Finite Group Databasebeta

← C59×#18354 #28430463

Subgroups — C59×#18354 #28430463

Order 15104.

1022 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C59×#3505C211yesmaximal, characteristic, complemented
2C59×#3193C211yesmaximal, characteristic, complemented
3C59×#3192C211yesmaximal, characteristic, complemented
4C59×#2635C211yesmaximal, characteristic, complemented
5C59×#1618C212yesmaximal, complemented
6C59×#1615C212yesmaximal, complemented
7C59×#1600C212yesmaximal, complemented
8C59×#1597C212yesmaximal, complemented
9C59×#1511C211yesmaximal, characteristic, complemented
10C59×#1510C211yesmaximal, characteristic, complemented
11C59×#1465C211yesmaximal, 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×C59C2211yescharacteristic
25C2×#121×C59C2211yescharacteristic
26C59×#518—21no—
27C2×C4×D4×C59C2211yescharacteristic
28C59×#484C2212yescomplemented
29C59×#481—21no—
30C59×#481C2212yes—
31C59×#480—21no—
32C59×#469—22no—
33C59×#468—22no—
34C59×#450C2212yescomplemented
35C59×#448—21no—
36C59×#447—21no—
37C59×#447C2212yes—
38C59×#407C2211yescharacteristic
39C59×#407C2211yescharacteristic
40C59×#400C2211yescharacteristic, complemented
41C59×#399C2211yescharacteristic, complemented
42C59×#394—21no—
43C59×#394C2211yescharacteristic, complemented
44C59×#392—21no—
45C59×#392C2211yescharacteristic, complemented
46C59×#388—21no—
47C59×#386—21no—
48C59×#381C2211yescharacteristic
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×C59D411yescharacteristic
64C23×C4×C59C2311yescharacteristic
65C2×SD16×C59—22no—
66C2×D8×C59—22no—
67C2×M16×C59—21no—
68C2×M16×C59—21no—
69#126×C59—22no—
70#126×C59—22no—
71#126×C59—22no—
72#125×C59—21no—
73#125×C59—22no—
74#124×C59—21no—
75#124×C59—22no—
76#123×C59—22no—
77#123×C59—22no—
78#123×C59—22no—
79#123×C59—22no—
80#123×C59—22no—
81C22⋊Q8×C59—21no—
82C22⋊Q8×C59—22no—
83C22⋊Q8×C59—21no—
84C22⋊Q8×C59—21no—
85C22⋊Q8×C59D412yescomplemented
86C22⋊Q8×C59C2312yes—
87#121×C59—21no—
88#121×C59—22no—
89#121×C59—22no—
90#121×C59—22no—
91#121×C59—21no—
92#121×C59—21no—
93#121×C59—21no—
94#121×C59—21no—
95#121×C59—21no—
96#121×C59—21no—
97#121×C59D412yescomplemented
98#121×C59C2312yes—
99#120×C59—22no—
100#120×C59—22no—
101C4×Q8×C59—21no—
102C4×D4×C59—22no—
103C4×D4×C59—22no—
104C4×D4×C59—22no—
105C4×D4×C59—21no—
106C4×D4×C59—21no—
107C4×D4×C59—21no—
108C4×D4×C59—21no—
109C4×D4×C59—21no—
110C4×D4×C59—22no—
111C4×D4×C59—22no—
112#117×C59—22no—
113#117×C59—21no—
114#117×C59—22no—
115C2×C4⋊C4×C59—21no—
116C2×C4⋊C4×C59—21no—
117C2×C4⋊C4×C59D411yescharacteristic, complemented
118C2×C4⋊C4×C59D411yescharacteristic, complemented
119C2×C4⋊C4×C59C2311yescharacteristic
120C2×C4⋊C4×C59C2311yescharacteristic
121C2×C22⋊C4×C59—22no—
122C2×C22⋊C4×C59—21no—
123C2×C22⋊C4×C59—21no—
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×C59D411yescharacteristic
131C2×C22⋊C4×C59C2311yescharacteristic
132C2×C42×C59D411yescharacteristic
133#107×C59—22no—
134#106×C59—22no—
135#103×C59—22no—
136#102×C59—22no—
137#102×C59—22no—
138#102×C59—22no—
139C22⋊C8×C59—21no—
140C22⋊C8×C59—21no—
141C22⋊C8×C59C2312yes—
142C22⋊C8×C59C2312yes—
143#95×C59—21no—
144#95×C59—21no—
145#95×C59—21no—
146#95×C59C2311yescharacteristic
147#95×C59C2311yescharacteristic
148C24×C59—21no—
149C24×C59—21no—
150C24×C59C2×D411yescharacteristic
151C24×C59C2×D411yescharacteristic
152#41×C59—82no—
153C2×Q8×C59—21no—
154C2×Q8×C59—81no—
155C2×Q8×C59C2×D412yes—
156C2×D4×C59—21no—
157C2×D4×C59—21no—
158C2×D4×C59—22no—
159C2×D4×C59—22no—
160C2×D4×C59—22no—
161C2×D4×C59—22no—
162C2×D4×C59—21no—
163C2×D4×C59—21no—
164C2×D4×C59—21no—
165C2×D4×C59—41no—
166C2×D4×C59—41no—
167C2×D4×C59—42no—
168C2×D4×C59—42no—
169C2×D4×C59—42no—
170C2×D4×C59—41no—
171C2×D4×C59—41no—
172C2×D4×C59—81no—
173C2×D4×C59—81no—
174C2×D4×C59—81no—
175C2×D4×C59—81no—
176C2×D4×C59—81no—
177C2×D4×C59—81no—
178C2×D4×C59C2×D412yes—
179C22×C4×C59—21no—
180C22×C4×C59—22no—
181C22×C4×C59—22no—
182C22×C4×C59—21no—
183C22×C4×C59—21no—
184C22×C4×C59—21no—
185C22×C4×C59—21no—
186C22×C4×C59—21no—
187C22×C4×C59—21no—
188C22×C4×C59—21no—
189C22×C4×C59—81no—
190C22×C4×C59—81no—
191C22×C4×C59C2×D411yescharacteristic
192C22×C4×C59C2×D411yescharacteristic
193C22×C4×C59C2×D411yescharacteristic
194C22×C4×C59C2×D411yescharacteristic
195C22×C4×C59C2×D411yescharacteristic
196C22×C4×C59C2×D411yescharacteristic
197C22×C4×C59C2×D411yescharacteristic
198C22×C4×C59C2×D411yescharacteristic
199C22×C4×C59C2411yescharacteristic
200SD16×C59—82no—
201D8×C59—82no—
202M16×C59—81no—
203M16×C59—81no—
204C2×C8×C59—22no—
205C2×C8×C59—22no—
206C4⋊C4×C59—22no—
207C4⋊C4×C59—22no—
208C4⋊C4×C59—22no—
209C4⋊C4×C59—22no—
210C4⋊C4×C59—22no—
211C4⋊C4×C59—21no—
212C4⋊C4×C59—21no—
213C4⋊C4×C59—22no—
214C4⋊C4×C59—21no—
215C4⋊C4×C59—21no—
216C4⋊C4×C59—21no—
217C4⋊C4×C59—21no—
218C4⋊C4×C59—81no—
219C4⋊C4×C59C2×D412yes—
220C4⋊C4×C59C2×D412yes—
221C22⋊C4×C59—22no—
222C22⋊C4×C59—22no—
223C22⋊C4×C59—22no—
224C22⋊C4×C59—22no—
225C22⋊C4×C59—22no—
226C22⋊C4×C59—22no—
227C22⋊C4×C59—21no—
228C22⋊C4×C59—22no—
229C22⋊C4×C59—21no—
230C22⋊C4×C59—22no—
231C22⋊C4×C59—22no—
232C22⋊C4×C59—22no—
233C22⋊C4×C59—21no—
234C22⋊C4×C59—21no—
235C22⋊C4×C59—42no—
236C22⋊C4×C59—41no—
237C22⋊C4×C59—41no—
238C22⋊C4×C59—81no—
239C22⋊C4×C59—81no—
240C22⋊C4×C59—81no—
241C22⋊C4×C59—81no—
242C42×C59—22no—
243C42×C59—22no—
244C42×C59—21no—
245C42×C59—21no—
246C23×C59—21no—
247C23×C59—21no—
248C23×C59—21no—
249C23×C59—22no—
250C23×C59—21no—
251C23×C59—21no—
252C23×C59—41no—
253C23×C59—41no—
254C23×C59—41no—
255C23×C59—41no—
256C23×C59—42no—
257C23×C59—41no—
258C23×C59—41no—
259C23×C59—41no—
260C23×C59—41no—
261C23×C59—41no—
262C23×C59—41no—
263C23×C59—41no—
264C23×C59—81no—
265C23×C59—81no—
266C23×C59#12011yescharacteristic
267C23×C59#12011yescharacteristic
268C23×C59C22×D411yescharacteristic
269Q8×C59—42no—
270Q8×C59—42no—
271D4×C59—42no—
272D4×C59—42no—
273D4×C59—42no—
274D4×C59—42no—
275D4×C59—42no—
276D4×C59—42no—
277D4×C59—44no—
278D4×C59—42no—
279D4×C59—42no—
280D4×C59—82no—
281D4×C59—82no—
282D4×C59—82no—
283D4×C59—82no—
284D4×C59—84no—
285C2×C4×C59—21no—
286C2×C4×C59—21no—
287C2×C4×C59—22no—
288C2×C4×C59—21no—
289C2×C4×C59—22no—
290C2×C4×C59—22no—
291C2×C4×C59—21no—
292C2×C4×C59—21no—
293C2×C4×C59—41no—
294C2×C4×C59—41no—
295C2×C4×C59—41no—
296C2×C4×C59—41no—
297C2×C4×C59—41no—
298C2×C4×C59—41no—
299C2×C4×C59—42no—
300C2×C4×C59—42no—
301C2×C4×C59—41no—
302C2×C4×C59—41no—
303C2×C4×C59—41no—
304C2×C4×C59—41no—
305C2×C4×C59—41no—
306C2×C4×C59—41no—
307C2×C4×C59—41no—
308C2×C4×C59—41no—
309C2×C4×C59—41no—
310C2×C4×C59—41no—
311C2×C4×C59—41no—
312C2×C4×C59—81no—
313C2×C4×C59—81no—
314C2×C4×C59—81no—
315C2×C4×C59—82no—
316C2×C4×C59—82no—
317C2×C4×C59#12011yescharacteristic
318C2×C4×C59#12011yescharacteristic
319C2×C4×C59C22×D411yescharacteristic
320C2×C4×C59C22×D411yescharacteristic
321C8×C59—42no—
322C8×C59—42no—
323#18354C5911yesmaximal, characteristic, direct product factor, Sylow
324C22×C59—21no—
325C22×C59—21no—
326C22×C59—21no—
327C22×C59—21no—
328C22×C59—21no—
329C22×C59—21no—
330C22×C59—21no—
331C22×C59—21no—
332C22×C59—42no—
333C22×C59—41no—
334C22×C59—42no—
335C22×C59—42no—
336C22×C59—41no—
337C22×C59—41no—
338C22×C59—42no—
339C22×C59—81no—
340C22×C59—81no—
341C22×C59—81no—
342C22×C59—81no—
343C22×C59—81no—
344C22×C59—81no—
345C22×C59—81no—
346C22×C59—81no—
347C22×C59—81no—
348C22×C59—81no—
349C22×C59—162no—
350C22×C59C2×#12011yescharacteristic
351C22×C59#57511yescharacteristic
352C22×C59#57511yescharacteristic
353C4×C59—21no—
354C4×C59—21no—
355C4×C59—21no—
356C4×C59—21no—
357C4×C59—41no—
358C4×C59—42no—
359C4×C59—41no—
360C4×C59—42no—
361C4×C59—41no—
362C4×C59—42no—
363C4×C59—81no—
364C4×C59—81no—
365C4×C59—81no—
366#3505C2×C5911yescharacteristic, complemented
367#3193C2×C5911yescharacteristic, complemented
368#3192C2×C5911yescharacteristic, complemented
369#2635C2×C5911yescharacteristic, complemented
370#1618C2×C5912yescomplemented
371#1615C2×C5912yescomplemented
372#1600C2×C5912yescomplemented
373#1597C2×C5912yescomplemented
374#1511C2×C5911yescharacteristic, complemented
375#1510C2×C5911yescharacteristic, complemented
376#1465C2×C5911yescharacteristic, complemented
377C2×C59—21no—
378C2×C59—21no—
379C2×C59—41no—
380C2×C59—41no—
381C2×C59—81no—
382C2×C59—82no—
383C2×C59—161no—
384C2×C59#300511yescharacteristic
385C2×C59#302111yescharacteristic
386C2×C59#302611yescharacteristic
387#553—22no—
388#553—21no—
389#552—21no—
390#551—22no—
391#548—21no—
392#546—21no—
393#539C22×C5912yes—
394#538C22×C5912yes—
395#534—21no—
396#529—21no—
397#525—21no—
398C2×C22⋊Q8C22×C5911yescharacteristic
399C2×#121C22×C5911yescharacteristic
400C2×#121C22×C5911yescharacteristic
401#518—21no—
402C2×C4×D4C22×C5911yescharacteristic
403#484C22×C5912yescomplemented
404#481—21no—
405#481C22×C5912yes—
406#480—21no—
407#469—22no—
408#468—22no—
409#450C22×C5912yescomplemented
410#448—21no—
411#447—21no—
412#447C22×C5912yes—
413#407C22×C5911yescharacteristic
414#407C22×C5911yescharacteristic
415#400C22×C5911yescharacteristic, complemented
416#399C22×C5911yescharacteristic, complemented
417#394—21no—
418#394C22×C5911yescharacteristic, complemented
419#392—21no—
420#392C22×C5911yescharacteristic, complemented
421#388—21no—
422#386—21no—
423#381C22×C5911yescharacteristic
424#328C22×C5912yescomplemented
425#328C22×C5912yescomplemented
426#327C22×C5912yes—
427#327C22×C5912yes—
428#324C22×C5912yescomplemented
429#323C22×C5912yescomplemented
430C59#1835411yescharacteristic, direct product factor, Sylow
431C2×#41—21no—
432C22×Q8D4×C5911yescharacteristic, complemented
433C22×D4—21no—
434C22×D4—21no—
435C22×D4—21no—
436C22×D4D4×C5911yescharacteristic
437C22×D4D4×C5911yescharacteristic, complemented
438C22×D4C23×C5911yescharacteristic
439C23×C4D4×C5911yescharacteristic
440C23×C4C23×C5911yescharacteristic
441C2×SD16—22no—
442C2×D8—22no—
443C2×M16—21no—
444C2×M16—21no—
445#126—22no—
446#126—22no—
447#126—22no—
448#125—21no—
449#125—22no—
450#124—21no—
451#124—22no—
452#123—22no—
453#123—22no—
454#123—22no—
455#123—22no—
456#123—22no—
457C22⋊Q8—21no—
458C22⋊Q8—22no—
459C22⋊Q8—21no—
460C22⋊Q8—21no—
461C22⋊Q8D4×C5912yescomplemented
462C22⋊Q8C23×C5912yes—
463#121—21no—
464#121—22no—
465#121—22no—
466#121—22no—
467#121—21no—
468#121—21no—
469#121—21no—
470#121—21no—
471#121—21no—
472#121—21no—
473#121D4×C5912yescomplemented
474#121C23×C5912yes—
475#120—22no—
476#120—22no—
477C4×Q8—21no—
478C4×D4—22no—
479C4×D4—22no—
480C4×D4—22no—
481C4×D4—21no—
482C4×D4—21no—
483C4×D4—21no—
484C4×D4—21no—
485C4×D4—21no—
486C4×D4—22no—
487C4×D4—22no—
488#117—22no—
489#117—21no—
490#117—22no—
491C2×C4⋊C4—21no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4D4×C5911yescharacteristic, complemented
494C2×C4⋊C4D4×C5911yescharacteristic, complemented
495C2×C4⋊C4C23×C5911yescharacteristic
496C2×C4⋊C4C23×C5911yescharacteristic
497C2×C22⋊C4—22no—
498C2×C22⋊C4—21no—
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—21no—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4—21no—
506C2×C22⋊C4D4×C5911yescharacteristic
507C2×C22⋊C4C23×C5911yescharacteristic
508C2×C42D4×C5911yescharacteristic
509#107—22no—
510#106—22no—
511#103—22no—
512#102—22no—
513#102—22no—
514#102—22no—
515C22⋊C8—21no—
516C22⋊C8—21no—
517C22⋊C8C23×C5912yes—
518C22⋊C8C23×C5912yes—
519#95—21no—
520#95—21no—
521#95—21no—
522#95C23×C5911yescharacteristic
523#95C23×C5911yescharacteristic
524C24—21no—
525C24—21no—
526C24C2×D4×C5911yescharacteristic
527C24C2×D4×C5911yescharacteristic
528#41—82no—
529C2×Q8—21no—
530C2×Q8—81no—
531C2×Q8C2×D4×C5912yes—
532C2×D4—21no—
533C2×D4—21no—
534C2×D4—22no—
535C2×D4—22no—
536C2×D4—22no—
537C2×D4—22no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—41no—
542C2×D4—41no—
543C2×D4—42no—
544C2×D4—42no—
545C2×D4—42no—
546C2×D4—41no—
547C2×D4—41no—
548C2×D4—81no—
549C2×D4—81no—
550C2×D4—81no—
551C2×D4—81no—
552C2×D4—81no—
553C2×D4—81no—
554C2×D4C2×D4×C5912yes—
555C22×C4—21no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—81no—
566C22×C4—81no—
567C22×C4C2×D4×C5911yescharacteristic
568C22×C4C2×D4×C5911yescharacteristic
569C22×C4C2×D4×C5911yescharacteristic
570C22×C4C2×D4×C5911yescharacteristic
571C22×C4C2×D4×C5911yescharacteristic
572C22×C4C2×D4×C5911yescharacteristic
573C22×C4C2×D4×C5911yescharacteristic
574C22×C4C2×D4×C5911yescharacteristic
575C22×C4C24×C5911yescharacteristic
576SD16—82no—
577D8—82no—
578M16—81no—
579M16—81no—
580C2×C8—22no—
581C2×C8—22no—
582C4⋊C4—22no—
583C4⋊C4—22no—
584C4⋊C4—22no—
585C4⋊C4—22no—
586C4⋊C4—22no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—22no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—81no—
595C4⋊C4C2×D4×C5912yes—
596C4⋊C4C2×D4×C5912yes—
597C22⋊C4—22no—
598C22⋊C4—22no—
599C22⋊C4—22no—
600C22⋊C4—22no—
601C22⋊C4—22no—
602C22⋊C4—22no—
603C22⋊C4—21no—
604C22⋊C4—22no—
605C22⋊C4—21no—
606C22⋊C4—22no—
607C22⋊C4—22no—
608C22⋊C4—22no—
609C22⋊C4—21no—
610C22⋊C4—21no—
611C22⋊C4—42no—
612C22⋊C4—41no—
613C22⋊C4—41no—
614C22⋊C4—81no—
615C22⋊C4—81no—
616C22⋊C4—81no—
617C22⋊C4—81no—
618C42—22no—
619C42—22no—
620C42—21no—
621C42—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—22no—
626C23—21no—
627C23—21no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—42no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—81no—
641C23—81no—
642C23#120×C5911yescharacteristic
643C23#120×C5911yescharacteristic
644C23C22×D4×C5911yescharacteristic
645Q8—42no—
646Q8—42no—
647D4—42no—
648D4—42no—
649D4—42no—
650D4—42no—
651D4—42no—
652D4—42no—
653D4—44no—
654D4—42no—
655D4—42no—
656D4—82no—
657D4—82no—
658D4—82no—
659D4—82no—
660D4—84no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—22no—
664C2×C4—21no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—81no—
689C2×C4—81no—
690C2×C4—81no—
691C2×C4—82no—
692C2×C4—82no—
693C2×C4#120×C5911yescharacteristic
694C2×C4#120×C5911yescharacteristic
695C2×C4C22×D4×C5911yescharacteristic
696C2×C4C22×D4×C5911yescharacteristic
697C8—42no—
698C8—42no—
699C22—21no—
700C22—21no—
701C22—21no—
702C22—21no—
703C22—21no—
704C22—21no—
705C22—21no—
706C22—21no—
707C22—42no—
708C22—41no—
709C22—42no—
710C22—42no—
711C22—41no—
712C22—41no—
713C22—42no—
714C22—81no—
715C22—81no—
716C22—81no—
717C22—81no—
718C22—81no—
719C22—81no—
720C22—81no—
721C22—81no—
722C22—81no—
723C22—81no—
724C22—162no—
725C22C2×#120×C5911yescharacteristic
726C22C59×#57511yescharacteristic
727C22C59×#57511yescharacteristic
728C4—21no—
729C4—21no—
730C4—21no—
731C4—21no—
732C4—41no—
733C4—42no—
734C4—41no—
735C4—42no—
736C4—41no—
737C4—42no—
738C4—81no—
739C4—81no—
740C4—81no—
741C2—21no—
742C2—21no—
743C2—41no—
744C2—41no—
745C2—81no—
746C2—82no—
747C2—161no—
748C2C59×#300511yescharacteristic
749C2C59×#302111yescharacteristic
750C2C59×#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×#3193C2semidirect
3. C59×#3192C2semidirect
4. C59×#2635C2semidirect
5. C59×#1618C2semidirect
6. C59×#1615C2semidirect
7. C59×#1600C2semidirect
8. C59×#1597C2semidirect
9. C59×#1511C2semidirect
10. C59×#1510C2semidirect
11. C59×#1465C2semidirect
28. C59×#484C22semidirect
34. C59×#450C22semidirect
40. C59×#400C22semidirect
41. C59×#399C22semidirect
43. C59×#394C22semidirect
45. C59×#392C22semidirect
49. C59×#328C22semidirect
50. C59×#328C22semidirect
53. C59×#324C22semidirect
54. C59×#323C22semidirect
56. C22×Q8×C59D4semidirect
61. C22×D4×C59D4semidirect
85. C22⋊Q8×C59D4semidirect
97. #121×C59D4semidirect
117. C2×C4⋊C4×C59D4semidirect
118. C2×C4⋊C4×C59D4semidirect
323. #18354C59direct (N × H)
366. #3505C2×C59semidirect
367. #3193C2×C59semidirect
368. #3192C2×C59semidirect
369. #2635C2×C59semidirect
370. #1618C2×C59semidirect
371. #1615C2×C59semidirect
372. #1600C2×C59semidirect
373. #1597C2×C59semidirect
374. #1511C2×C59semidirect
375. #1510C2×C59semidirect
376. #1465C2×C59semidirect
403. #484C22×C59semidirect
409. #450C22×C59semidirect
415. #400C22×C59semidirect
416. #399C22×C59semidirect
418. #394C22×C59semidirect
420. #392C22×C59semidirect
424. #328C22×C59semidirect
425. #328C22×C59semidirect
428. #324C22×C59semidirect
429. #323C22×C59semidirect
430. C59#18354direct (N × H)
432. C22×Q8D4×C59semidirect
437. C22×D4D4×C59semidirect
461. C22⋊Q8D4×C59semidirect
473. #121D4×C59semidirect
493. C2×C4⋊C4D4×C59semidirect
494. 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×#31932
C59×#31922
C59×#26352
C59×#16182
C59×#16152
C59×#16002
C59×#15972
C59×#15112
C59×#15102
C59×#14652
#1835459