81no—
368D4×C59—81no—
369D4×C59—81no—
370D4×C59—81no—
371D4×C59—81no—
372D4×C59—81no—
373D4×C59—81no—
374D4×C59—81no—
375C2×C4×C59—22no—
376C2×C4×C59—22no—
377C2×C4×C59—22no—
378C2×C4×C59—21no—
379C2×C4×C59—21no—
380C2×C4×C59—21no—
381C2×C4×C59—21no—
382C2×C4×C59—21no—
383C2×C4×C59—21no—
384C2×C4×C59—21no—
385C2×C4×C59—21no—
386C2×C4×C59—21no—
387C2×C4×C59—21no—
388C2×C4×C59—41no—
389C2×C4×C59—41no—
390C2×C4×C59—41no—
391C2×C4×C59—41no—
392C2×C4×C59—41no—
393C2×C4×C59—41no—
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—81no—
406C2×C4×C59—81no—
407C2×C4×C59—81no—
408C2×C4×C59—81no—
409C2×C4×C59—81no—
410C2×C4×C59—81no—
411C2×C4×C59—81no—
412C2×C4×C59—84no—
413C2×C4×C59#12011yescharacteristic
414C2×C4×C59#12011yescharacteristic
415C2×C4×C59C22×D411yescharacteristic
416C2×C4×C59C22×D411yescharacteristic
417C8×C59—41no—
418C8×C59—41no—
419C8×C59—41no—
420C8×C59—41no—
421#18262C5911yesmaximal, characteristic, direct product factor, Sylow
422C22×C59—21no—
423C22×C59—21no—
424C22×C59—21no—
425C22×C59—21no—
426C22×C59—21no—
427C22×C59—21no—
428C22×C59—21no—
429C22×C59—42no—
430C22×C59—42no—
431C22×C59—41no—
432C22×C59—41no—
433C22×C59—41no—
434C22×C59—41no—
435C22×C59—41no—
436C22×C59—41no—
437C22×C59—41no—
438C22×C59—41no—
439C22×C59—41no—
440C22×C59—41no—
441C22×C59—41no—
442C22×C59—41no—
443C22×C59—81no—
444C22×C59—81no—
445C22×C59—162no—
446C22×C59—162no—
447C22×C59#45812yes—
448C22×C59C2×#12011yescharacteristic
449C22×C59#57611yescharacteristic
450C22×C59#57711yescharacteristic
451C4×C59—21no—
452C4×C59—21no—
453C4×C59—21no—
454C4×C59—21no—
455C4×C59—42no—
456C4×C59—41no—
457C4×C59—41no—
458C4×C59—41no—
459C4×C59—41no—
460C4×C59—41no—
461C4×C59—41no—
462C4×C59—41no—
463C4×C59—41no—
464C4×C59—81no—
465C4×C59—81no—
466C4×C59—81no—
467#3534C2×C5911yescharacteristic
468#3094C2×C5911yescharacteristic, complemented
469#3091C2×C5911yescharacteristic, complemented
470#2498C2×C5911yescharacteristic, complemented
471#1618C2×C5911yescharacteristic, complemented
472#1616C2×C5911yescharacteristic, complemented
473#1615C2×C5911yescharacteristic, complemented
474#1613C2×C5911yescharacteristic, complemented
475#1612C2×C5911yescharacteristic, complemented
476#1610C2×C5911yescharacteristic, complemented
477#1609C2×C5911yescharacteristic, complemented
478#1607C2×C5911yescharacteristic, complemented
479#1504C2×C5911yescharacteristic, complemented
480C2×#327C2×C5911yescharacteristic, complemented
481#1468C2×C5911yescharacteristic, complemented
482C2×C59—21no—
483C2×C59—21no—
484C2×C59—22no—
485C2×C59—41no—
486C2×C59—81no—
487C2×C59—81no—
488C2×C59—81no—
489C2×C59—81no—
490C2×C59#301211yescharacteristic
491C2×C59#301811yescharacteristic
492C2×C59C2×#45811yescharacteristic
493#562—21no—
494#560—21no—
495#553—21no—
496#551—21no—
497#546—21no—
498#546—21no—
499#546—21no—
500D42—21no—
501#540—21no—
502#539—21no—
503#539C22×C5911yescharacteristic
504#538—21no—
505#538C22×C5911yescharacteristic
506#537C22×C5911yescharacteristic
507#534—21no—
508#534C22×C5911yescharacteristic
509#525C22×C5911yescharacteristic
510C2×#123C22×C5911yescharacteristic
511C2×#121C22×C5911yescharacteristic
512C2×#117C22×C5911yescharacteristic, complemented
513#485—21no—
514#484C22×C5911yescharacteristic, complemented
515#483C22×C5911yescharacteristic, complemented
516#482—21no—
517#482—21no—
518#482—21no—
519#481C22×C5911yescharacteristic
520#481C22×C5911yescharacteristic, complemented
521#481C22×C5911yescharacteristic, complemented
522#480C22×C5911yescharacteristic
523#480C22×C5911yescharacteristic, complemented
524#480C22×C5911yescharacteristic, complemented
525#428—21no—
526#427—21no—
527#418—21no—
528#416—21no—
529#407C22×C5911yescharacteristic, complemented
530C2×C22⋊C8C22×C5911yescharacteristic, complemented
531#400C22×C5911yescharacteristic, complemented
532#399C22×C5911yescharacteristic, complemented
533#398C22×C5911yescharacteristic, complemented
534#397C22×C5911yescharacteristic, complemented
535#388—21no—
536#387—21no—
537#386—21no—
538#380—21no—
539C2×#95C22×C5911yescharacteristic, complemented
540#328C22×C5911yescharacteristic, complemented
541#328C22×C5911yescharacteristic, complemented
542#327C22×C5911yescharacteristic
543#327C22×C5911yescharacteristic
544#327C22×C5911yescharacteristic, complemented
545#327C22×C5911yescharacteristic, complemented
546#327C22×C5911yescharacteristic, complemented
547#327C22×C5911yescharacteristic, complemented
548#324C22×C5911yescharacteristic, complemented
549#324C22×C5911yescharacteristic, complemented
550#323C22×C5911yescharacteristic, complemented
551#323C22×C5911yescharacteristic, complemented
552C59#1826211yescharacteristic, direct product factor, Sylow
553C2×#41—21no—
554C2×#41D4×C5911yescharacteristic
555C22×D4—21no—
556C22×D4—21no—
557C22×D4—21no—
558C22×D4D4×C5911yescharacteristic
559C22×D4D4×C5911yescharacteristic
560C23×C4—21no—
561C23×C4C23×C5911yescharacteristic
562C2×M16—21no—
563C22×C8—21no—
564#127—21no—
565#126—21no—
566#126—21no—
567#126—21no—
568#126—21no—
569#125—21no—
570#125—21no—
571#124—21no—
572#124—21no—
573#124—21no—
574#123—21no—
575#123—21no—
576#123—21no—
577#123—21no—
578#123—21no—
579#123—21no—
580#123—21no—
581#123—21no—
582#123—21no—
583#123—21no—
584#123—21no—
585#123—21no—
586#123—21no—
587#123—21no—
588C22⋊Q8—21no—
589C22⋊Q8—21no—
590C22⋊Q8—21no—
591C22⋊Q8—21no—
592C22⋊Q8—21no—
593C22⋊Q8D4×C5911yescharacteristic
594C22⋊Q8C23×C5911yescharacteristic
595#121—21no—
596#121—21no—
597#121—21no—
598#121—21no—
599#121—21no—
600#121—21no—
601#121—21no—
602#121—21no—
603#121—21no—
604#121—21no—
605#121—21no—
606#121—21no—
607#121—21no—
608#121—21no—
609#121—21no—
610#121D4×C5911yescharacteristic
611#121D4×C5911yescharacteristic
612#121D4×C5911yescharacteristic
613#121C23×C5911yescharacteristic
614#121C23×C5911yescharacteristic
615#121C23×C5911yescharacteristic
616#120—21no—
617#120—21no—
618#120—21no—
619#120—21no—
620#120—21no—
621#120—21no—
622#120—21no—
623#120—21no—
624C4×D4—21no—
625C4×D4—21no—
626C4×D4—21no—
627C4×D4—21no—
628C4×D4—21no—
629C4×D4—21no—
630C4×D4—21no—
631C4×D4—21no—
632#117—21no—
633#117—21no—
634#117—21no—
635#117—21no—
636#117—21no—
637#117D4×C5911yescharacteristic
638C2×C4⋊C4—21no—
639C2×C4⋊C4—21no—
640C2×C4⋊C4D4×C5911yescharacteristic
641C2×C4⋊C4D4×C5911yescharacteristic
642C2×C4⋊C4C23×C5911yescharacteristic
643C2×C4⋊C4C23×C5911yescharacteristic
644C2×C4⋊C4C23×C5911yescharacteristic
645C2×C22⋊C4—21no—
646C2×C22⋊C4—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4D4×C5911yescharacteristic
652C2×C22⋊C4D4×C5911yescharacteristic
653C2×C22⋊C4C23×C5911yescharacteristic
654C2×C42—21no—
655#107—21no—
656#107—21no—
657#107—21no—
658#107—21no—
659#106—21no—
660#106—21no—
661#106—21no—
662#106—21no—
663#103—21no—
664#103—21no—
665#102—21no—
666#102—21no—
667#102—21no—
668#102—21no—
669#102—21no—
670#102—21no—
671C22⋊C8—21no—
672C22⋊C8—21no—
673C22⋊C8C23×C5911yescharacteristic
674C22⋊C8C23×C5911yescharacteristic
675C22⋊C8C23×C5911yescharacteristic
676C22⋊C8C23×C5911yescharacteristic
677#95—21no—
678#95—21no—
679#95—21no—
680#95—21no—
681#95—21no—
682#95C23×C5911yescharacteristic
683#95C23×C5911yescharacteristic
684C24—21no—
685C24—21no—
686C24C2×D4×C5911yescharacteristic
687C24C2×D4×C5911yescharacteristic
688#41—42no—
689#41—81no—
690#41—81no—
691C2×Q8—21no—
692C2×Q8C2×D4×C5911yescharacteristic
693C2×D4—21no—
694C2×D4—21no—
695C2×D4—21no—
696C2×D4—21no—
697C2×D4—21no—
698C2×D4—21no—
699C2×D4—21no—
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—42no—
711C2×D4—42no—
712C2×D4—81no—
713C2×D4—81no—
714C2×D4—81no—
715C2×D4—81no—
716C2×D4—82no—
717C2×D4C2×D4×C5911yescharacteristic
718C2×D4C2×D4×C5911yescharacteristic
719C2×D4C2×D4×C5911yescharacteristic
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—42no—
732C22×C4—42no—
733C22×C4—42no—
734C22×C4—81no—
735C22×C4C2×D4×C5911yescharacteristic
736C22×C4C2×D4×C5911yescharacteristic
737C22×C4C2×D4×C5911yescharacteristic
738C22×C4C2×D4×C5911yescharacteristic
739C22×C4C2×D4×C5911yescharacteristic
740C22×C4C2×D4×C5911yescharacteristic
741C22×C4C2×D4×C5911yescharacteristic
742C22×C4C2×D4×C5911yescharacteristic
743C22×C4C24×C5911yescharacteristic
744M16—42no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—21no—
749C2×C8—42no—
750C4⋊C4—21no—
751C4⋊C4—21no—
752C4⋊C4—21no—
753C4⋊C4—21no—
754C4⋊C4—21no—
755C4⋊C4—21no—
756C4⋊C4—21no—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—21no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—21no—
766C4⋊C4—21no—
767C4⋊C4—42no—
768C4⋊C4—81no—
769C4⋊C4C2×D4×C5911yescharacteristic
770C4⋊C4C2×D4×C5911yescharacteristic
771C4⋊C4C2×D4×C5911yescharacteristic
772C4⋊C4C2×D4×C5911yescharacteristic
773C22⋊C4—21no—
774C22⋊C4—21no—
775C22⋊C4—21no—
776C22⋊C4—21no—
777C22⋊C4—21no—
778C22⋊C4—21no—
779C22⋊C4—21no—
780C22⋊C4—21no—
781C22⋊C4—21no—
782C22⋊C4—21no—
783C22⋊C4—21no—
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—42no—
799C22⋊C4—41no—
800C22⋊C4—41no—
801C22⋊C4—81no—
802C42—21no—
803C42—21no—
804C42—21no—
805C42—41no—
806C42—41no—
807C23—22no—
808C23—21no—
809C23—21no—
810C23—21no—
811C23—21no—
812C23—21no—
813C23—21no—
814C23—21no—
815C23—21no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—42no—
820C23—81no—
821C23—81no—
822C23—81no—
823C23—81no—
824C23—81no—
825C23#120×C5911yescharacteristic
826C23#120×C5911yescharacteristic
827C23C22×D4×C5911yescharacteristic
828Q8—41no—
829Q8—81no—
830D4—41no—
831D4—41no—
832D4—41no—
833D4—42no—
834D4—42no—
835D4—41no—
836D4—41no—
837D4—41no—
838D4—41no—
839D4—41no—
840D4—41no—
841D4—81no—
842D4—81no—
843D4—81no—
844D4—81no—
845D4—81no—
846D4—81no—
847D4—81no—
848D4—81no—
849D4—81no—
850D4—81no—
851D4—81no—
852D4—81no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—21no—
863C2×C4—21no—
864C2×C4—21no—
865C2×C4—21no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—81no—
884C2×C4—81no—
885C2×C4—81no—
886C2×C4—81no—
887C2×C4—81no—
888C2×C4—81no—
889C2×C4—81no—
890C2×C4—84no—
891C2×C4#120×C5911yescharacteristic
892C2×C4#120×C5911yescharacteristic
893C2×C4C22×D4×C5911yescharacteristic
894C2×C4C22×D4×C5911yescharacteristic
895C8—41no—
896C8—41no—
897C8—41no—
898C8—41no—
899C22—21no—
900C22—21no—
901C22—21no—
902C22—21no—
903C22—21no—
904C22—21no—
905C22—21no—
906C22—42no—
907C22—42no—
908C22—41no—
909C22—41no—
910C22—41no—
911C22—41no—
912C22—41no—
913C22—41no—
914C22—41no—
915C22—41no—
916C22—41no—
917C22—41no—
918C22—41no—
919C22—41no—
920C22—81no—
921C22—81no—
922C22—162no—
923C22—162no—
924C22C59×#45812yes—
925C22C2×#120×C5911yescharacteristic
926C22C59×#57611yescharacteristic
927C22C59×#57711yescharacteristic
928C4—21no—
929C4—21no—
930C4—21no—
931C4—21no—
932C4—42no—
933C4—41no—
934C4—41no—
935C4—41no—
936C4—41no—
937C4—41no—
938C4—41no—
939C4—41no—
940C4—41no—
941C4—81no—
942C4—81no—
943C4—81no—
944C2—21no—
945C2—21no—
946C2—22no—
947C2—41no—
948C2—81no—
949C2—81no—
950C2—81no—
951C2—81no—
952C2C59×#301211yescharacteristic
953C2C59×#301811yescharacteristic
954C2C2×C59×#45811yescharacteristic
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×#3094C2semidirect
3. C59×#3091C2semidirect
4. C59×#2498C2semidirect
5. C59×#1618C2semidirect
6. C59×#1616C2semidirect
7. C59×#1615C2semidirect
8. C59×#1613C2semidirect
9. C59×#1612C2semidirect
10. C59×#1610C2semidirect
11. C59×#1609C2semidirect
12. C59×#1607C2semidirect
13. C59×#1504C2semidirect
14. C2×C59×#327C2semidirect
15. C59×#1468C2semidirect
35. C2×#117×C59C22semidirect
37. C59×#484C22semidirect
38. C59×#483C22semidirect
43. C59×#481C22semidirect
44. C59×#481C22semidirect
46. C59×#480C22semidirect
47. C59×#480C22semidirect
52. C59×#407C22semidirect
53. C2×C22⋊C8×C59C22semidirect
54. C59×#400C22semidirect
55. C59×#399C22semidirect
56. C59×#398C22semidirect
57. C59×#397C22semidirect
62. C2×#95×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
421. #18262C59direct (N × H)
468. #3094C2×C59semidirect
469. #3091C2×C59semidirect
470. #2498C2×C59semidirect
471. #1618C2×C59semidirect
472. #1616C2×C59semidirect
473. #1615C2×C59semidirect
474. #1613C2×C59semidirect
475. #1612C2×C59semidirect
476. #1610C2×C59semidirect
477. #1609C2×C59semidirect
478. #1607C2×C59semidirect
479. #1504C2×C59semidirect
480. C2×#327C2×C59semidirect
481. #1468C2×C59semidirect
512. C2×#117C22×C59semidirect
514. #484C22×C59semidirect
515. #483C22×C59semidirect
520. #481C22×C59semidirect
521. #481C22×C59semidirect
523. #480C22×C59semidirect
524. #480C22×C59semidirect
529. #407C22×C59semidirect
530. C2×C22⋊C8C22×C59semidirect
531. #400C22×C59semidirect
532. #399C22×C59semidirect
533. #398C22×C59semidirect
534. #397C22×C59semidirect
539. C2×#95C22×C59semidirect
540. #328C22×C59semidirect
541. #328C22×C59semidirect
544. #327C22×C59semidirect
545. #327C22×C59semidirect
546. #327C22×C59semidirect
547. #327C22×C59semidirect
548. #324C22×C59semidirect
549. #324C22×C59semidirect
550. #323C22×C59semidirect
551. #323C22×C59semidirect
552. C59#18262direct (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×#30942
C59×#30912
C59×#24982
C59×#16182
C59×#16162
C59×#16152
C59×#16132
C59×#16122
C59×#16102
C59×#16092
C59×#16072
C59×#15042
C2×C59×#3272
C59×#14682
#1826259