Finite Group Databasebeta

← C59×#18384 #28430493

Subgroups — C59×#18384 #28430493

Order 15104.

1082 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C59×#3505C211yesmaximal, characteristic, complemented
2C59×#3187C211yesmaximal, characteristic, complemented
3C59×#3186C211yesmaximal, characteristic, complemented
4C59×#2543C211yesmaximal, characteristic, complemented
5C59×#1612C212yesmaximal, complemented
6C59×#1609C212yesmaximal, complemented
7C59×#1600C212yesmaximal, complemented
8C59×#1597C212yesmaximal, complemented
9C2×C59×#328C211yesmaximal, characteristic, complemented
10C2×C59×#327C211yesmaximal, characteristic, complemented
11C59×#1459C211yesmaximal, characteristic, complemented
12C59×#553—22no—
13C59×#553—21no—
14C59×#552—21no—
15C59×#551—22no—
16C59×#548—21no—
17C59×#546—21no—
18C59×#539C2212yes—
19C59×#538C2212yes—
20C59×#534—21no—
21C59×#529—21no—
22C59×#525—21no—
23C2×C22⋊Q8×C59C2211yescharacteristic
24C2×#121×C59—21no—
25C2×#121×C59C2211yescharacteristic
26C2×#121×C59C2211yescharacteristic
27C59×#518—21no—
28C2×C4×D4×C59C2211yescharacteristic
29C59×#483C2212yescomplemented
30C59×#481—21no—
31C59×#480—21no—
32C59×#480C2212yes—
33C59×#466—22no—
34C59×#465—22no—
35C59×#450C2212yescomplemented
36C59×#448—21no—
37C59×#447—21no—
38C59×#447C2212yes—
39C2×C22⋊C8×C59C2211yescharacteristic
40C2×C22⋊C8×C59C2211yescharacteristic
41C59×#398C2211yescharacteristic, complemented
42C59×#397C2211yescharacteristic, complemented
43C59×#394C2211yescharacteristic, complemented
44C59×#392C2211yescharacteristic, complemented
45C59×#388—21no—
46C59×#386—21no—
47C59×#386—21no—
48C2×#95×C59C2211yescharacteristic
49C59×#328C2212yescomplemented
50C59×#328C2212yescomplemented
51C59×#327C2212yes—
52C59×#327C2212yes—
53C59×#324C2212yescomplemented
54C59×#323C2212yescomplemented
55C2×#41×C59—21no—
56C22×Q8×C59D411yescharacteristic, complemented
57C22×D4×C59—21no—
58C22×D4×C59—21no—
59C22×D4×C59—21no—
60C22×D4×C59D411yescharacteristic
61C22×D4×C59D411yescharacteristic, complemented
62C22×D4×C59C2311yescharacteristic
63C23×C4×C59—21no—
64C23×C4×C59D411yescharacteristic
65C23×C4×C59C2311yescharacteristic
66C2×SD16×C59—22no—
67C2×D8×C59—22no—
68C22×C8×C59—21no—
69C22×C8×C59—21no—
70#126×C59—22no—
71#126×C59—22no—
72#126×C59—22no—
73#125×C59—21no—
74#125×C59—22no—
75#124×C59—21no—
76#124×C59—22no—
77#123×C59—22no—
78#123×C59—22no—
79#123×C59—22no—
80#123×C59—22no—
81#123×C59—22no—
82C22⋊Q8×C59—21no—
83C22⋊Q8×C59—22no—
84C22⋊Q8×C59—21no—
85C22⋊Q8×C59—21no—
86C22⋊Q8×C59D412yescomplemented
87C22⋊Q8×C59C2312yes—
88#121×C59—21no—
89#121×C59—22no—
90#121×C59—22no—
91#121×C59—22no—
92#121×C59—21no—
93#121×C59—21no—
94#121×C59—21no—
95#121×C59—21no—
96#121×C59—21no—
97#121×C59—21no—
98#121×C59—44no—
99#121×C59D412yescomplemented
100#121×C59C2312yes—
101#120×C59—22no—
102#120×C59—22no—
103C4×Q8×C59—21no—
104C4×D4×C59—22no—
105C4×D4×C59—22no—
106C4×D4×C59—22no—
107C4×D4×C59—21no—
108C4×D4×C59—21no—
109C4×D4×C59—21no—
110C4×D4×C59—21no—
111C4×D4×C59—21no—
112C4×D4×C59—22no—
113C4×D4×C59—22no—
114#117×C59—22no—
115#117×C59—21no—
116#117×C59—22no—
117C2×C4⋊C4×C59—21no—
118C2×C4⋊C4×C59—21no—
119C2×C4⋊C4×C59D411yescharacteristic, complemented
120C2×C4⋊C4×C59D411yescharacteristic, complemented
121C2×C4⋊C4×C59C2311yescharacteristic
122C2×C4⋊C4×C59C2311yescharacteristic
123C2×C22⋊C4×C59—22no—
124C2×C22⋊C4×C59—21no—
125C2×C22⋊C4×C59—21no—
126C2×C22⋊C4×C59—21no—
127C2×C22⋊C4×C59—21no—
128C2×C22⋊C4×C59—21no—
129C2×C22⋊C4×C59—21no—
130C2×C22⋊C4×C59—21no—
131C2×C22⋊C4×C59D411yescharacteristic
132C2×C22⋊C4×C59C2311yescharacteristic
133C2×C42×C59D411yescharacteristic
134#107×C59—22no—
135#106×C59—22no—
136#103×C59—22no—
137#102×C59—22no—
138#102×C59—22no—
139#102×C59—22no—
140C22⋊C8×C59—21no—
141C22⋊C8×C59—21no—
142C22⋊C8×C59C2312yes—
143C22⋊C8×C59C2312yes—
144#95×C59—21no—
145#95×C59—21no—
146#95×C59—21no—
147#95×C59C2311yescharacteristic
148#95×C59C2311yescharacteristic
149C24×C59—21no—
150C24×C59—21no—
151C24×C59C2×D411yescharacteristic
152C24×C59C2×D411yescharacteristic
153#41×C59—82no—
154C2×Q8×C59—21no—
155C2×Q8×C59—81no—
156C2×Q8×C59C2×D412yes—
157C2×D4×C59—21no—
158C2×D4×C59—21no—
159C2×D4×C59—22no—
160C2×D4×C59—22no—
161C2×D4×C59—22no—
162C2×D4×C59—22no—
163C2×D4×C59—22no—
164C2×D4×C59—22no—
165C2×D4×C59—21no—
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—41no—
173C2×D4×C59—41no—
174C2×D4×C59—42no—
175C2×D4×C59—42no—
176C2×D4×C59—81no—
177C2×D4×C59—81no—
178C2×D4×C59—81no—
179C2×D4×C59C2×D412yes—
180C22×C4×C59—21no—
181C22×C4×C59—21no—
182C22×C4×C59—22no—
183C22×C4×C59—22no—
184C22×C4×C59—21no—
185C22×C4×C59—21no—
186C22×C4×C59—21no—
187C22×C4×C59—21no—
188C22×C4×C59—21no—
189C22×C4×C59—21no—
190C22×C4×C59—42no—
191C22×C4×C59—42no—
192C22×C4×C59—81no—
193C22×C4×C59—81no—
194C22×C4×C59—81no—
195C22×C4×C59C2×D411yescharacteristic
196C22×C4×C59C2×D411yescharacteristic
197C22×C4×C59C2×D411yescharacteristic
198C22×C4×C59C2×D411yescharacteristic
199C22×C4×C59C2×D411yescharacteristic
200C22×C4×C59C2×D411yescharacteristic
201C22×C4×C59C2×D411yescharacteristic
202C22×C4×C59C2×D411yescharacteristic
203C22×C4×C59C2411yescharacteristic
204SD16×C59—82no—
205D8×C59—82no—
206C2×C8×C59—22no—
207C2×C8×C59—22no—
208C2×C8×C59—81no—
209C2×C8×C59—81no—
210C4⋊C4×C59—22no—
211C4⋊C4×C59—22no—
212C4⋊C4×C59—22no—
213C4⋊C4×C59—22no—
214C4⋊C4×C59—22no—
215C4⋊C4×C59—21no—
216C4⋊C4×C59—21no—
217C4⋊C4×C59—22no—
218C4⋊C4×C59—21no—
219C4⋊C4×C59—21no—
220C4⋊C4×C59—21no—
221C4⋊C4×C59—21no—
222C4⋊C4×C59—42no—
223C4⋊C4×C59C2×D412yes—
224C4⋊C4×C59C2×D412yes—
225C22⋊C4×C59—22no—
226C22⋊C4×C59—22no—
227C22⋊C4×C59—22no—
228C22⋊C4×C59—22no—
229C22⋊C4×C59—22no—
230C22⋊C4×C59—22no—
231C22⋊C4×C59—21no—
232C22⋊C4×C59—22no—
233C22⋊C4×C59—21no—
234C22⋊C4×C59—22no—
235C22⋊C4×C59—22no—
236C22⋊C4×C59—22no—
237C22⋊C4×C59—21no—
238C22⋊C4×C59—21no—
239C22⋊C4×C59—42no—
240C22⋊C4×C59—42no—
241C22⋊C4×C59—42no—
242C22⋊C4×C59—41no—
243C22⋊C4×C59—41no—
244C22⋊C4×C59—81no—
245C42×C59—22no—
246C42×C59—22no—
247C42×C59—21no—
248C42×C59—21no—
249C23×C59—21no—
250C23×C59—22no—
251C23×C59—21no—
252C23×C59—21no—
253C23×C59—41no—
254C23×C59—41no—
255C23×C59—41no—
256C23×C59—41no—
257C23×C59—41no—
258C23×C59—41no—
259C23×C59—41no—
260C23×C59—41no—
261C23×C59—42no—
262C23×C59—41no—
263C23×C59—41no—
264C23×C59—41no—
265C23×C59—81no—
266C23×C59—81no—
267C23×C59#12011yescharacteristic
268C23×C59#12011yescharacteristic
269C23×C59#13512yes—
270C23×C59AGL(1,ℤ/8)12yes—
271C23×C59C22×D411yescharacteristic
272Q8×C59—42no—
273Q8×C59—42no—
274D4×C59—42no—
275D4×C59—42no—
276D4×C59—42no—
277D4×C59—42no—
278D4×C59—42no—
279D4×C59—42no—
280D4×C59—42no—
281D4×C59—42no—
282D4×C59—44no—
283D4×C59—82no—
284D4×C59—82no—
285D4×C59—84no—
286D4×C59—82no—
287D4×C59—82no—
288C2×C4×C59—22no—
289C2×C4×C59—21no—
290C2×C4×C59—21no—
291C2×C4×C59—22no—
292C2×C4×C59—21no—
293C2×C4×C59—22no—
294C2×C4×C59—22no—
295C2×C4×C59—21no—
296C2×C4×C59—21no—
297C2×C4×C59—41no—
298C2×C4×C59—41no—
299C2×C4×C59—41no—
300C2×C4×C59—41no—
301C2×C4×C59—41no—
302C2×C4×C59—41no—
303C2×C4×C59—42no—
304C2×C4×C59—41no—
305C2×C4×C59—41no—
306C2×C4×C59—42no—
307C2×C4×C59—41no—
308C2×C4×C59—41no—
309C2×C4×C59—41no—
310C2×C4×C59—41no—
311C2×C4×C59—41no—
312C2×C4×C59—41no—
313C2×C4×C59—41no—
314C2×C4×C59—41no—
315C2×C4×C59—81no—
316C2×C4×C59—81no—
317C2×C4×C59—81no—
318C2×C4×C59—82no—
319C2×C4×C59—82no—
320C2×C4×C59—84no—
321C2×C4×C59#12011yescharacteristic
322C2×C4×C59#12011yescharacteristic
323C2×C4×C59C22×D411yescharacteristic
324C2×C4×C59C22×D411yescharacteristic
325C8×C59—42no—
326C8×C59—42no—
327#18384C5911yesmaximal, characteristic, direct product factor, Sylow
328C22×C59—21no—
329C22×C59—21no—
330C22×C59—21no—
331C22×C59—21no—
332C22×C59—21no—
333C22×C59—21no—
334C22×C59—42no—
335C22×C59—42no—
336C22×C59—42no—
337C22×C59—41no—
338C22×C59—42no—
339C22×C59—42no—
340C22×C59—41no—
341C22×C59—41no—
342C22×C59—42no—
343C22×C59—81no—
344C22×C59—81no—
345C22×C59—81no—
346C22×C59—81no—
347C22×C59—81no—
348C22×C59—81no—
349C22×C59—81no—
350C22×C59—81no—
351C22×C59—162no—
352C22×C59#44912yes—
353C22×C59#44912yes—
354C22×C59C2×#12011yescharacteristic
355C22×C59C2×#13511yescharacteristic
356C22×C59C2×AGL(1,ℤ/8)11yescharacteristic
357C4×C59—21no—
358C4×C59—21no—
359C4×C59—21no—
360C4×C59—21no—
361C4×C59—42no—
362C4×C59—41no—
363C4×C59—42no—
364C4×C59—41no—
365C4×C59—42no—
366C4×C59—41no—
367C4×C59—42no—
368C4×C59—81no—
369C4×C59—81no—
370#3505C2×C5911yescharacteristic, complemented
371#3187C2×C5911yescharacteristic, complemented
372#3186C2×C5911yescharacteristic, complemented
373#2543C2×C5911yescharacteristic, complemented
374#1612C2×C5912yescomplemented
375#1609C2×C5912yescomplemented
376#1600C2×C5912yescomplemented
377#1597C2×C5912yescomplemented
378C2×#328C2×C5911yescharacteristic, complemented
379C2×#327C2×C5911yescharacteristic, complemented
380#1459C2×C5911yescharacteristic, complemented
381C2×C59—21no—
382C2×C59—21no—
383C2×C59—22no—
384C2×C59—22no—
385C2×C59—81no—
386C2×C59—82no—
387C2×C59—161no—
388C2×C59C2×#44911yescharacteristic
389C2×C59#301811yescharacteristic
390C2×C59#302611yescharacteristic
391#553—22no—
392#553—21no—
393#552—21no—
394#551—22no—
395#548—21no—
396#546—21no—
397#539C22×C5912yes—
398#538C22×C5912yes—
399#534—21no—
400#529—21no—
401#525—21no—
402C2×C22⋊Q8C22×C5911yescharacteristic
403C2×#121—21no—
404C2×#121C22×C5911yescharacteristic
405C2×#121C22×C5911yescharacteristic
406#518—21no—
407C2×C4×D4C22×C5911yescharacteristic
408#483C22×C5912yescomplemented
409#481—21no—
410#480—21no—
411#480C22×C5912yes—
412#466—22no—
413#465—22no—
414#450C22×C5912yescomplemented
415#448—21no—
416#447—21no—
417#447C22×C5912yes—
418C2×C22⋊C8C22×C5911yescharacteristic
419C2×C22⋊C8C22×C5911yescharacteristic
420#398C22×C5911yescharacteristic, complemented
421#397C22×C5911yescharacteristic, complemented
422#394C22×C5911yescharacteristic, complemented
423#392C22×C5911yescharacteristic, complemented
424#388—21no—
425#386—21no—
426#386—21no—
427C2×#95C22×C5911yescharacteristic
428#328C22×C5912yescomplemented
429#328C22×C5912yescomplemented
430#327C22×C5912yes—
431#327C22×C5912yes—
432#324C22×C5912yescomplemented
433#323C22×C5912yescomplemented
434C59#1838411yescharacteristic, direct product factor, Sylow
435C2×#41—21no—
436C22×Q8D4×C5911yescharacteristic, complemented
437C22×D4—21no—
438C22×D4—21no—
439C22×D4—21no—
440C22×D4D4×C5911yescharacteristic
441C22×D4D4×C5911yescharacteristic, complemented
442C22×D4C23×C5911yescharacteristic
443C23×C4—21no—
444C23×C4D4×C5911yescharacteristic
445C23×C4C23×C5911yescharacteristic
446C2×SD16—22no—
447C2×D8—22no—
448C22×C8—21no—
449C22×C8—21no—
450#126—22no—
451#126—22no—
452#126—22no—
453#125—21no—
454#125—22no—
455#124—21no—
456#124—22no—
457#123—22no—
458#123—22no—
459#123—22no—
460#123—22no—
461#123—22no—
462C22⋊Q8—21no—
463C22⋊Q8—22no—
464C22⋊Q8—21no—
465C22⋊Q8—21no—
466C22⋊Q8D4×C5912yescomplemented
467C22⋊Q8C23×C5912yes—
468#121—21no—
469#121—22no—
470#121—22no—
471#121—22no—
472#121—21no—
473#121—21no—
474#121—21no—
475#121—21no—
476#121—21no—
477#121—21no—
478#121—44no—
479#121D4×C5912yescomplemented
480#121C23×C5912yes—
481#120—22no—
482#120—22no—
483C4×Q8—21no—
484C4×D4—22no—
485C4×D4—22no—
486C4×D4—22no—
487C4×D4—21no—
488C4×D4—21no—
489C4×D4—21no—
490C4×D4—21no—
491C4×D4—21no—
492C4×D4—22no—
493C4×D4—22no—
494#117—22no—
495#117—21no—
496#117—22no—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4D4×C5911yescharacteristic, complemented
500C2×C4⋊C4D4×C5911yescharacteristic, complemented
501C2×C4⋊C4C23×C5911yescharacteristic
502C2×C4⋊C4C23×C5911yescharacteristic
503C2×C22⋊C4—22no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4—21no—
506C2×C22⋊C4—21no—
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4D4×C5911yescharacteristic
512C2×C22⋊C4C23×C5911yescharacteristic
513C2×C42D4×C5911yescharacteristic
514#107—22no—
515#106—22no—
516#103—22no—
517#102—22no—
518#102—22no—
519#102—22no—
520C22⋊C8—21no—
521C22⋊C8—21no—
522C22⋊C8C23×C5912yes—
523C22⋊C8C23×C5912yes—
524#95—21no—
525#95—21no—
526#95—21no—
527#95C23×C5911yescharacteristic
528#95C23×C5911yescharacteristic
529C24—21no—
530C24—21no—
531C24C2×D4×C5911yescharacteristic
532C24C2×D4×C5911yescharacteristic
533#41—82no—
534C2×Q8—21no—
535C2×Q8—81no—
536C2×Q8C2×D4×C5912yes—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—22no—
540C2×D4—22no—
541C2×D4—22no—
542C2×D4—22no—
543C2×D4—22no—
544C2×D4—22no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—42no—
549C2×D4—42no—
550C2×D4—42no—
551C2×D4—42no—
552C2×D4—41no—
553C2×D4—41no—
554C2×D4—42no—
555C2×D4—42no—
556C2×D4—81no—
557C2×D4—81no—
558C2×D4—81no—
559C2×D4C2×D4×C5912yes—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—42no—
571C22×C4—42no—
572C22×C4—81no—
573C22×C4—81no—
574C22×C4—81no—
575C22×C4C2×D4×C5911yescharacteristic
576C22×C4C2×D4×C5911yescharacteristic
577C22×C4C2×D4×C5911yescharacteristic
578C22×C4C2×D4×C5911yescharacteristic
579C22×C4C2×D4×C5911yescharacteristic
580C22×C4C2×D4×C5911yescharacteristic
581C22×C4C2×D4×C5911yescharacteristic
582C22×C4C2×D4×C5911yescharacteristic
583C22×C4C24×C5911yescharacteristic
584SD16—82no—
585D8—82no—
586C2×C8—22no—
587C2×C8—22no—
588C2×C8—81no—
589C2×C8—81no—
590C4⋊C4—22no—
591C4⋊C4—22no—
592C4⋊C4—22no—
593C4⋊C4—22no—
594C4⋊C4—22no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—22no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—42no—
603C4⋊C4C2×D4×C5912yes—
604C4⋊C4C2×D4×C5912yes—
605C22⋊C4—22no—
606C22⋊C4—22no—
607C22⋊C4—22no—
608C22⋊C4—22no—
609C22⋊C4—22no—
610C22⋊C4—22no—
611C22⋊C4—21no—
612C22⋊C4—22no—
613C22⋊C4—21no—
614C22⋊C4—22no—
615C22⋊C4—22no—
616C22⋊C4—22no—
617C22⋊C4—21no—
618C22⋊C4—21no—
619C22⋊C4—42no—
620C22⋊C4—42no—
621C22⋊C4—42no—
622C22⋊C4—41no—
623C22⋊C4—41no—
624C22⋊C4—81no—
625C42—22no—
626C42—22no—
627C42—21no—
628C42—21no—
629C23—21no—
630C23—22no—
631C23—21no—
632C23—21no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—42no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—81no—
646C23—81no—
647C23#120×C5911yescharacteristic
648C23#120×C5911yescharacteristic
649C23#135×C5912yes—
650C23AGL(1,ℤ/8)×C5912yes—
651C23C22×D4×C5911yescharacteristic
652Q8—42no—
653Q8—42no—
654D4—42no—
655D4—42no—
656D4—42no—
657D4—42no—
658D4—42no—
659D4—42no—
660D4—44no—
661D4—42no—
662D4—42no—
663D4—82no—
664D4—82no—
665D4—84no—
666D4—82no—
667D4—82no—
668C2×C4—22no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—22no—
672C2×C4—21no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—42no—
684C2×C4—41no—
685C2×C4—42no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—81no—
696C2×C4—81no—
697C2×C4—81no—
698C2×C4—82no—
699C2×C4—82no—
700C2×C4—84no—
701C2×C4#120×C5911yescharacteristic
702C2×C4#120×C5911yescharacteristic
703C2×C4C22×D4×C5911yescharacteristic
704C2×C4C22×D4×C5911yescharacteristic
705C8—42no—
706C8—42no—
707C22—21no—
708C22—21no—
709C22—21no—
710C22—21no—
711C22—21no—
712C22—21no—
713C22—42no—
714C22—42no—
715C22—42no—
716C22—41no—
717C22—42no—
718C22—42no—
719C22—41no—
720C22—41no—
721C22—42no—
722C22—81no—
723C22—81no—
724C22—81no—
725C22—81no—
726C22—81no—
727C22—81no—
728C22—81no—
729C22—81no—
730C22—162no—
731C22C59×#44912yes—
732C22C59×#44912yes—
733C22C2×#120×C5911yescharacteristic
734C22C2×#135×C5911yescharacteristic
735C22C2×AGL(1,ℤ/8)×C5911yescharacteristic
736C4—21no—
737C4—21no—
738C4—21no—
739C4—21no—
740C4—42no—
741C4—41no—
742C4—42no—
743C4—41no—
744C4—42no—
745C4—41no—
746C4—42no—
747C4—81no—
748C4—81no—
749C2—21no—
750C2—21no—
751C2—22no—
752C2—22no—
753C2—81no—
754C2—82no—
755C2—161no—
756C2C2×C59×#44911yescharacteristic
757C2C59×#301811yescharacteristic
758C2C59×#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×#3505C2semidirect
2. C59×#3187C2semidirect
3. C59×#3186C2semidirect
4. C59×#2543C2semidirect
5. C59×#1612C2semidirect
6. C59×#1609C2semidirect
7. C59×#1600C2semidirect
8. C59×#1597C2semidirect
9. C2×C59×#328C2semidirect
10. C2×C59×#327C2semidirect
11. C59×#1459C2semidirect
29. C59×#483C22semidirect
35. C59×#450C22semidirect
41. C59×#398C22semidirect
42. C59×#397C22semidirect
43. C59×#394C22semidirect
44. C59×#392C22semidirect
49. C59×#328C22semidirect
50. C59×#328C22semidirect
53. C59×#324C22semidirect
54. C59×#323C22semidirect
56. C22×Q8×C59D4semidirect
61. C22×D4×C59D4semidirect
86. C22⋊Q8×C59D4semidirect
99. #121×C59D4semidirect
119. C2×C4⋊C4×C59D4semidirect
120. C2×C4⋊C4×C59D4semidirect
327. #18384C59direct (N × H)
370. #3505C2×C59semidirect
371. #3187C2×C59semidirect
372. #3186C2×C59semidirect
373. #2543C2×C59semidirect
374. #1612C2×C59semidirect
375. #1609C2×C59semidirect
376. #1600C2×C59semidirect
377. #1597C2×C59semidirect
378. C2×#328C2×C59semidirect
379. C2×#327C2×C59semidirect
380. #1459C2×C59semidirect
408. #483C22×C59semidirect
414. #450C22×C59semidirect
420. #398C22×C59semidirect
421. #397C22×C59semidirect
422. #394C22×C59semidirect
423. #392C22×C59semidirect
428. #328C22×C59semidirect
429. #328C22×C59semidirect
432. #324C22×C59semidirect
433. #323C22×C59semidirect
434. C59#18384direct (N × H)
436. C22×Q8D4×C59semidirect
441. C22×D4D4×C59semidirect
466. C22⋊Q8D4×C59semidirect
479. #121D4×C59semidirect
499. C2×C4⋊C4D4×C59semidirect
500. 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×#35052
C59×#31872
C59×#31862
C59×#25432
C59×#16122
C59×#16092
C59×#16002
C59×#15972
C2×C59×#3282
C2×C59×#3272
C59×#14592
#1838459