Finite Group Databasebeta

← C59×#14045 #28426154

Subgroups — C59×#14045 #28426154

Order 15104.

1530 conjugacy classes of subgroups.

The subgroup lattice has 690 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C59×#389C211yesmaximal, characteristic
2C2×C59×#389C211yesmaximal, characteristic
3C2×C59×#389C211yesmaximal, characteristic
4C2×C4×C4⋊C4×C59C211yesmaximal, characteristic
5C2×C4×C4⋊C4×C59C211yesmaximal, characteristic
6C59×#1444C212yesmaximal
7C59×#1441C212yesmaximal
8C59×#1436C212yesmaximal
9C59×C4⋊#95C212yesmaximal
10C59×C4⋊#95C211yesmaximal, characteristic
11C59×C4⋊#95C211yesmaximal, characteristic
12C22×C4⋊C4×C59C2211yescharacteristic
13C22×C4⋊C4×C59C2211yescharacteristic
14C22×C4⋊C4×C59C2212yes—
15C22×C4⋊C4×C59C2211yescharacteristic
16C22×C4⋊C4×C59C2211yescharacteristic
17C22×C4⋊C4×C59C2211yescharacteristic
18C22×C4⋊C4×C59C2212yes—
19C22×C4⋊C4×C59C2212yes—
20C22×C4⋊C4×C59C2211yescharacteristic
21C22×C42×C59C2211yescharacteristic
22C22×C42×C59C2212yes—
23C22×C42×C59C2211yescharacteristic
24C22×C42×C59C2211yescharacteristic
25C59×#389—24no—
26C59×#389—24no—
27C59×#389C418yescomplemented
28C4×C4⋊C4×C59—24no—
29C4×C4⋊C4×C59—24no—
30C2×#95×C59C2211yescharacteristic
31C2×#95×C59C2211yescharacteristic
32C2×#95×C59C2212yes—
33C2×#95×C59C2212yes—
34C2×#95×C59C2212yes—
35C2×#95×C59C2212yes—
36C2×#95×C59C2212yes—
37C2×#95×C59C2212yes—
38C2×#95×C59C2212yes—
39C2×#95×C59C2212yes—
40C23×C4×C59C2312yes—
41C23×C4×C59C2311yescharacteristic
42C23×C4×C59C2312yes—
43C23×C4×C59C2311yescharacteristic
44C23×C4×C59C2311yescharacteristic
45C23×C4×C59C2312yes—
46C23×C4×C59C2311yescharacteristic
47C23×C4×C59C2312yes—
48C23×C4×C59C2311yescharacteristic
49C23×C4×C59C2311yescharacteristic
50C23×C4×C59C2311yescharacteristic
51C2×C4⋊C4×C59—22no—
52C2×C4⋊C4×C59—22no—
53C2×C4⋊C4×C59—22no—
54C2×C4⋊C4×C59—22no—
55C2×C4⋊C4×C59—22no—
56C2×C4⋊C4×C59—22no—
57C2×C4⋊C4×C59—22no—
58C2×C4⋊C4×C59—22no—
59C2×C4⋊C4×C59—22no—
60C2×C4⋊C4×C59—24no—
61C2×C4⋊C4×C59—24no—
62C2×C4⋊C4×C59—22no—
63C2×C4⋊C4×C59—22no—
64C2×C4⋊C4×C59—24no—
65C2×C4⋊C4×C59—22no—
66C2×C4⋊C4×C59—42no—
67C2×C4⋊C4×C59—42no—
68C2×C4⋊C4×C59—42no—
69C2×C4⋊C4×C59—42no—
70C2×C4⋊C4×C59—42no—
71C2×C4⋊C4×C59C2×C414yes—
72C2×C4⋊C4×C59C2×C418yes—
73C2×C4⋊C4×C59C2×C414yes—
74C2×C4⋊C4×C59D414yes—
75C2×C4⋊C4×C59Q814yes—
76C2×C4⋊C4×C59Q814yes—
77C2×C4⋊C4×C59Q814yes—
78C2×C42×C59—22no—
79C2×C42×C59—22no—
80C2×C42×C59—22no—
81C2×C42×C59—22no—
82C2×C42×C59—24no—
83C2×C42×C59—22no—
84C2×C42×C59—22no—
85C2×C42×C59—24no—
86C2×C42×C59—22no—
87C2×C42×C59—42no—
88C2×C42×C59C2×C414yes—
89C2×C42×C59D414yes—
90#95×C59—22no—
91#95×C59—24no—
92#95×C59—22no—
93#95×C59—24no—
94#95×C59—24no—
95#95×C59—24no—
96#95×C59—42no—
97#95×C59—42no—
98#95×C59—42no—
99#95×C59C2×C418yes—
100C24×C59C2411yescharacteristic
101C22×C4×C59—21no—
102C22×C4×C59—21no—
103C22×C4×C59—21no—
104C22×C4×C59—22no—
105C22×C4×C59—21no—
106C22×C4×C59—21no—
107C22×C4×C59—21no—
108C22×C4×C59—22no—
109C22×C4×C59—21no—
110C22×C4×C59—22no—
111C22×C4×C59—22no—
112C22×C4×C59—21no—
113C22×C4×C59—21no—
114C22×C4×C59—21no—
115C22×C4×C59—21no—
116C22×C4×C59—21no—
117C22×C4×C59—22no—
118C22×C4×C59—21no—
119C22×C4×C59—22no—
120C22×C4×C59—21no—
121C22×C4×C59—22no—
122C22×C4×C59—21no—
123C22×C4×C59—21no—
124C22×C4×C59—21no—
125C22×C4×C59—21no—
126C22×C4×C59—22no—
127C22×C4×C59—22no—
128C22×C4×C59—22no—
129C22×C4×C59—21no—
130C22×C4×C59—21no—
131C22×C4×C59—21no—
132C22×C4×C59—21no—
133C22×C4×C59—21no—
134C22×C4×C59—21no—
135C22×C4×C59—21no—
136C22×C4×C59—22no—
137C22×C4×C59—22no—
138C22×C4×C59—22no—
139C22×C4×C59—22no—
140C22×C4×C59—21no—
141C22×C4×C59—21no—
142C22×C4×C59—22no—
143C22×C4×C59—21no—
144C22×C4×C59—21no—
145C22×C4×C59—21no—
146C22×C4×C59—21no—
147C22×C4×C59—22no—
148C22×C4×C59—21no—
149C22×C4×C59—22no—
150C22×C4×C59—22no—
151C22×C4×C59—22no—
152C22×C4×C59—22no—
153C22×C4×C59—22no—
154C22×C4×C59—22no—
155C22×C4×C59—22no—
156C22×C4×C59C22×C414yes—
157C22×C4×C59C22×C412yes—
158C22×C4×C59C22×C414yes—
159C22×C4×C59C22×C412yes—
160C22×C4×C59C22×C412yes—
161C22×C4×C59C2×D412yes—
162C22×C4×C59C2×D414yes—
163C22×C4×C59C2×D412yes—
164C22×C4×C59C2×D412yes—
165C22×C4×C59C2×D412yes—
166C22×C4×C59C2×Q812yes—
167C22×C4×C59C2×Q814yes—
168C22×C4×C59C2×Q814yes—
169C22×C4×C59C2×Q812yes—
170C22×C4×C59C2×Q812yes—
171C22×C4×C59C2×Q812yes—
172C22×C4×C59C2×Q812yes—
173C22×C4×C59#4112yes—
174C22×C4×C59#4112yes—
175C22×C4×C59#4112yes—
176C22×C4×C59#4112yes—
177C22×C4×C59#4112yes—
178C4⋊C4×C59—28no—
179C4⋊C4×C59—28no—
180C4⋊C4×C59—28no—
181C4⋊C4×C59—28no—
182C4⋊C4×C59—48no—
183C4⋊C4×C59—48no—
184C4⋊C4×C59—48no—
185C4⋊C4×C59—44no—
186C4⋊C4×C59C4⋊C4116yescomplemented
187C42×C59—28no—
188C42×C59—28no—
189C42×C59—48no—
190C42×C59—44no—
191C23×C59C23×C411yescharacteristic
192C23×C59C22×D411yescharacteristic
193C23×C59C22×D411yescharacteristic
194C23×C59C22×Q811yescharacteristic
195C23×C59C22×Q811yescharacteristic
196C23×C59C22×Q811yescharacteristic
197C23×C59C2×#4111yescharacteristic
198C23×C59C2×#4111yescharacteristic
199C23×C59C2×#4111yescharacteristic
200C23×C59C2×#4111yescharacteristic
201C23×C59C2×#4111yescharacteristic
202C23×C59H(5,𝔽2)11yescharacteristic
203C23×C59H(5,𝔽2)11yescharacteristic
204C23×C59H(5,𝔽2)11yescharacteristic
205C23×C592−1+411yescharacteristic
206C2×C4×C59—22no—
207C2×C4×C59—24no—
208C2×C4×C59—22no—
209C2×C4×C59—24no—
210C2×C4×C59—22no—
211C2×C4×C59—22no—
212C2×C4×C59—22no—
213C2×C4×C59—22no—
214C2×C4×C59—22no—
215C2×C4×C59—22no—
216C2×C4×C59—22no—
217C2×C4×C59—24no—
218C2×C4×C59—24no—
219C2×C4×C59—22no—
220C2×C4×C59—22no—
221C2×C4×C59—24no—
222C2×C4×C59—24no—
223C2×C4×C59—22no—
224C2×C4×C59—22no—
225C2×C4×C59—24no—
226C2×C4×C59—22no—
227C2×C4×C59—24no—
228C2×C4×C59—22no—
229C2×C4×C59—24no—
230C2×C4×C59—22no—
231C2×C4×C59—22no—
232C2×C4×C59—24no—
233C2×C4×C59—22no—
234C2×C4×C59—22no—
235C2×C4×C59—22no—
236C2×C4×C59—22no—
237C2×C4×C59—22no—
238C2×C4×C59—22no—
239C2×C4×C59—22no—
240C2×C4×C59—24no—
241C2×C4×C59—24no—
242C2×C4×C59—41no—
243C2×C4×C59—41no—
244C2×C4×C59—42no—
245C2×C4×C59—42no—
246C2×C4×C59—41no—
247C2×C4×C59—41no—
248C2×C4×C59—41no—
249C2×C4×C59—42no—
250C2×C4×C59—41no—
251C2×C4×C59—41no—
252C2×C4×C59—42no—
253C2×C4×C59—42no—
254C2×C4×C59—41no—
255C2×C4×C59—42no—
256C2×C4×C59—42no—
257C2×C4×C59—41no—
258C2×C4×C59—41no—
259C2×C4×C59—41no—
260C2×C4×C59—41no—
261C2×C4×C59—42no—
262C2×C4×C59—41no—
263C2×C4×C59—41no—
264C2×C4×C59—41no—
265C2×C4×C59—41no—
266C2×C4×C59—42no—
267C2×C4×C59—42no—
268C2×C4×C59—42no—
269C2×C4×C59—42no—
270C2×C4×C59—42no—
271C2×C4×C59—42no—
272C2×C4×C59—42no—
273C2×C4×C59C2×C4⋊C418yes—
274C2×C4×C59C2×C4⋊C414yes—
275C2×C4×C59C4×D414yes—
276C2×C4×C59C4×Q814yes—
277C2×C4×C59C4×Q814yes—
278C2×C4×C59#12114yes—
279C2×C4×C59C22⋊Q814yes—
280C2×C4×C59C22⋊Q814yes—
281C2×C4×C59#12514yes—
282C2×C4×C59C4⋊Q814yes—
283#14045C5911yesmaximal, characteristic, direct product factor, Sylow
284C22×C59C22×C4⋊C411yescharacteristic
285C22×C59C2×C4×D411yescharacteristic
286C22×C59C2×C4×Q811yescharacteristic
287C22×C59C2×C4×Q811yescharacteristic
288C22×C59C4×#4111yescharacteristic
289C22×C59#51811yescharacteristic
290C22×C59#52011yescharacteristic
291C22×C59C2×#12111yescharacteristic
292C22×C59C2×C22⋊Q811yescharacteristic
293C22×C59C2×C22⋊Q811yescharacteristic
294C22×C59#52511yescharacteristic
295C22×C59C2×#12511yescharacteristic
296C22×C59#52911yescharacteristic
297C22×C59C2×C4⋊Q811yescharacteristic
298C22×C59#53311yescharacteristic
299C22×C59#53511yescharacteristic
300C22×C59#53711yescharacteristic
301C22×C59#54011yescharacteristic
302C22×C59#54211yescharacteristic
303C22×C59#54611yescharacteristic
304C22×C59#54611yescharacteristic
305C22×C59D4×Q811yescharacteristic
306C22×C59#55011yescharacteristic
307C22×C59#55211yescharacteristic
308C22×C59#55311yescharacteristic
309C22×C59#55411yescharacteristic
310C22×C59#55411yescharacteristic
311C22×C59#55411yescharacteristic
312C22×C59#55411yescharacteristic
313C22×C59#55411yescharacteristic
314C22×C59#55511yescharacteristic
315C22×C59#55711yescharacteristic
316C22×C59#55711yescharacteristic
317C22×C59Q8211yescharacteristic
318C22×C59Q8211yescharacteristic
319C4×C59—28no—
320C4×C59—24no—
321C4×C59—24no—
322C4×C59—42no—
323C4×C59—44no—
324C4×C59—42no—
325C4×C59—42no—
326C4×C59—42no—
327C4×C59—44no—
328C4×C59—82no—
329C4×C59#38918yes—
330C2×#389C2×C5911yescharacteristic
331C2×#389C2×C5911yescharacteristic
332C2×#389C2×C5911yescharacteristic
333C2×C4×C4⋊C4C2×C5911yescharacteristic
334C2×C4×C4⋊C4C2×C5911yescharacteristic
335#1444C2×C5912yes—
336#1441C2×C5912yes—
337#1436C2×C5912yes—
338C4⋊#95C2×C5911yescharacteristic
339C4⋊#95C2×C5912yes—
340C4⋊#95C2×C5911yescharacteristic
341C2×C59C2×#38911yescharacteristic
342C2×C59C4×C22⋊Q811yescharacteristic
343C2×C59#232411yescharacteristic
344C2×C59#234911yescharacteristic
345C2×C59Q8×C4⋊C411yescharacteristic
346C2×C59#236911yescharacteristic
347C2×C59#237011yescharacteristic
348C2×C59#241411yescharacteristic
349C2×C59#241711yescharacteristic
350C2×C59#245111yescharacteristic
351C2×C59#245411yescharacteristic
352C2×C59#250711yescharacteristic
353C2×C59#250811yescharacteristic
354C2×C59#256711yescharacteristic
355C2×C59#258411yescharacteristic
356C22×C4⋊C4C22×C5911yescharacteristic
357C22×C4⋊C4C22×C5911yescharacteristic
358C22×C4⋊C4C22×C5912yes—
359C22×C4⋊C4C22×C5911yescharacteristic
360C22×C4⋊C4C22×C5911yescharacteristic
361C22×C4⋊C4C22×C5911yescharacteristic
362C22×C4⋊C4C22×C5912yes—
363C22×C4⋊C4C22×C5912yes—
364C22×C4⋊C4C22×C5911yescharacteristic
365C22×C42C22×C5911yescharacteristic
366C22×C42C22×C5912yes—
367C22×C42C22×C5911yescharacteristic
368C22×C42C22×C5911yescharacteristic
369#389—24no—
370#389—24no—
371#389C4×C5918yescomplemented
372C4×C4⋊C4—24no—
373C4×C4⋊C4—24no—
374C2×#95C22×C5911yescharacteristic
375C2×#95C22×C5912yes—
376C2×#95C22×C5912yes—
377C2×#95C22×C5912yes—
378C2×#95C22×C5911yescharacteristic
379C2×#95C22×C5912yes—
380C2×#95C22×C5912yes—
381C2×#95C22×C5912yes—
382C2×#95C22×C5912yes—
383C2×#95C22×C5912yes—
384C59#1404511yescharacteristic, direct product factor, Sylow
385C23×C4C23×C5912yes—
386C23×C4C23×C5912yes—
387C23×C4C23×C5911yescharacteristic
388C23×C4C23×C5911yescharacteristic
389C23×C4C23×C5911yescharacteristic
390C23×C4C23×C5912yes—
391C23×C4C23×C5911yescharacteristic
392C23×C4C23×C5912yes—
393C23×C4C23×C5911yescharacteristic
394C23×C4C23×C5911yescharacteristic
395C23×C4C23×C5911yescharacteristic
396C2×C4⋊C4—22no—
397C2×C4⋊C4—22no—
398C2×C4⋊C4—22no—
399C2×C4⋊C4—22no—
400C2×C4⋊C4—22no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4—22no—
404C2×C4⋊C4—22no—
405C2×C4⋊C4—24no—
406C2×C4⋊C4—24no—
407C2×C4⋊C4—22no—
408C2×C4⋊C4—22no—
409C2×C4⋊C4—24no—
410C2×C4⋊C4—22no—
411C2×C4⋊C4—42no—
412C2×C4⋊C4—42no—
413C2×C4⋊C4—42no—
414C2×C4⋊C4—42no—
415C2×C4⋊C4—42no—
416C2×C4⋊C4C2×C4×C5914yes—
417C2×C4⋊C4C2×C4×C5918yes—
418C2×C4⋊C4C2×C4×C5914yes—
419C2×C4⋊C4D4×C5914yes—
420C2×C4⋊C4Q8×C5914yes—
421C2×C4⋊C4Q8×C5914yes—
422C2×C4⋊C4Q8×C5914yes—
423C2×C42—22no—
424C2×C42—22no—
425C2×C42—22no—
426C2×C42—22no—
427C2×C42—24no—
428C2×C42—22no—
429C2×C42—22no—
430C2×C42—24no—
431C2×C42—22no—
432C2×C42—42no—
433C2×C42C2×C4×C5914yes—
434C2×C42D4×C5914yes—
435#95—22no—
436#95—24no—
437#95—22no—
438#95—24no—
439#95—24no—
440#95—24no—
441#95—42no—
442#95—42no—
443#95—42no—
444#95C2×C4×C5918yes—
445C24C24×C5911yescharacteristic
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—22no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—22no—
454C22×C4—21no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—22no—
463C22×C4—21no—
464C22×C4—22no—
465C22×C4—21no—
466C22×C4—22no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—22no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—22no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4C22×C4×C5914yes—
502C22×C4C22×C4×C5912yes—
503C22×C4C22×C4×C5914yes—
504C22×C4C22×C4×C5912yes—
505C22×C4C22×C4×C5912yes—
506C22×C4C2×D4×C5912yes—
507C22×C4C2×D4×C5914yes—
508C22×C4C2×D4×C5912yes—
509C22×C4C2×D4×C5912yes—
510C22×C4C2×D4×C5912yes—
511C22×C4C2×Q8×C5912yes—
512C22×C4C2×Q8×C5914yes—
513C22×C4C2×Q8×C5914yes—
514C22×C4C2×Q8×C5912yes—
515C22×C4C2×Q8×C5912yes—
516C22×C4C2×Q8×C5912yes—
517C22×C4C2×Q8×C5912yes—
518C22×C4#41×C5912yes—
519C22×C4#41×C5912yes—
520C22×C4#41×C5912yes—
521C22×C4#41×C5912yes—
522C22×C4#41×C5912yes—
523C4⋊C4—28no—
524C4⋊C4—28no—
525C4⋊C4—28no—
526C4⋊C4—28no—
527C4⋊C4—48no—
528C4⋊C4—48no—
529C4⋊C4—48no—
530C4⋊C4—44no—
531C4⋊C4C4⋊C4×C59116yescomplemented
532C42—28no—
533C42—28no—
534C42—48no—
535C42—44no—
536C23C23×C4×C5911yescharacteristic
537C23C22×D4×C5911yescharacteristic
538C23C22×D4×C5911yescharacteristic
539C23C22×Q8×C5911yescharacteristic
540C23C22×Q8×C5911yescharacteristic
541C23C22×Q8×C5911yescharacteristic
542C23C2×#41×C5911yescharacteristic
543C23C2×#41×C5911yescharacteristic
544C23C2×#41×C5911yescharacteristic
545C23C2×#41×C5911yescharacteristic
546C23C2×#41×C5911yescharacteristic
547C23H(5,𝔽2)×C5911yescharacteristic
548C23H(5,𝔽2)×C5911yescharacteristic
549C23H(5,𝔽2)×C5911yescharacteristic
550C232−1+4×C5911yescharacteristic
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—24no—
554C2×C4—24no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—24no—
563C2×C4—24no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—24no—
567C2×C4—24no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—24no—
571C2×C4—22no—
572C2×C4—24no—
573C2×C4—22no—
574C2×C4—24no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—24no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—24no—
586C2×C4—24no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—42no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—41no—
600C2×C4—42no—
601C2×C4—42no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—42no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—42no—
612C2×C4—42no—
613C2×C4—42no—
614C2×C4—42no—
615C2×C4—42no—
616C2×C4—42no—
617C2×C4—42no—
618C2×C4C2×C4⋊C4×C5918yes—
619C2×C4C2×C4⋊C4×C5914yes—
620C2×C4C4×D4×C5914yes—
621C2×C4C4×Q8×C5914yes—
622C2×C4C4×Q8×C5914yes—
623C2×C4#121×C5914yes—
624C2×C4C22⋊Q8×C5914yes—
625C2×C4C22⋊Q8×C5914yes—
626C2×C4#125×C5914yes—
627C2×C4C4⋊Q8×C5914yes—
628C22C22×C4⋊C4×C5911yescharacteristic
629C22C2×C4×D4×C5911yescharacteristic
630C22C2×C4×Q8×C5911yescharacteristic
631C22C2×C4×Q8×C5911yescharacteristic
632C22C4×#41×C5911yescharacteristic
633C22C59×#51811yescharacteristic
634C22C59×#52011yescharacteristic
635C22C2×#121×C5911yescharacteristic
636C22C2×C22⋊Q8×C5911yescharacteristic
637C22C2×C22⋊Q8×C5911yescharacteristic
638C22C59×#52511yescharacteristic
639C22C2×#125×C5911yescharacteristic
640C22C59×#52911yescharacteristic
641C22C2×C4⋊Q8×C5911yescharacteristic
642C22C59×#53311yescharacteristic
643C22C59×#53511yescharacteristic
644C22C59×#53711yescharacteristic
645C22C59×#54011yescharacteristic
646C22C59×#54211yescharacteristic
647C22C59×#54611yescharacteristic
648C22C59×#54611yescharacteristic
649C22D4×Q8×C5911yescharacteristic
650C22C59×#55011yescharacteristic
651C22C59×#55211yescharacteristic
652C22C59×#55311yescharacteristic
653C22C59×#55411yescharacteristic
654C22C59×#55411yescharacteristic
655C22C59×#55411yescharacteristic
656C22C59×#55411yescharacteristic
657C22C59×#55411yescharacteristic
658C22C59×#55511yescharacteristic
659C22C59×#55711yescharacteristic
660C22C59×#55711yescharacteristic
661C22Q82×C5911yescharacteristic
662C22Q82×C5911yescharacteristic
663C4—24no—
664C4—28no—
665C4—24no—
666C4—42no—
667C4—44no—
668C4—42no—
669C4—42no—
670C4—42no—
671C4—44no—
672C4—82no—
673C4C59×#38918yes—
674C2C2×C59×#38911yescharacteristic
675C2C4×C22⋊Q8×C5911yescharacteristic
676C2C59×#232411yescharacteristic
677C2C59×#234911yescharacteristic
678C2Q8×C4⋊C4×C5911yescharacteristic
679C2C59×#236911yescharacteristic
680C2C59×#237011yescharacteristic
681C2C59×#241411yescharacteristic
682C2C59×#241711yescharacteristic
683C2C59×#245111yescharacteristic
684C2C59×#245411yescharacteristic
685C2C59×#250711yescharacteristic
686C2C59×#250811yescharacteristic
687C2C59×#256711yescharacteristic
688C2C59×#258411yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C59C24
commutatorC23C23×C4×C59
Frattini, cosocleC24C24×C59
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C59 ◁ G

Complements

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

NH ≅ G/Ntype
27. C59×#389C4semidirect
186. C4⋊C4×C59C4⋊C4semidirect
283. #14045C59direct (N × H)
371. #389C4×C59semidirect
384. C59#14045direct (N × H)
531. C4⋊C4C4⋊C4×C59semidirect

Maximal subgroups

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

subgroupindex
C2×C59×#3892
C2×C4×C4⋊C4×C592
C59×#14442
C59×#14412
C59×#14362
C59×C4⋊#952
#1404559