Finite Group Databasebeta

← C59×#25585 #28437694

Subgroups — C59×#25585 #28437694

Order 15104.

1636 conjugacy classes of subgroups.

The subgroup lattice has 786 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C59×#3505C211yesmaximal, characteristic, complemented
2C59×#2435C211yesmaximal, characteristic, complemented
3C59×#2433C211yesmaximal, characteristic, complemented
4C59×#2408C211yesmaximal, characteristic, complemented
5C59×#2021C214yesmaximal, complemented
6C59×#1996C211yesmaximal, characteristic, complemented
7C59×#1964C211yesmaximal, characteristic, complemented
8C59×#1889C214yesmaximal, complemented
9C4×#99×C59C211yesmaximal, characteristic, complemented
10C23×D4×C59C2211yescharacteristic
11C59×#553—21no—
12C59×#553—22no—
13C59×#552—21no—
14C59×#551—22no—
15C59×#548—21no—
16C59×#546—21no—
17C59×#539—21no—
18C59×#538—21no—
19C59×#534C2212yes—
20C2×#127×C59—21no—
21C59×#529—21no—
22C2×#124×C59—21no—
23C59×#525—21no—
24C2×C22⋊Q8×C59C2211yescharacteristic
25C2×#121×C59—21no—
26C2×#121×C59C2211yescharacteristic
27C2×#120×C59C2214yes—
28C2×#120×C59C2212yes—
29C59×#518C2212yes—
30C2×C4×D4×C59C2211yescharacteristic
31C2×#99×C59C2212yes—
32C2×#99×C59C2214yes—
33C59×#394—21no—
34C59×#394—22no—
35C59×#392—21no—
36C59×#392—22no—
37C59×#390—21no—
38C59×#390—21no—
39C59×#390—21no—
40C59×#380C2211yescharacteristic
41C59×#379C2214yes—
42C59×#379C2212yes—
43C4×C22⋊C4×C59C2211yescharacteristic
44C4×C22⋊C4×C59C2211yescharacteristic
45C59×#342C2214yes—
46C59×#342C2212yes—
47C25×C59C2312yes—
48C2×#41×C59—21no—
49C22×Q8×C59D411yescharacteristic, complemented
50C22×D4×C59—22no—
51C22×D4×C59—24no—
52C22×D4×C59—21no—
53C22×D4×C59—21no—
54C22×D4×C59—21no—
55C22×D4×C59—21no—
56C22×D4×C59—21no—
57C22×D4×C59—21no—
58C22×D4×C59—44no—
59C22×D4×C59D411yescharacteristic, complemented
60C22×D4×C59C2311yescharacteristic
61C22×D4×C59C2312yes—
62C23×C4×C59D411yescharacteristic, complemented
63C23×C4×C59C2311yescharacteristic
64#127×C59—44no—
65#126×C59—22no—
66#126×C59—22no—
67#126×C59—22no—
68#125×C59—21no—
69#125×C59—22no—
70#124×C59—21no—
71#124×C59—22no—
72#124×C59—44no—
73#123×C59—22no—
74#123×C59—22no—
75#123×C59—22no—
76#123×C59—22no—
77#123×C59—22no—
78C22⋊Q8×C59—21no—
79C22⋊Q8×C59—22no—
80C22⋊Q8×C59—21no—
81C22⋊Q8×C59—21no—
82C22⋊Q8×C59—21no—
83C22⋊Q8×C59—21no—
84#121×C59—21no—
85#121×C59—22no—
86#121×C59—21no—
87#121×C59—21no—
88#121×C59—21no—
89#121×C59—21no—
90#121×C59—22no—
91#121×C59—22no—
92#121×C59—44no—
93#120×C59—22no—
94#120×C59—22no—
95#120×C59—28no—
96#120×C59—44no—
97#120×C59—44no—
98C4×Q8×C59—21no—
99C4×D4×C59—22no—
100C4×D4×C59—21no—
101C4×D4×C59—21no—
102C4×D4×C59—21no—
103C4×D4×C59—21no—
104C4×D4×C59—21no—
105C4×D4×C59—22no—
106C4×D4×C59—22no—
107C4×D4×C59—22no—
108C4×D4×C59—22no—
109#117×C59—21no—
110#117×C59—22no—
111#117×C59—22no—
112C2×C4⋊C4×C59—21no—
113C2×C4⋊C4×C59D411yescharacteristic, complemented
114C2×C4⋊C4×C59D411yescharacteristic, complemented
115C2×C4⋊C4×C59D411yescharacteristic, complemented
116C2×C4⋊C4×C59D412yescomplemented
117C2×C22⋊C4×C59—22no—
118C2×C22⋊C4×C59—22no—
119C2×C22⋊C4×C59—24no—
120C2×C22⋊C4×C59—24no—
121C2×C22⋊C4×C59—22no—
122C2×C22⋊C4×C59—22no—
123C2×C22⋊C4×C59—24no—
124C2×C22⋊C4×C59D411yescharacteristic, complemented
125C2×C22⋊C4×C59D412yescomplemented
126C2×C22⋊C4×C59C2312yes—
127C2×C22⋊C4×C59C2312yes—
128C2×C22⋊C4×C59C2311yescharacteristic
129C2×C22⋊C4×C59C2312yes—
130C2×C22⋊C4×C59C2312yes—
131C2×C42×C59—21no—
132C2×C42×C59—21no—
133C2×C42×C59D411yescharacteristic, complemented
134#99×C59—24no—
135#99×C59—44no—
136#95×C59—21no—
137#95×C59—21no—
138#95×C59—21no—
139C24×C59—22no—
140C24×C59—22no—
141C24×C59—22no—
142C24×C59—24no—
143C24×C59—24no—
144C24×C59—44no—
145C24×C59—82no—
146C24×C59C2×D412yes—
147C24×C59C2×D411yescharacteristic
148C24×C59C2411yescharacteristic
149#41×C59—82no—
150C2×Q8×C59—21no—
151C2×Q8×C59—21no—
152C2×Q8×C59—42no—
153C2×D4×C59—24no—
154C2×D4×C59—24no—
155C2×D4×C59—24no—
156C2×D4×C59—21no—
157C2×D4×C59—22no—
158C2×D4×C59—21no—
159C2×D4×C59—22no—
160C2×D4×C59—22no—
161C2×D4×C59—24no—
162C2×D4×C59—24no—
163C2×D4×C59—22no—
164C2×D4×C59—22no—
165C2×D4×C59—22no—
166C2×D4×C59—21no—
167C2×D4×C59—21no—
168C2×D4×C59—42no—
169C2×D4×C59—42no—
170C2×D4×C59—42no—
171C2×D4×C59—42no—
172C2×D4×C59—48no—
173C2×D4×C59—44no—
174C2×D4×C59—44no—
175C2×D4×C59—44no—
176C2×D4×C59—44no—
177C2×D4×C59—44no—
178C2×D4×C59—48no—
179C2×D4×C59—41no—
180C2×D4×C59—41no—
181C2×D4×C59—41no—
182C2×D4×C59—41no—
183C2×D4×C59—84no—
184C2×D4×C59—82no—
185C22×C4×C59—22no—
186C22×C4×C59—22no—
187C22×C4×C59—22no—
188C22×C4×C59—21no—
189C22×C4×C59—21no—
190C22×C4×C59—22no—
191C22×C4×C59—22no—
192C22×C4×C59—42no—
193C22×C4×C59—42no—
194C22×C4×C59C2×D411yescharacteristic
195C22×C4×C59C2×D412yes—
196C22×C4×C59C2×D411yescharacteristic
197C22×C4×C59C2×D411yescharacteristic
198C22×C4×C59C2×D411yescharacteristic
199C22×C4×C59C2×D411yescharacteristic
200C22×C4×C59C2×D412yes—
201C22×C4×C59C2×D411yescharacteristic
202C22×C4×C59C2×D412yes—
203C22×C4×C59C2×D411yescharacteristic
204C22×C4×C59C2×D411yescharacteristic
205C22×C4×C59C2×D411yescharacteristic
206C4⋊C4×C59—22no—
207C4⋊C4×C59—22no—
208C4⋊C4×C59—22no—
209C4⋊C4×C59—22no—
210C4⋊C4×C59—21no—
211C4⋊C4×C59—22no—
212C4⋊C4×C59—21no—
213C4⋊C4×C59—21no—
214C4⋊C4×C59—21no—
215C4⋊C4×C59—21no—
216C4⋊C4×C59—22no—
217C4⋊C4×C59—21no—
218C4⋊C4×C59—42no—
219C22⋊C4×C59—22no—
220C22⋊C4×C59—22no—
221C22⋊C4×C59—22no—
222C22⋊C4×C59—22no—
223C22⋊C4×C59—22no—
224C22⋊C4×C59—22no—
225C22⋊C4×C59—21no—
226C22⋊C4×C59—22no—
227C22⋊C4×C59—21no—
228C22⋊C4×C59—22no—
229C22⋊C4×C59—22no—
230C22⋊C4×C59—22no—
231C22⋊C4×C59—21no—
232C22⋊C4×C59—21no—
233C22⋊C4×C59—22no—
234C22⋊C4×C59—22no—
235C22⋊C4×C59—22no—
236C22⋊C4×C59—24no—
237C22⋊C4×C59—48no—
238C22⋊C4×C59—44no—
239C22⋊C4×C59—44no—
240C22⋊C4×C59—48no—
241C22⋊C4×C59—84no—
242C22⋊C4×C59—82no—
243C22⋊C4×C59#4114yescomplemented
244C42×C59—22no—
245C42×C59—22no—
246C42×C59—21no—
247C42×C59—21no—
248C42×C59—42no—
249C42×C59—42no—
250C23×C59—24no—
251C23×C59—24no—
252C23×C59—24no—
253C23×C59—21no—
254C23×C59—22no—
255C23×C59—21no—
256C23×C59—21no—
257C23×C59—24no—
258C23×C59—41no—
259C23×C59—41no—
260C23×C59—41no—
261C23×C59—41no—
262C23×C59—44no—
263C23×C59—42no—
264C23×C59—42no—
265C23×C59—42no—
266C23×C59—42no—
267C23×C59—42no—
268C23×C59—44no—
269C23×C59—42no—
270C23×C59—42no—
271C23×C59—42no—
272C23×C59—42no—
273C23×C59—42no—
274C23×C59—44no—
275C23×C59—44no—
276C23×C59—88no—
277C23×C59—88no—
278C23×C59C22×D411yescharacteristic
279C23×C59C22×D411yescharacteristic
280C23×C59C22×D411yescharacteristic
281C23×C59C2×#4112yes—
282C23×C59H(5,𝔽2)12yes—
283Q8×C59—42no—
284Q8×C59—81no—
285D4×C59—44no—
286D4×C59—44no—
287D4×C59—44no—
288D4×C59—42no—
289D4×C59—42no—
290D4×C59—42no—
291D4×C59—42no—
292D4×C59—44no—
293D4×C59—44no—
294D4×C59—42no—
295D4×C59—81no—
296D4×C59—82no—
297D4×C59—82no—
298D4×C59—816no—
299D4×C59—88no—
300C2×C4×C59—22no—
301C2×C4×C59—22no—
302C2×C4×C59—22no—
303C2×C4×C59—21no—
304C2×C4×C59—22no—
305C2×C4×C59—21no—
306C2×C4×C59—21no—
307C2×C4×C59—22no—
308C2×C4×C59—22no—
309C2×C4×C59—21no—
310C2×C4×C59—21no—
311C2×C4×C59—24no—
312C2×C4×C59—24no—
313C2×C4×C59—41no—
314C2×C4×C59—41no—
315C2×C4×C59—41no—
316C2×C4×C59—42no—
317C2×C4×C59—42no—
318C2×C4×C59—42no—
319C2×C4×C59—41no—
320C2×C4×C59—42no—
321C2×C4×C59—41no—
322C2×C4×C59—42no—
323C2×C4×C59—42no—
324C2×C4×C59—42no—
325C2×C4×C59—42no—
326C2×C4×C59—42no—
327C2×C4×C59—42no—
328C2×C4×C59—42no—
329C2×C4×C59—81no—
330C2×C4×C59—82no—
331C2×C4×C59—82no—
332C2×C4×C59#12011yescharacteristic
333C2×C4×C59#12011yescharacteristic
334C2×C4×C59#12011yescharacteristic
335C2×C4×C59#12011yescharacteristic
336#25585C5911yesmaximal, characteristic, direct product factor, Sylow
337C22×C59—21no—
338C22×C59—21no—
339C22×C59—21no—
340C22×C59—21no—
341C22×C59—21no—
342C22×C59—21no—
343C22×C59—42no—
344C22×C59—42no—
345C22×C59—42no—
346C22×C59—48no—
347C22×C59—44no—
348C22×C59—48no—
349C22×C59—44no—
350C22×C59—41no—
351C22×C59—42no—
352C22×C59—41no—
353C22×C59—42no—
354C22×C59—44no—
355C22×C59—42no—
356C22×C59—41no—
357C22×C59—84no—
358C22×C59—81no—
359C22×C59—84no—
360C22×C59—82no—
361C22×C59—84no—
362C22×C59—82no—
363C22×C59—82no—
364C22×C59—82no—
365C22×C59C2×#12011yescharacteristic
366C22×C59#53211yescharacteristic
367C22×C59#53511yescharacteristic
368C22×C59#54612yes—
369C22×C59#55012yes—
370C4×C59—21no—
371C4×C59—21no—
372C4×C59—21no—
373C4×C59—44no—
374C4×C59—41no—
375C4×C59—42no—
376C4×C59—41no—
377C4×C59—42no—
378C4×C59—41no—
379C4×C59—42no—
380C4×C59—82no—
381C4×C59—82no—
382C4×C59B(4,𝔽2)12yes—
383#3505C2×C5911yescharacteristic, complemented
384#2435C2×C5911yescharacteristic, complemented
385#2433C2×C5911yescharacteristic, complemented
386#2408C2×C5911yescharacteristic, complemented
387#2021C2×C5914yescomplemented
388#1996C2×C5911yescharacteristic, complemented
389#1964C2×C5911yescharacteristic, complemented
390#1889C2×C5914yescomplemented
391C4×#99C2×C5911yescharacteristic, complemented
392C2×C59—22no—
393C2×C59—21no—
394C2×C59—22no—
395C2×C59—21no—
396C2×C59—84no—
397C2×C59—81no—
398C2×C59—82no—
399C2×C59#243111yescharacteristic
400C2×C59C2×B(4,𝔽2)11yescharacteristic
401C2×C59#302711yescharacteristic
402C23×D4C22×C5911yescharacteristic
403#553—21no—
404#553—22no—
405#552—21no—
406#551—22no—
407#548—21no—
408#546—21no—
409#539—21no—
410#538—21no—
411#534C22×C5912yes—
412C2×#127—21no—
413#529—21no—
414C2×#124—21no—
415#525—21no—
416C2×C22⋊Q8C22×C5911yescharacteristic
417C2×#121—21no—
418C2×#121C22×C5911yescharacteristic
419C2×#120C22×C5914yes—
420C2×#120C22×C5912yes—
421#518C22×C5912yes—
422C2×C4×D4C22×C5911yescharacteristic
423C2×#99C22×C5912yes—
424C2×#99C22×C5914yes—
425#394—21no—
426#394—22no—
427#392—21no—
428#392—22no—
429#390—21no—
430#390—21no—
431#390—21no—
432#380C22×C5911yescharacteristic
433#379C22×C5912yes—
434#379C22×C5914yes—
435C4×C22⋊C4C22×C5911yescharacteristic
436C4×C22⋊C4C22×C5911yescharacteristic
437#342C22×C5912yes—
438#342C22×C5914yes—
439C59#2558511yescharacteristic, direct product factor, Sylow
440C25C23×C5912yes—
441C2×#41—21no—
442C22×Q8D4×C5911yescharacteristic, complemented
443C22×D4—22no—
444C22×D4—24no—
445C22×D4—21no—
446C22×D4—21no—
447C22×D4—21no—
448C22×D4—21no—
449C22×D4—21no—
450C22×D4—21no—
451C22×D4—44no—
452C22×D4D4×C5911yescharacteristic, complemented
453C22×D4C23×C5911yescharacteristic
454C22×D4C23×C5912yes—
455C23×C4D4×C5911yescharacteristic, complemented
456C23×C4C23×C5911yescharacteristic
457#127—44no—
458#126—22no—
459#126—22no—
460#126—22no—
461#125—21no—
462#125—22no—
463#124—21no—
464#124—22no—
465#124—44no—
466#123—22no—
467#123—22no—
468#123—22no—
469#123—22no—
470#123—22no—
471C22⋊Q8—21no—
472C22⋊Q8—22no—
473C22⋊Q8—21no—
474C22⋊Q8—21no—
475C22⋊Q8—21no—
476C22⋊Q8—21no—
477#121—21no—
478#121—22no—
479#121—21no—
480#121—21no—
481#121—21no—
482#121—21no—
483#121—22no—
484#121—22no—
485#121—44no—
486#120—22no—
487#120—22no—
488#120—28no—
489#120—44no—
490#120—44no—
491C4×Q8—21no—
492C4×D4—22no—
493C4×D4—21no—
494C4×D4—21no—
495C4×D4—21no—
496C4×D4—21no—
497C4×D4—21no—
498C4×D4—22no—
499C4×D4—22no—
500C4×D4—22no—
501C4×D4—22no—
502#117—21no—
503#117—22no—
504#117—22no—
505C2×C4⋊C4—21no—
506C2×C4⋊C4D4×C5911yescharacteristic, complemented
507C2×C4⋊C4D4×C5911yescharacteristic, complemented
508C2×C4⋊C4D4×C5911yescharacteristic, complemented
509C2×C4⋊C4D4×C5912yescomplemented
510C2×C22⋊C4—22no—
511C2×C22⋊C4—24no—
512C2×C22⋊C4—22no—
513C2×C22⋊C4—22no—
514C2×C22⋊C4—24no—
515C2×C22⋊C4—22no—
516C2×C22⋊C4—24no—
517C2×C22⋊C4D4×C5911yescharacteristic, complemented
518C2×C22⋊C4D4×C5912yescomplemented
519C2×C22⋊C4C23×C5912yes—
520C2×C22⋊C4C23×C5912yes—
521C2×C22⋊C4C23×C5911yescharacteristic
522C2×C22⋊C4C23×C5912yes—
523C2×C22⋊C4C23×C5912yes—
524C2×C42—21no—
525C2×C42—21no—
526C2×C42D4×C5911yescharacteristic, complemented
527#99—24no—
528#99—44no—
529#95—21no—
530#95—21no—
531#95—21no—
532C24—22no—
533C24—22no—
534C24—22no—
535C24—24no—
536C24—24no—
537C24—44no—
538C24—82no—
539C24C2×D4×C5912yes—
540C24C2×D4×C5911yescharacteristic
541C24C24×C5911yescharacteristic
542#41—82no—
543C2×Q8—21no—
544C2×Q8—21no—
545C2×Q8—42no—
546C2×D4—24no—
547C2×D4—24no—
548C2×D4—24no—
549C2×D4—21no—
550C2×D4—22no—
551C2×D4—21no—
552C2×D4—22no—
553C2×D4—22no—
554C2×D4—24no—
555C2×D4—24no—
556C2×D4—22no—
557C2×D4—22no—
558C2×D4—22no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—42no—
562C2×D4—42no—
563C2×D4—42no—
564C2×D4—42no—
565C2×D4—48no—
566C2×D4—44no—
567C2×D4—44no—
568C2×D4—44no—
569C2×D4—44no—
570C2×D4—44no—
571C2×D4—48no—
572C2×D4—41no—
573C2×D4—41no—
574C2×D4—41no—
575C2×D4—41no—
576C2×D4—84no—
577C2×D4—82no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—42no—
586C22×C4—42no—
587C22×C4C2×D4×C5911yescharacteristic
588C22×C4C2×D4×C5912yes—
589C22×C4C2×D4×C5911yescharacteristic
590C22×C4C2×D4×C5911yescharacteristic
591C22×C4C2×D4×C5911yescharacteristic
592C22×C4C2×D4×C5911yescharacteristic
593C22×C4C2×D4×C5912yes—
594C22×C4C2×D4×C5911yescharacteristic
595C22×C4C2×D4×C5912yes—
596C22×C4C2×D4×C5911yescharacteristic
597C22×C4C2×D4×C5911yescharacteristic
598C22×C4C2×D4×C5911yescharacteristic
599C4⋊C4—22no—
600C4⋊C4—22no—
601C4⋊C4—22no—
602C4⋊C4—22no—
603C4⋊C4—21no—
604C4⋊C4—22no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—22no—
610C4⋊C4—21no—
611C4⋊C4—42no—
612C22⋊C4—22no—
613C22⋊C4—22no—
614C22⋊C4—22no—
615C22⋊C4—22no—
616C22⋊C4—22no—
617C22⋊C4—22no—
618C22⋊C4—21no—
619C22⋊C4—22no—
620C22⋊C4—21no—
621C22⋊C4—22no—
622C22⋊C4—22no—
623C22⋊C4—22no—
624C22⋊C4—21no—
625C22⋊C4—21no—
626C22⋊C4—22no—
627C22⋊C4—22no—
628C22⋊C4—22no—
629C22⋊C4—24no—
630C22⋊C4—48no—
631C22⋊C4—44no—
632C22⋊C4—44no—
633C22⋊C4—48no—
634C22⋊C4—84no—
635C22⋊C4—82no—
636C22⋊C4#41×C5914yescomplemented
637C42—22no—
638C42—22no—
639C42—21no—
640C42—21no—
641C42—42no—
642C42—42no—
643C23—24no—
644C23—24no—
645C23—24no—
646C23—21no—
647C23—22no—
648C23—21no—
649C23—21no—
650C23—24no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—44no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—44no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—44no—
668C23—44no—
669C23—88no—
670C23—88no—
671C23C22×D4×C5911yescharacteristic
672C23C22×D4×C5911yescharacteristic
673C23C22×D4×C5911yescharacteristic
674C23C2×#41×C5912yes—
675C23H(5,𝔽2)×C5912yes—
676Q8—42no—
677Q8—81no—
678D4—44no—
679D4—44no—
680D4—44no—
681D4—42no—
682D4—42no—
683D4—42no—
684D4—42no—
685D4—44no—
686D4—44no—
687D4—42no—
688D4—81no—
689D4—82no—
690D4—82no—
691D4—816no—
692D4—88no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—21no—
697C2×C4—22no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—41no—
713C2×C4—42no—
714C2×C4—41no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—81no—
723C2×C4—82no—
724C2×C4—82no—
725C2×C4#120×C5911yescharacteristic
726C2×C4#120×C5911yescharacteristic
727C2×C4#120×C5911yescharacteristic
728C2×C4#120×C5911yescharacteristic
729C22—21no—
730C22—21no—
731C22—21no—
732C22—21no—
733C22—21no—
734C22—21no—
735C22—42no—
736C22—42no—
737C22—42no—
738C22—48no—
739C22—44no—
740C22—48no—
741C22—44no—
742C22—41no—
743C22—42no—
744C22—44no—
745C22—42no—
746C22—41no—
747C22—41no—
748C22—42no—
749C22—84no—
750C22—81no—
751C22—84no—
752C22—82no—
753C22—84no—
754C22—82no—
755C22—82no—
756C22—82no—
757C22C2×#120×C5911yescharacteristic
758C22C59×#53211yescharacteristic
759C22C59×#53511yescharacteristic
760C22C59×#54612yes—
761C22C59×#55012yes—
762C4—21no—
763C4—21no—
764C4—21no—
765C4—44no—
766C4—41no—
767C4—42no—
768C4—41no—
769C4—42no—
770C4—41no—
771C4—42no—
772C4—82no—
773C4—82no—
774C4C59×B(4,𝔽2)12yes—
775C2—22no—
776C2—21no—
777C2—22no—
778C2—21no—
779C2—84no—
780C2—81no—
781C2—82no—
782C2C59×#243111yescharacteristic
783C2C2×C59×B(4,𝔽2)11yescharacteristic
784C2C59×#302711yescharacteristic
subgroupG/H
center, socleC22×C59C2×#120
commutator, Frattini, cosocleC24C24×C59
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C59 ◁ C23×C4×C59 ◁ G

Complements

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

NH ≅ G/Ntype
1. C59×#3505C2semidirect
2. C59×#2435C2semidirect
3. C59×#2433C2semidirect
4. C59×#2408C2semidirect
5. C59×#2021C2semidirect
6. C59×#1996C2semidirect
7. C59×#1964C2semidirect
8. C59×#1889C2semidirect
9. C4×#99×C59C2semidirect
49. C22×Q8×C59D4semidirect
59. C22×D4×C59D4semidirect
62. C23×C4×C59D4semidirect
113. C2×C4⋊C4×C59D4semidirect
114. C2×C4⋊C4×C59D4semidirect
115. C2×C4⋊C4×C59D4semidirect
116. C2×C4⋊C4×C59D4semidirect
124. C2×C22⋊C4×C59D4semidirect
125. C2×C22⋊C4×C59D4semidirect
133. C2×C42×C59D4semidirect
243. C22⋊C4×C59#41semidirect
336. #25585C59direct (N × H)
383. #3505C2×C59semidirect
384. #2435C2×C59semidirect
385. #2433C2×C59semidirect
386. #2408C2×C59semidirect
387. #2021C2×C59semidirect
388. #1996C2×C59semidirect
389. #1964C2×C59semidirect
390. #1889C2×C59semidirect
391. C4×#99C2×C59semidirect
439. C59#25585direct (N × H)
442. C22×Q8D4×C59semidirect
452. C22×D4D4×C59semidirect
455. C23×C4D4×C59semidirect
506. C2×C4⋊C4D4×C59semidirect
507. C2×C4⋊C4D4×C59semidirect
508. C2×C4⋊C4D4×C59semidirect
509. C2×C4⋊C4D4×C59semidirect
517. C2×C22⋊C4D4×C59semidirect
518. C2×C22⋊C4D4×C59semidirect
526. C2×C42D4×C59semidirect
636. C22⋊C4#41×C59semidirect

Maximal subgroups

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

subgroupindex
C59×#35052
C59×#24352
C59×#24332
C59×#24082
C59×#20212
C59×#19962
C59×#19642
C59×#18892
C4×#99×C592
#2558559