Finite Group Databasebeta

← C59×#22080 #28434189

Subgroups — C59×#22080 #28434189

Order 15104.

908 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C59×#482C211yesmaximal, characteristic
2C4×#121×C59C211yesmaximal, characteristic
3C59×#2296C211yesmaximal, characteristic, complemented
4C59×#1942C211yesmaximal, characteristic, complemented
5C59×#1941C211yesmaximal, characteristic, complemented
6C59×#1934C211yesmaximal, characteristic, complemented
7C59×#1934C211yesmaximal, characteristic, complemented
8C59×#1921C211yesmaximal, characteristic, complemented
9C59×#1919C211yesmaximal, characteristic, complemented
10C59×#1875C211yesmaximal, characteristic
11C59×#1864C211yesmaximal, characteristic, complemented
12C59×#1862C211yesmaximal, characteristic, complemented
13C59×#1854C211yesmaximal, characteristic, complemented
14C59×#1825C211yesmaximal, characteristic, complemented
15C4×C22⋊C8×C59C211yesmaximal, characteristic, complemented
16C2×#121×C59C2211yescharacteristic
17C2×C4×D4×C59—21no—
18C2×C4×D4×C59C2211yescharacteristic
19C2×#117×C59C2211yescharacteristic
20C2×#117×C59C2211yescharacteristic
21C22×C42×C59C2211yescharacteristic
22C59×#482C418yescomplemented
23C2×#107×C59C2211yescharacteristic
24C2×#107×C59C2211yescharacteristic
25C2×#106×C59C2211yescharacteristic
26C2×#106×C59C2211yescharacteristic
27C2×#102×C59C2211yescharacteristic
28C2×#102×C59C2211yescharacteristic
29C2×#102×C59C2211yescharacteristic
30C2×#102×C59C2211yescharacteristic
31C2×C22⋊C8×C59C2211yescharacteristic
32C2×C22⋊C8×C59C2211yescharacteristic
33C2×C4×C8×C59C2211yescharacteristic
34C2×C4×C8×C59C2211yescharacteristic
35C59×#390C2211yescharacteristic
36C59×#389C2211yescharacteristic
37C59×#389C2211yescharacteristic
38C59×#389C2211yescharacteristic
39C59×#389C2211yescharacteristic
40C59×#389C2211yescharacteristic
41C59×#388—21no—
42C59×#386—21no—
43C59×#385—21no—
44C59×#385—21no—
45C59×#380C2211yescharacteristic
46C4×C4⋊C4×C59—21no—
47C4×C4⋊C4×C59—21no—
48C4×C4⋊C4×C59C2211yescharacteristic
49C4×C22⋊C4×C59—21no—
50C59×#340C2211yescharacteristic
51C59×#340C2211yescharacteristic
52C59×#340C2211yescharacteristic
53C59×#340C2211yescharacteristic
54C59×#340C2211yescharacteristic
55C59×#340C2211yescharacteristic
56C59×#340C2211yescharacteristic
57C59×#340C2211yescharacteristic
58C59×#336C2211yescharacteristic
59C59×#336C2211yescharacteristic
60C22×D4×C59—21no—
61C22×D4×C59C2311yescharacteristic
62C23×C4×C59—21no—
63C23×C4×C59D411yescharacteristic
64C23×C4×C59D411yescharacteristic
65C23×C4×C59C2311yescharacteristic
66C22×C8×C59C2311yescharacteristic
67C22×C8×C59C2311yescharacteristic
68C22×C8×C59C2311yescharacteristic
69C22×C8×C59C2311yescharacteristic
70#121×C59—22no—
71#121×C59C2×C414yes—
72C4×D4×C59—41no—
73C4×D4×C59—41no—
74C4×D4×C59—44no—
75#117×C59—22no—
76#117×C59—41no—
77#117×C59—41no—
78#117×C59C2×C414yescomplemented
79C2×C4⋊C4×C59—21no—
80C2×C4⋊C4×C59—21no—
81C2×C4⋊C4×C59—21no—
82C2×C4⋊C4×C59—21no—
83C2×C4⋊C4×C59—21no—
84C2×C4⋊C4×C59C2311yescharacteristic
85C2×C4⋊C4×C59C2311yescharacteristic
86C2×C4⋊C4×C59C2311yescharacteristic
87C2×C4⋊C4×C59C2311yescharacteristic
88C2×C4⋊C4×C59C2311yescharacteristic
89C2×C4⋊C4×C59C2311yescharacteristic
90C2×C4⋊C4×C59C2311yescharacteristic
91C2×C22⋊C4×C59—21no—
92C2×C22⋊C4×C59—21no—
93C2×C22⋊C4×C59—21no—
94C2×C22⋊C4×C59—21no—
95C2×C22⋊C4×C59—21no—
96C2×C22⋊C4×C59—21no—
97C2×C22⋊C4×C59—21no—
98C2×C42×C59—21no—
99C2×C42×C59—21no—
100C2×C42×C59—21no—
101C2×C42×C59—41no—
102C2×C42×C59—41no—
103C2×C42×C59D411yescharacteristic
104C2×C42×C59D411yescharacteristic
105C2×C42×C59C2311yescharacteristic
106C2×C42×C59C2311yescharacteristic
107#107×C59—41no—
108#107×C59C2×C414yescomplemented
109#106×C59—41no—
110#106×C59C2×C414yescomplemented
111#102×C59—41no—
112#102×C59—41no—
113#102×C59C2×C414yescomplemented
114#102×C59C2×C414yescomplemented
115C22⋊C8×C59—22no—
116C22⋊C8×C59C2×C414yescomplemented
117C4×C8×C59—41no—
118C4×C8×C59—41no—
119#95×C59—21no—
120#95×C59—21no—
121#95×C59—21no—
122#95×C59—21no—
123#95×C59—21no—
124#95×C59—21no—
125#95×C59—21no—
126C24×C59—21no—
127C24×C59C2×D411yescharacteristic
128C2×D4×C59—24no—
129C2×D4×C59—21no—
130C2×D4×C59—21no—
131C2×D4×C59—21no—
132C2×D4×C59—21no—
133C2×D4×C59—21no—
134C2×D4×C59—42no—
135C2×D4×C59—42no—
136C2×D4×C59C22×C412yes—
137C22×C4×C59—21no—
138C22×C4×C59—21no—
139C22×C4×C59—21no—
140C22×C4×C59—21no—
141C22×C4×C59—21no—
142C22×C4×C59—21no—
143C22×C4×C59—21no—
144C22×C4×C59—22no—
145C22×C4×C59—22no—
146C22×C4×C59—22no—
147C22×C4×C59—21no—
148C22×C4×C59—21no—
149C22×C4×C59—21no—
150C22×C4×C59—21no—
151C22×C4×C59—41no—
152C22×C4×C59—41no—
153C22×C4×C59—41no—
154C22×C4×C59—42no—
155C22×C4×C59—42no—
156C22×C4×C59—42no—
157C22×C4×C59C22×C412yes—
158C22×C4×C59C2×D411yescharacteristic
159C22×C4×C59C2×D411yescharacteristic
160C22×C4×C59C2×D411yescharacteristic
161C22×C4×C59C2×D411yescharacteristic
162C22×C4×C59C2×D411yescharacteristic
163C22×C4×C59#4112yes—
164C22×C4×C59C2411yescharacteristic
165C2×C8×C59—21no—
166C2×C8×C59—21no—
167C2×C8×C59—21no—
168C2×C8×C59—21no—
169C2×C8×C59—21no—
170C2×C8×C59—21no—
171C2×C8×C59—21no—
172C2×C8×C59—21no—
173C2×C8×C59—21no—
174C2×C8×C59—21no—
175C2×C8×C59C22×C412yes—
176C2×C8×C59C22×C412yes—
177C4⋊C4×C59—21no—
178C4⋊C4×C59—21no—
179C4⋊C4×C59—21no—
180C4⋊C4×C59—21no—
181C4⋊C4×C59—21no—
182C4⋊C4×C59—21no—
183C4⋊C4×C59—21no—
184C4⋊C4×C59—21no—
185C4⋊C4×C59—21no—
186C4⋊C4×C59—21no—
187C4⋊C4×C59—21no—
188C4⋊C4×C59—42no—
189C4⋊C4×C59—42no—
190C4⋊C4×C59—42no—
191C4⋊C4×C59—42no—
192C4⋊C4×C59—42no—
193C4⋊C4×C59C22×C412yes—
194C4⋊C4×C59C22×C412yes—
195C4⋊C4×C59C22×C412yes—
196C22⋊C4×C59—24no—
197C22⋊C4×C59—24no—
198C22⋊C4×C59—42no—
199C22⋊C4×C59—42no—
200C22⋊C4×C59—42no—
201C22⋊C4×C59—42no—
202C22⋊C4×C59—42no—
203C42×C59—24no—
204C42×C59—21no—
205C42×C59—21no—
206C42×C59—21no—
207C42×C59—21no—
208C42×C59—41no—
209C42×C59—41no—
210C42×C59—42no—
211C42×C59—42no—
212C23×C59—21no—
213C23×C59—21no—
214C23×C59—21no—
215C23×C59—21no—
216C23×C59—21no—
217C23×C59—21no—
218C23×C59—22no—
219C23×C59—41no—
220C23×C59—41no—
221C23×C59—41no—
222C23×C59—41no—
223C23×C59—41no—
224C23×C59—41no—
225C23×C59C4×D412yes—
226C23×C59C22×D411yescharacteristic
227D4×C59—22no—
228D4×C59—22no—
229D4×C59—48no—
230D4×C59—41no—
231D4×C59—41no—
232C2×C4×C59—21no—
233C2×C4×C59—21no—
234C2×C4×C59—21no—
235C2×C4×C59—21no—
236C2×C4×C59—21no—
237C2×C4×C59—21no—
238C2×C4×C59—21no—
239C2×C4×C59—21no—
240C2×C4×C59—22no—
241C2×C4×C59—22no—
242C2×C4×C59—22no—
243C2×C4×C59—22no—
244C2×C4×C59—22no—
245C2×C4×C59—22no—
246C2×C4×C59—22no—
247C2×C4×C59—21no—
248C2×C4×C59—21no—
249C2×C4×C59—21no—
250C2×C4×C59—44no—
251C2×C4×C59—44no—
252C2×C4×C59—41no—
253C2×C4×C59—41no—
254C2×C4×C59—41no—
255C2×C4×C59—41no—
256C2×C4×C59—41no—
257C2×C4×C59—41no—
258C2×C4×C59—41no—
259C2×C4×C59—41no—
260C2×C4×C59—41no—
261C2×C4×C59—41no—
262C2×C4×C59—41no—
263C2×C4×C59—41no—
264C2×C4×C59—41no—
265C2×C4×C59—41no—
266C2×C4×C59—41no—
267C2×C4×C59—41no—
268C2×C4×C59—41no—
269C2×C4×C59—41no—
270C2×C4×C59—84no—
271C2×C4×C59C4×D412yes—
272C2×C4×C59#13512yes—
273C2×C4×C59#13512yes—
274C2×C4×C59AGL(1,ℤ/8)12yes—
275C2×C4×C59C23×C411yescharacteristic
276C2×C4×C59C2×#4111yescharacteristic
277C2×C4×C59H(5,𝔽2)11yescharacteristic
278C2×C4×C59H(5,𝔽2)11yescharacteristic
279C2×C4×C592−1+411yescharacteristic
280C2×C4×C592−1+411yescharacteristic
281C8×C59—22no—
282C8×C59—22no—
283C8×C59—41no—
284C8×C59—41no—
285#22080C5911yesmaximal, characteristic, direct product factor, Sylow
286C22×C59—22no—
287C22×C59—22no—
288C22×C59—22no—
289C22×C59—41no—
290C22×C59—41no—
291C22×C59—41no—
292C22×C59—41no—
293C22×C59—42no—
294C22×C59—42no—
295C22×C59—42no—
296C22×C59—81no—
297C22×C59—81no—
298C22×C59—81no—
299C22×C59—81no—
300C22×C59C2×C4×D411yescharacteristic
301C22×C59#53411yescharacteristic
302C22×C59#53611yescharacteristic
303C22×C59C2×#13511yescharacteristic
304C22×C59C2×#13511yescharacteristic
305C22×C59C2×AGL(1,ℤ/8)11yescharacteristic
306C22×C59#57511yescharacteristic
307C4×C59—22no—
308C4×C59—22no—
309C4×C59—22no—
310C4×C59—22no—
311C4×C59—41no—
312C4×C59—42no—
313C4×C59—42no—
314C4×C59—42no—
315C4×C59—81no—
316C4×C59—81no—
317C4×C59—81no—
318C4×C59—81no—
319C4×C59#52011yescharacteristic
320C4×C59#52011yescharacteristic
321C4×C59#53911yescharacteristic
322C4×C59#53911yescharacteristic
323C2×#482C2×C5911yescharacteristic
324C4×#121C2×C5911yescharacteristic
325#2296C2×C5911yescharacteristic, complemented
326#1942C2×C5911yescharacteristic, complemented
327#1941C2×C5911yescharacteristic, complemented
328#1934C2×C5911yescharacteristic, complemented
329#1934C2×C5911yescharacteristic, complemented
330#1921C2×C5911yescharacteristic, complemented
331#1919C2×C5911yescharacteristic, complemented
332#1875C2×C5911yescharacteristic
333#1864C2×C5911yescharacteristic, complemented
334#1862C2×C5911yescharacteristic, complemented
335#1854C2×C5911yescharacteristic, complemented
336#1825C2×C5911yescharacteristic, complemented
337C4×C22⋊C8C2×C5911yescharacteristic, complemented
338C2×C59—42no—
339C2×C59—82no—
340C2×C59#232211yescharacteristic
341C2×C59C4×#13511yescharacteristic
342C2×C59C4×AGL(1,ℤ/8)11yescharacteristic
343C2×C59#318811yescharacteristic
344C2×C59#319111yescharacteristic
345C2×C59#322811yescharacteristic
346C2×C59#323311yescharacteristic
347C2×#121C22×C5911yescharacteristic
348C2×C4×D4—21no—
349C2×C4×D4C22×C5911yescharacteristic
350C2×#117C22×C5911yescharacteristic
351C2×#117C22×C5911yescharacteristic
352C22×C42C22×C5911yescharacteristic
353#482C4×C5918yescomplemented
354C2×#107C22×C5911yescharacteristic
355C2×#107C22×C5911yescharacteristic
356C2×#106C22×C5911yescharacteristic
357C2×#106C22×C5911yescharacteristic
358C2×#102C22×C5911yescharacteristic
359C2×#102C22×C5911yescharacteristic
360C2×#102C22×C5911yescharacteristic
361C2×#102C22×C5911yescharacteristic
362C2×C22⋊C8C22×C5911yescharacteristic
363C2×C22⋊C8C22×C5911yescharacteristic
364C2×C4×C8C22×C5911yescharacteristic
365C2×C4×C8C22×C5911yescharacteristic
366#390C22×C5911yescharacteristic
367#389C22×C5911yescharacteristic
368#389C22×C5911yescharacteristic
369#389C22×C5911yescharacteristic
370#389C22×C5911yescharacteristic
371#389C22×C5911yescharacteristic
372#388—21no—
373#386—21no—
374#385—21no—
375#385—21no—
376#380C22×C5911yescharacteristic
377C4×C4⋊C4—21no—
378C4×C4⋊C4—21no—
379C4×C4⋊C4C22×C5911yescharacteristic
380C4×C22⋊C4—21no—
381#340C22×C5911yescharacteristic
382#340C22×C5911yescharacteristic
383#340C22×C5911yescharacteristic
384#340C22×C5911yescharacteristic
385#340C22×C5911yescharacteristic
386#340C22×C5911yescharacteristic
387#340C22×C5911yescharacteristic
388#340C22×C5911yescharacteristic
389#336C22×C5911yescharacteristic
390#336C22×C5911yescharacteristic
391C59#2208011yescharacteristic, direct product factor, Sylow
392C22×D4—21no—
393C22×D4C23×C5911yescharacteristic
394C23×C4—21no—
395C23×C4D4×C5911yescharacteristic
396C23×C4D4×C5911yescharacteristic
397C23×C4C23×C5911yescharacteristic
398C22×C8C23×C5911yescharacteristic
399C22×C8C23×C5911yescharacteristic
400C22×C8C23×C5911yescharacteristic
401C22×C8C23×C5911yescharacteristic
402#121—22no—
403#121C2×C4×C5914yes—
404C4×D4—41no—
405C4×D4—41no—
406C4×D4—44no—
407#117—22no—
408#117—41no—
409#117—41no—
410#117C2×C4×C5914yescomplemented
411C2×C4⋊C4—21no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4C23×C5911yescharacteristic
417C2×C4⋊C4C23×C5911yescharacteristic
418C2×C4⋊C4C23×C5911yescharacteristic
419C2×C4⋊C4C23×C5911yescharacteristic
420C2×C4⋊C4C23×C5911yescharacteristic
421C2×C4⋊C4C23×C5911yescharacteristic
422C2×C4⋊C4C23×C5911yescharacteristic
423C2×C22⋊C4—21no—
424C2×C22⋊C4—21no—
425C2×C22⋊C4—21no—
426C2×C22⋊C4—21no—
427C2×C22⋊C4—21no—
428C2×C22⋊C4—21no—
429C2×C22⋊C4—21no—
430C2×C42—21no—
431C2×C42—21no—
432C2×C42—21no—
433C2×C42—41no—
434C2×C42—41no—
435C2×C42D4×C5911yescharacteristic
436C2×C42D4×C5911yescharacteristic
437C2×C42C23×C5911yescharacteristic
438C2×C42C23×C5911yescharacteristic
439#107—41no—
440#107C2×C4×C5914yescomplemented
441#106—41no—
442#106C2×C4×C5914yescomplemented
443#102—41no—
444#102—41no—
445#102C2×C4×C5914yescomplemented
446#102C2×C4×C5914yescomplemented
447C22⋊C8—22no—
448C22⋊C8C2×C4×C5914yescomplemented
449C4×C8—41no—
450C4×C8—41no—
451#95—21no—
452#95—21no—
453#95—21no—
454#95—21no—
455#95—21no—
456#95—21no—
457#95—21no—
458C24—21no—
459C24C2×D4×C5911yescharacteristic
460C2×D4—24no—
461C2×D4—21no—
462C2×D4—21no—
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—42no—
467C2×D4—42no—
468C2×D4C22×C4×C5912yes—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—41no—
484C22×C4—41no—
485C22×C4—41no—
486C22×C4—42no—
487C22×C4—42no—
488C22×C4—42no—
489C22×C4C22×C4×C5912yes—
490C22×C4C2×D4×C5911yescharacteristic
491C22×C4C2×D4×C5911yescharacteristic
492C22×C4C2×D4×C5911yescharacteristic
493C22×C4C2×D4×C5911yescharacteristic
494C22×C4C2×D4×C5911yescharacteristic
495C22×C4#41×C5912yes—
496C22×C4C24×C5911yescharacteristic
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8C22×C4×C5912yes—
508C2×C8C22×C4×C5912yes—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—42no—
521C4⋊C4—42no—
522C4⋊C4—42no—
523C4⋊C4—42no—
524C4⋊C4—42no—
525C4⋊C4C22×C4×C5912yes—
526C4⋊C4C22×C4×C5912yes—
527C4⋊C4C22×C4×C5912yes—
528C22⋊C4—24no—
529C22⋊C4—24no—
530C22⋊C4—42no—
531C22⋊C4—42no—
532C22⋊C4—42no—
533C22⋊C4—42no—
534C22⋊C4—42no—
535C42—24no—
536C42—21no—
537C42—21no—
538C42—21no—
539C42—21no—
540C42—41no—
541C42—41no—
542C42—42no—
543C42—42no—
544C23—21no—
545C23—21no—
546C23—21no—
547C23—21no—
548C23—21no—
549C23—21no—
550C23—22no—
551C23—41no—
552C23—41no—
553C23—41no—
554C23—41no—
555C23—41no—
556C23—41no—
557C23C4×D4×C5912yes—
558C23C22×D4×C5911yescharacteristic
559D4—22no—
560D4—22no—
561D4—48no—
562D4—41no—
563D4—41no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—44no—
583C2×C4—44no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—84no—
603C2×C4C4×D4×C5912yes—
604C2×C4#135×C5912yes—
605C2×C4#135×C5912yes—
606C2×C4AGL(1,ℤ/8)×C5912yes—
607C2×C4C23×C4×C5911yescharacteristic
608C2×C4C2×#41×C5911yescharacteristic
609C2×C4H(5,𝔽2)×C5911yescharacteristic
610C2×C4H(5,𝔽2)×C5911yescharacteristic
611C2×C42−1+4×C5911yescharacteristic
612C2×C42−1+4×C5911yescharacteristic
613C8—22no—
614C8—22no—
615C8—41no—
616C8—41no—
617C22—22no—
618C22—22no—
619C22—22no—
620C22—41no—
621C22—41no—
622C22—41no—
623C22—41no—
624C22—42no—
625C22—42no—
626C22—42no—
627C22—81no—
628C22—81no—
629C22—81no—
630C22—81no—
631C22C2×C4×D4×C5911yescharacteristic
632C22C59×#53411yescharacteristic
633C22C59×#53611yescharacteristic
634C22C2×#135×C5911yescharacteristic
635C22C2×#135×C5911yescharacteristic
636C22C2×AGL(1,ℤ/8)×C5911yescharacteristic
637C22C59×#57511yescharacteristic
638C4—22no—
639C4—22no—
640C4—22no—
641C4—22no—
642C4—41no—
643C4—42no—
644C4—42no—
645C4—42no—
646C4—81no—
647C4—81no—
648C4—81no—
649C4—81no—
650C4C59×#52011yescharacteristic
651C4C59×#52011yescharacteristic
652C4C59×#53911yescharacteristic
653C4C59×#53911yescharacteristic
654C2—42no—
655C2—82no—
656C2C59×#232211yescharacteristic
657C2C4×#135×C5911yescharacteristic
658C2C4×AGL(1,ℤ/8)×C5911yescharacteristic
659C2C59×#318811yescharacteristic
660C2C59×#319111yescharacteristic
661C2C59×#322811yescharacteristic
662C2C59×#323311yescharacteristic
subgroupG/H
center, socleC23×C59C22×D4
commutatorC2×C4C23×C4×C59
Frattini, cosocleC22×C4C24×C59
prime radicalC2×#121×C59C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C59 ◁ C22×C42×C59 ◁ G

Complements

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

NH ≅ G/Ntype
3. C59×#2296C2semidirect
4. C59×#1942C2semidirect
5. C59×#1941C2semidirect
6. C59×#1934C2semidirect
7. C59×#1934C2semidirect
8. C59×#1921C2semidirect
9. C59×#1919C2semidirect
11. C59×#1864C2semidirect
12. C59×#1862C2semidirect
13. C59×#1854C2semidirect
14. C59×#1825C2semidirect
15. C4×C22⋊C8×C59C2semidirect
22. C59×#482C4semidirect
78. #117×C59C2×C4semidirect
108. #107×C59C2×C4semidirect
110. #106×C59C2×C4semidirect
113. #102×C59C2×C4semidirect
114. #102×C59C2×C4semidirect
116. C22⋊C8×C59C2×C4semidirect
285. #22080C59direct (N × H)
325. #2296C2×C59semidirect
326. #1942C2×C59semidirect
327. #1941C2×C59semidirect
328. #1934C2×C59semidirect
329. #1934C2×C59semidirect
330. #1921C2×C59semidirect
331. #1919C2×C59semidirect
333. #1864C2×C59semidirect
334. #1862C2×C59semidirect
335. #1854C2×C59semidirect
336. #1825C2×C59semidirect
337. C4×C22⋊C8C2×C59semidirect
353. #482C4×C59semidirect
391. C59#22080direct (N × H)
410. #117C2×C4×C59semidirect
440. #107C2×C4×C59semidirect
442. #106C2×C4×C59semidirect
445. #102C2×C4×C59semidirect
446. #102C2×C4×C59semidirect
448. C22⋊C8C2×C4×C59semidirect

Maximal subgroups

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

subgroupindex
C2×C59×#4822
C4×#121×C592
C59×#22962
C59×#19422
C59×#19412
C59×#19342
C59×#19212
C59×#19192
C59×#18752
C59×#18642
C59×#18622
C59×#18542
C59×#18252
C4×C22⋊C8×C592
#2208059