Finite Group Databasebeta

← C59×#24491 #28436600

Subgroups — C59×#24491 #28436600

Order 15104.

964 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C59×#483C211yesmaximal, characteristic, complemented
2C2×C59×#417C211yesmaximal, characteristic
3C59×#2432C211yesmaximal, characteristic
4C59×#2345C211yesmaximal, characteristic, complemented
5C59×#2066C211yesmaximal, characteristic, complemented
6C59×#2065C211yesmaximal, characteristic, complemented
7C59×#2043C211yesmaximal, characteristic, complemented
8C59×#2042C211yesmaximal, characteristic, complemented
9C59×#1983C211yesmaximal, characteristic, complemented
10C59×#1981C211yesmaximal, characteristic, complemented
11C59×#1927C211yesmaximal, characteristic, complemented
12C59×#1926C211yesmaximal, characteristic, complemented
13C59×#1894C211yesmaximal, characteristic, complemented
14C59×#1851C211yesmaximal, characteristic, complemented
15C59×#1788C211yesmaximal, characteristic
16C22×#41×C59C2211yescharacteristic
17C22×M16×C59C2211yescharacteristic
18C2×C4⋊Q8×C59C2211yescharacteristic
19C2×#124×C59C2211yescharacteristic
20C2×C22⋊Q8×C59C2211yescharacteristic
21C22×C4⋊C4×C59C2211yescharacteristic
22C59×#483—24no—
23C2×#106×C59C2211yescharacteristic
24C2×#106×C59C2211yescharacteristic
25C2×C4⋊C8×C59C2211yescharacteristic
26C2×C4⋊C8×C59C2211yescharacteristic
27C59×#417—24no—
28C2×#103×C59C2211yescharacteristic
29C2×#103×C59C2211yescharacteristic
30C2×#103×C59C2211yescharacteristic
31C2×#103×C59C2211yescharacteristic
32C2×#103×C59C2211yescharacteristic
33C2×#103×C59C2211yescharacteristic
34C2×#103×C59C2211yescharacteristic
35C2×#103×C59C2211yescharacteristic
36C2×#102×C59C2211yescharacteristic
37C2×#102×C59C2211yescharacteristic
38C2×#102×C59C2211yescharacteristic
39C2×#102×C59C2211yescharacteristic
40C2×C22⋊C8×C59C2211yescharacteristic
41C59×#394—21no—
42C59×#394—21no—
43C59×#391C2211yescharacteristic
44C59×#390C2211yescharacteristic
45C59×#389C2211yescharacteristic
46C59×#389C2211yescharacteristic
47C59×#387—21no—
48C59×#387—21no—
49C59×#385—21no—
50C59×#385—21no—
51C59×#380—21no—
52C59×#380C2211yescharacteristic
53C4×C4⋊C4×C59C2211yescharacteristic
54C4×C4⋊C4×C59C2211yescharacteristic
55C4×C22⋊C4×C59—21no—
56C4×C22⋊C4×C59C2211yescharacteristic
57C59×#340C2211yescharacteristic
58C59×#340C2211yescharacteristic
59C59×#336C2211yescharacteristic
60C59×#336C2211yescharacteristic
61C2×#41×C59—22no—
62C2×#41×C59—22no—
63C2×#41×C59—22no—
64C2×#41×C59—22no—
65C2×#41×C59—41no—
66C2×#41×C59—41no—
67C22×Q8×C59C2311yescharacteristic
68C22×Q8×C59C2311yescharacteristic
69C22×D4×C59—21no—
70C22×D4×C59C2311yescharacteristic
71C23×C4×C59—21no—
72C23×C4×C59—21no—
73C23×C4×C59C2311yescharacteristic
74C2×M16×C59—22no—
75C2×M16×C59—41no—
76C2×M16×C59—41no—
77C22×C8×C59C2311yescharacteristic
78C22×C8×C59C2311yescharacteristic
79C22×C8×C59C2311yescharacteristic
80C22×C8×C59C2311yescharacteristic
81C4⋊Q8×C59—22no—
82C4⋊Q8×C59—41no—
83#124×C59—22no—
84#124×C59—41no—
85C22⋊Q8×C59—22no—
86C22⋊Q8×C59—22no—
87C2×C4⋊C4×C59—21no—
88C2×C4⋊C4×C59—22no—
89C2×C4⋊C4×C59—21no—
90C2×C4⋊C4×C59—21no—
91C2×C4⋊C4×C59—21no—
92C2×C4⋊C4×C59—21no—
93C2×C4⋊C4×C59—21no—
94C2×C4⋊C4×C59D414yes—
95C2×C4⋊C4×C59C2311yescharacteristic
96C2×C4⋊C4×C59C2311yescharacteristic
97C2×C4⋊C4×C59C2311yescharacteristic
98C2×C4⋊C4×C59C2311yescharacteristic
99C2×C4⋊C4×C59C2311yescharacteristic
100C2×C22⋊C4×C59—21no—
101C2×C22⋊C4×C59—21no—
102C2×C22⋊C4×C59—21no—
103C2×C22⋊C4×C59—21no—
104C2×C22⋊C4×C59—21no—
105C2×C22⋊C4×C59—21no—
106C2×C22⋊C4×C59D411yescharacteristic
107C2×C22⋊C4×C59D411yescharacteristic
108C2×C42×C59—21no—
109C2×C42×C59—21no—
110C2×C42×C59C2311yescharacteristic
111C2×C42×C59C2311yescharacteristic
112#106×C59—22no—
113#106×C59—22no—
114C4⋊C8×C59—41no—
115C4⋊C8×C59—41no—
116#103×C59—22no—
117#103×C59—22no—
118#103×C59—22no—
119#103×C59—22no—
120#103×C59—22no—
121#103×C59—41no—
122#103×C59—41no—
123#103×C59—41no—
124#102×C59—22no—
125#102×C59—22no—
126#102×C59—22no—
127#102×C59—41no—
128C22⋊C8×C59—22no—
129#95×C59—21no—
130#95×C59—21no—
131#95×C59—21no—
132#95×C59—21no—
133#95×C59—21no—
134#95×C59—21no—
135#95×C59—21no—
136#95×C59D411yescharacteristic
137#95×C59D411yescharacteristic
138C24×C59—21no—
139C24×C59C2×D411yescharacteristic
140#41×C59—28no—
141#41×C59—44no—
142#41×C59—44no—
143#41×C59—44no—
144C2×Q8×C59—21no—
145C2×Q8×C59—21no—
146C2×Q8×C59—21no—
147C2×Q8×C59—21no—
148C2×Q8×C59—21no—
149C2×Q8×C59—21no—
150C2×Q8×C59—21no—
151C2×Q8×C59—21no—
152C2×Q8×C59—21no—
153C2×Q8×C59—21no—
154C2×Q8×C59—21no—
155C2×Q8×C59#4112yes—
156C2×D4×C59—21no—
157C2×D4×C59—21no—
158C2×D4×C59—21no—
159C2×D4×C59—21no—
160C2×D4×C59—21no—
161C2×D4×C59—42no—
162C2×D4×C59—42no—
163C2×D4×C59—42no—
164C2×D4×C59#4112yes—
165C22×C4×C59—21no—
166C22×C4×C59—21no—
167C22×C4×C59—21no—
168C22×C4×C59—21no—
169C22×C4×C59—21no—
170C22×C4×C59—21no—
171C22×C4×C59—21no—
172C22×C4×C59—24no—
173C22×C4×C59—21no—
174C22×C4×C59—21no—
175C22×C4×C59—21no—
176C22×C4×C59—21no—
177C22×C4×C59—42no—
178C22×C4×C59—42no—
179C22×C4×C59—42no—
180C22×C4×C59—81no—
181C22×C4×C59—81no—
182C22×C4×C59C2×D411yescharacteristic
183C22×C4×C59C2×D411yescharacteristic
184C22×C4×C59C2×D411yescharacteristic
185C22×C4×C59C2×D411yescharacteristic
186C22×C4×C59C2×D412yes—
187C22×C4×C59C2×D411yescharacteristic
188C22×C4×C59#4112yes—
189C22×C4×C59C2411yescharacteristic
190M16×C59—44no—
191C2×C8×C59—21no—
192C2×C8×C59—21no—
193C2×C8×C59—21no—
194C2×C8×C59—21no—
195C2×C8×C59—21no—
196C2×C8×C59—21no—
197C2×C8×C59—21no—
198C2×C8×C59—21no—
199C2×C8×C59—21no—
200C2×C8×C59—21no—
201C2×C8×C59—21no—
202C2×C8×C59—21no—
203C4⋊C4×C59—24no—
204C4⋊C4×C59—21no—
205C4⋊C4×C59—21no—
206C4⋊C4×C59—21no—
207C4⋊C4×C59—21no—
208C4⋊C4×C59—21no—
209C4⋊C4×C59—21no—
210C4⋊C4×C59—21no—
211C4⋊C4×C59—21no—
212C4⋊C4×C59—42no—
213C4⋊C4×C59—42no—
214C4⋊C4×C59—42no—
215C4⋊C4×C59—81no—
216C4⋊C4×C59—81no—
217C4⋊C4×C59C2×D412yes—
218C4⋊C4×C59C2×D412yes—
219C22⋊C4×C59—22no—
220C22⋊C4×C59—41no—
221C22⋊C4×C59—42no—
222C22⋊C4×C59—42no—
223C22⋊C4×C59—42no—
224C22⋊C4×C59—42no—
225C22⋊C4×C59—42no—
226C22⋊C4×C59—42no—
227C42×C59—21no—
228C42×C59—21no—
229C42×C59—21no—
230C42×C59—21no—
231C42×C59—81no—
232C42×C59—81no—
233C23×C59—21no—
234C23×C59—21no—
235C23×C59—21no—
236C23×C59—21no—
237C23×C59—21no—
238C23×C59—21no—
239C23×C59—22no—
240C23×C59—41no—
241C23×C59—41no—
242C23×C59—41no—
243C23×C59—41no—
244C23×C59—41no—
245C23×C59—41no—
246C23×C59#12112yes—
247C23×C59C22×D411yescharacteristic
248Q8×C59—22no—
249Q8×C59—22no—
250Q8×C59—41no—
251Q8×C59—41no—
252Q8×C59—41no—
253Q8×C59—41no—
254Q8×C59—41no—
255Q8×C59—41no—
256D4×C59—22no—
257D4×C59—22no—
258D4×C59—48no—
259D4×C59—41no—
260D4×C59—41no—
261C2×C4×C59—21no—
262C2×C4×C59—21no—
263C2×C4×C59—21no—
264C2×C4×C59—21no—
265C2×C4×C59—22no—
266C2×C4×C59—22no—
267C2×C4×C59—22no—
268C2×C4×C59—22no—
269C2×C4×C59—22no—
270C2×C4×C59—22no—
271C2×C4×C59—21no—
272C2×C4×C59—21no—
273C2×C4×C59—21no—
274C2×C4×C59—22no—
275C2×C4×C59—21no—
276C2×C4×C59—21no—
277C2×C4×C59—21no—
278C2×C4×C59—21no—
279C2×C4×C59—21no—
280C2×C4×C59—21no—
281C2×C4×C59—48no—
282C2×C4×C59—41no—
283C2×C4×C59—41no—
284C2×C4×C59—41no—
285C2×C4×C59—41no—
286C2×C4×C59—41no—
287C2×C4×C59—41no—
288C2×C4×C59—41no—
289C2×C4×C59—41no—
290C2×C4×C59—41no—
291C2×C4×C59—41no—
292C2×C4×C59—41no—
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—41no—
300C2×C4×C59—84no—
301C2×C4×C59#12112yes—
302C2×C4×C59#13712yes—
303C2×C4×C59C22×D411yescharacteristic
304C2×C4×C59C2×#4111yescharacteristic
305C2×C4×C59C2×#4111yescharacteristic
306C2×C4×C59C2×#4111yescharacteristic
307C2×C4×C59H(5,𝔽2)11yescharacteristic
308C2×C4×C59H(5,𝔽2)11yescharacteristic
309C8×C59—41no—
310C8×C59—41no—
311C8×C59—41no—
312C8×C59—41no—
313#24491C5911yesmaximal, characteristic, direct product factor, Sylow
314C22×C59—22no—
315C22×C59—22no—
316C22×C59—22no—
317C22×C59—41no—
318C22×C59—41no—
319C22×C59—41no—
320C22×C59—41no—
321C22×C59—42no—
322C22×C59—42no—
323C22×C59—42no—
324C22×C59—81no—
325C22×C59—81no—
326C22×C59—81no—
327C22×C59—81no—
328C22×C59C2×#12111yescharacteristic
329C22×C59#54611yescharacteristic
330C22×C59#54611yescharacteristic
331C22×C59C2×#13711yescharacteristic
332C22×C59#57511yescharacteristic
333C22×C59#57711yescharacteristic
334C22×C59#57711yescharacteristic
335C4×C59—22no—
336C4×C59—22no—
337C4×C59—41no—
338C4×C59—42no—
339C4×C59—42no—
340C4×C59—42no—
341C4×C59—41no—
342C4×C59—41no—
343C4×C59—81no—
344C4×C59—81no—
345C4×C59—81no—
346C4×C59—81no—
347C4×C59#52511yescharacteristic
348C4×C59#53511yescharacteristic
349C4×C59#55111yescharacteristic
350C4×C59#55111yescharacteristic
351C2×#483C2×C5911yescharacteristic, complemented
352C2×#417C2×C5911yescharacteristic
353#2432C2×C5911yescharacteristic
354#2345C2×C5911yescharacteristic, complemented
355#2066C2×C5911yescharacteristic, complemented
356#2065C2×C5911yescharacteristic, complemented
357#2043C2×C5911yescharacteristic, complemented
358#2042C2×C5911yescharacteristic, complemented
359#1983C2×C5911yescharacteristic, complemented
360#1981C2×C5911yescharacteristic, complemented
361#1927C2×C5911yescharacteristic, complemented
362#1926C2×C5911yescharacteristic, complemented
363#1894C2×C5911yescharacteristic, complemented
364#1851C2×C5911yescharacteristic, complemented
365#1788C2×C5911yescharacteristic
366C2×C59—42no—
367C2×C59—82no—
368C2×C59#241111yescharacteristic
369C2×C59#303711yescharacteristic
370C2×C59#304211yescharacteristic
371C2×C59#330711yescharacteristic
372C2×C59#331611yescharacteristic
373C2×C59#332611yescharacteristic
374C2×C59#333111yescharacteristic
375C22×#41C22×C5911yescharacteristic
376C22×M16C22×C5911yescharacteristic
377C2×C4⋊Q8C22×C5911yescharacteristic
378C2×#124C22×C5911yescharacteristic
379C2×C22⋊Q8C22×C5911yescharacteristic
380C22×C4⋊C4C22×C5911yescharacteristic
381#483—24no—
382C2×#106C22×C5911yescharacteristic
383C2×#106C22×C5911yescharacteristic
384C2×C4⋊C8C22×C5911yescharacteristic
385C2×C4⋊C8C22×C5911yescharacteristic
386#417—24no—
387C2×#103C22×C5911yescharacteristic
388C2×#103C22×C5911yescharacteristic
389C2×#103C22×C5911yescharacteristic
390C2×#103C22×C5911yescharacteristic
391C2×#103C22×C5911yescharacteristic
392C2×#103C22×C5911yescharacteristic
393C2×#103C22×C5911yescharacteristic
394C2×#103C22×C5911yescharacteristic
395C2×#102C22×C5911yescharacteristic
396C2×#102C22×C5911yescharacteristic
397C2×#102C22×C5911yescharacteristic
398C2×#102C22×C5911yescharacteristic
399C2×C22⋊C8C22×C5911yescharacteristic
400#394—21no—
401#394—21no—
402#391C22×C5911yescharacteristic
403#390C22×C5911yescharacteristic
404#389C22×C5911yescharacteristic
405#389C22×C5911yescharacteristic
406#387—21no—
407#387—21no—
408#385—21no—
409#385—21no—
410#380—21no—
411#380C22×C5911yescharacteristic
412C4×C4⋊C4C22×C5911yescharacteristic
413C4×C4⋊C4C22×C5911yescharacteristic
414C4×C22⋊C4—21no—
415C4×C22⋊C4C22×C5911yescharacteristic
416#340C22×C5911yescharacteristic
417#340C22×C5911yescharacteristic
418#336C22×C5911yescharacteristic
419#336C22×C5911yescharacteristic
420C59#2449111yescharacteristic, direct product factor, Sylow
421C2×#41—22no—
422C2×#41—22no—
423C2×#41—22no—
424C2×#41—22no—
425C2×#41—41no—
426C2×#41—41no—
427C22×Q8C23×C5911yescharacteristic
428C22×Q8C23×C5911yescharacteristic
429C22×D4—21no—
430C22×D4C23×C5911yescharacteristic
431C23×C4—21no—
432C23×C4—21no—
433C23×C4C23×C5911yescharacteristic
434C2×M16—22no—
435C2×M16—41no—
436C2×M16—41no—
437C22×C8C23×C5911yescharacteristic
438C22×C8C23×C5911yescharacteristic
439C22×C8C23×C5911yescharacteristic
440C22×C8C23×C5911yescharacteristic
441C4⋊Q8—22no—
442C4⋊Q8—41no—
443#124—22no—
444#124—41no—
445C22⋊Q8—22no—
446C22⋊Q8—22no—
447C2×C4⋊C4—21no—
448C2×C4⋊C4—22no—
449C2×C4⋊C4—21no—
450C2×C4⋊C4—21no—
451C2×C4⋊C4—21no—
452C2×C4⋊C4—21no—
453C2×C4⋊C4—21no—
454C2×C4⋊C4D4×C5914yes—
455C2×C4⋊C4C23×C5911yescharacteristic
456C2×C4⋊C4C23×C5911yescharacteristic
457C2×C4⋊C4C23×C5911yescharacteristic
458C2×C4⋊C4C23×C5911yescharacteristic
459C2×C4⋊C4C23×C5911yescharacteristic
460C2×C22⋊C4—21no—
461C2×C22⋊C4—21no—
462C2×C22⋊C4—21no—
463C2×C22⋊C4—21no—
464C2×C22⋊C4—21no—
465C2×C22⋊C4—21no—
466C2×C22⋊C4D4×C5911yescharacteristic
467C2×C22⋊C4D4×C5911yescharacteristic
468C2×C42—21no—
469C2×C42—21no—
470C2×C42C23×C5911yescharacteristic
471C2×C42C23×C5911yescharacteristic
472#106—22no—
473#106—22no—
474C4⋊C8—41no—
475C4⋊C8—41no—
476#103—22no—
477#103—22no—
478#103—22no—
479#103—22no—
480#103—22no—
481#103—41no—
482#103—41no—
483#103—41no—
484#102—22no—
485#102—22no—
486#102—22no—
487#102—41no—
488C22⋊C8—22no—
489#95—21no—
490#95—21no—
491#95—21no—
492#95—21no—
493#95—21no—
494#95—21no—
495#95—21no—
496#95D4×C5911yescharacteristic
497#95D4×C5911yescharacteristic
498C24—21no—
499C24C2×D4×C5911yescharacteristic
500#41—28no—
501#41—44no—
502#41—44no—
503#41—44no—
504C2×Q8—21no—
505C2×Q8—21no—
506C2×Q8—21no—
507C2×Q8—21no—
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—21no—
511C2×Q8—21no—
512C2×Q8—21no—
513C2×Q8—21no—
514C2×Q8—21no—
515C2×Q8#41×C5912yes—
516C2×D4—21no—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—42no—
522C2×D4—42no—
523C2×D4—42no—
524C2×D4#41×C5912yes—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—24no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—42no—
538C22×C4—42no—
539C22×C4—42no—
540C22×C4—81no—
541C22×C4—81no—
542C22×C4C2×D4×C5911yescharacteristic
543C22×C4C2×D4×C5911yescharacteristic
544C22×C4C2×D4×C5911yescharacteristic
545C22×C4C2×D4×C5911yescharacteristic
546C22×C4C2×D4×C5912yes—
547C22×C4C2×D4×C5911yescharacteristic
548C22×C4#41×C5912yes—
549C22×C4C24×C5911yescharacteristic
550M16—44no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—21no—
563C4⋊C4—24no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—42no—
573C4⋊C4—42no—
574C4⋊C4—42no—
575C4⋊C4—81no—
576C4⋊C4—81no—
577C4⋊C4C2×D4×C5912yes—
578C4⋊C4C2×D4×C5912yes—
579C22⋊C4—22no—
580C22⋊C4—41no—
581C22⋊C4—42no—
582C22⋊C4—42no—
583C22⋊C4—42no—
584C22⋊C4—42no—
585C22⋊C4—42no—
586C22⋊C4—42no—
587C42—21no—
588C42—21no—
589C42—21no—
590C42—21no—
591C42—81no—
592C42—81no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—21no—
599C23—22no—
600C23—41no—
601C23—41no—
602C23—41no—
603C23—41no—
604C23—41no—
605C23—41no—
606C23#121×C5912yes—
607C23C22×D4×C5911yescharacteristic
608Q8—22no—
609Q8—22no—
610Q8—41no—
611Q8—41no—
612Q8—41no—
613Q8—41no—
614Q8—41no—
615Q8—41no—
616D4—22no—
617D4—22no—
618D4—48no—
619D4—41no—
620D4—41no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—22no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—48no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—84no—
661C2×C4#121×C5912yes—
662C2×C4#137×C5912yes—
663C2×C4C22×D4×C5911yescharacteristic
664C2×C4C2×#41×C5911yescharacteristic
665C2×C4C2×#41×C5911yescharacteristic
666C2×C4C2×#41×C5911yescharacteristic
667C2×C4H(5,𝔽2)×C5911yescharacteristic
668C2×C4H(5,𝔽2)×C5911yescharacteristic
669C8—41no—
670C8—41no—
671C8—41no—
672C8—41no—
673C22—22no—
674C22—22no—
675C22—22no—
676C22—41no—
677C22—41no—
678C22—41no—
679C22—41no—
680C22—42no—
681C22—42no—
682C22—42no—
683C22—81no—
684C22—81no—
685C22—81no—
686C22—81no—
687C22C2×#121×C5911yescharacteristic
688C22C59×#54611yescharacteristic
689C22C59×#54611yescharacteristic
690C22C2×#137×C5911yescharacteristic
691C22C59×#57511yescharacteristic
692C22C59×#57711yescharacteristic
693C22C59×#57711yescharacteristic
694C4—22no—
695C4—22no—
696C4—42no—
697C4—42no—
698C4—41no—
699C4—41no—
700C4—41no—
701C4—42no—
702C4—81no—
703C4—81no—
704C4—81no—
705C4—81no—
706C4C59×#52511yescharacteristic
707C4C59×#53511yescharacteristic
708C4C59×#55111yescharacteristic
709C4C59×#55111yescharacteristic
710C2—42no—
711C2—82no—
712C2C59×#241111yescharacteristic
713C2C59×#303711yescharacteristic
714C2C59×#304211yescharacteristic
715C2C59×#330711yescharacteristic
716C2C59×#331611yescharacteristic
717C2C59×#332611yescharacteristic
718C2C59×#333111yescharacteristic
subgroupG/H
center, socleC23×C59C22×D4
commutator, Frattini, cosocleC22×C4C24×C59
prime radicalC22×#41×C59C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C59 ◁ C4×C22⋊C4×C59 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C59×#483C2semidirect
4. C59×#2345C2semidirect
5. C59×#2066C2semidirect
6. C59×#2065C2semidirect
7. C59×#2043C2semidirect
8. C59×#2042C2semidirect
9. C59×#1983C2semidirect
10. C59×#1981C2semidirect
11. C59×#1927C2semidirect
12. C59×#1926C2semidirect
13. C59×#1894C2semidirect
14. C59×#1851C2semidirect
313. #24491C59direct (N × H)
351. C2×#483C2×C59semidirect
354. #2345C2×C59semidirect
355. #2066C2×C59semidirect
356. #2065C2×C59semidirect
357. #2043C2×C59semidirect
358. #2042C2×C59semidirect
359. #1983C2×C59semidirect
360. #1981C2×C59semidirect
361. #1927C2×C59semidirect
362. #1926C2×C59semidirect
363. #1894C2×C59semidirect
364. #1851C2×C59semidirect
420. C59#24491direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C59×#4832
C2×C59×#4172
C59×#24322
C59×#23452
C59×#20662
C59×#20652
C59×#20432
C59×#20422
C59×#19832
C59×#19812
C59×#19272
C59×#19262
C59×#18942
C59×#18512
C59×#17882
#2449159