Finite Group Databasebeta

← C59×#35846 #28447955

Subgroups — C59×#35846 #28447955

Order 15104.

2262 conjugacy classes of subgroups.

The subgroup lattice has 706 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C59×#556C211yesmaximal, characteristic, complemented
2C2×C59×#520C211yesmaximal, characteristic
3C59×#2638C212yesmaximal, complemented
4C59×#2621C211yesmaximal, characteristic, complemented
5C59×#2583C212yesmaximal, complemented
6C59×#2581C211yesmaximal, characteristic, complemented
7C59×#2546C211yesmaximal, characteristic, complemented
8C59×#2484C212yesmaximal, complemented
9C59×#2478C214yesmaximal, complemented
10C59×#2466C214yesmaximal, complemented
11C59×#2447C212yesmaximal, complemented
12C59×#2432C212yesmaximal
13C59×#2396C211yesmaximal, characteristic, complemented
14C59×#2395C212yesmaximal, complemented
15C59×#2365C212yesmaximal, complemented
16C59×#2360C212yesmaximal, complemented
17C59×#2357C211yesmaximal, characteristic, complemented
18C22×#41×C59C2211yescharacteristic
19C59×#556—28no—
20C2×C4⋊Q8×C59C2212yes—
21C2×C4⋊Q8×C59C2211yescharacteristic
22C2×#126×C59C2214yes—
23C2×#124×C59C2212yes—
24C2×C22⋊Q8×C59C2212yes—
25C2×C22⋊Q8×C59C2212yes—
26C59×#520—28no—
27C2×C4×Q8×C59C2211yescharacteristic
28C2×C4×Q8×C59C2211yescharacteristic
29C2×C4×Q8×C59C2212yes—
30C2×C4×Q8×C59C2211yescharacteristic
31C2×C4×D4×C59C2212yes—
32C2×C4×D4×C59C2211yescharacteristic
33C2×C4×D4×C59C2212yes—
34C2×C4×D4×C59C2211yescharacteristic
35C2×#117×C59C2212yes—
36C2×#117×C59C2211yescharacteristic
37C2×#117×C59C2212yes—
38C22×C4⋊C4×C59C2212yes—
39C22×C4⋊C4×C59C2211yescharacteristic
40C59×#400C2211yescharacteristic
41C59×#400C2212yes—
42C59×#399C2211yescharacteristic
43C59×#398C2212yes—
44C59×#398C2212yes—
45C59×#398C2212yes—
46C59×#398C2212yes—
47C59×#398C2212yes—
48C59×#397C2212yes—
49C59×#397C2212yes—
50C59×#397C2214yes—
51C59×#397C2214yes—
52C59×#396C2212yes—
53C59×#395C2212yes—
54C59×#395C2211yescharacteristic
55C59×#394C2214yes—
56C59×#394C2214yes—
57C59×#393C2211yescharacteristic
58C59×#391C2212yes—
59C59×#391C2212yes—
60C59×#391C2212yes—
61C59×#390C2212yes—
62C59×#389C2214yes—
63C59×#389C2212yes—
64C59×#389C2214yes—
65C59×#389C2214yes—
66C59×#388C2214yes—
67C59×#387C2214yes—
68C59×#387C2214yes—
69C59×#387C2214yes—
70C59×#387C2214yes—
71C59×#385C2214yes—
72C59×#385C2214yes—
73C59×#385C2214yes—
74C59×#385C2214yes—
75C59×#382C2211yescharacteristic
76C59×#381C2212yes—
77C59×#381C2214yes—
78C4×C4⋊C4×C59C2211yescharacteristic
79C4×C4⋊C4×C59C2212yes—
80C4×C4⋊C4×C59C2214yes—
81C4×C4⋊C4×C59C2212yes—
82C4×C22⋊C4×C59C2212yes—
83C4×C22⋊C4×C59C2214yes—
84C4×C22⋊C4×C59C2212yes—
85C2×#41×C59—24no—
86C2×#41×C59—24no—
87C2×#41×C59—24no—
88C22×Q8×C59C2312yes—
89C22×Q8×C59C2311yescharacteristic
90C22×Q8×C59C2311yescharacteristic
91C22×D4×C59C2312yes—
92C22×D4×C59C2311yescharacteristic
93C23×C4×C59C2312yes—
94C23×C4×C59C2311yescharacteristic
95C23×C4×C59C2312yes—
96C23×C4×C59C2312yes—
97C23×C4×C59C2312yes—
98C4⋊Q8×C59—28no—
99C4⋊Q8×C59—24no—
100#126×C59—216no—
101#124×C59—28no—
102C22⋊Q8×C59—28no—
103C22⋊Q8×C59—28no—
104C4×Q8×C59—24no—
105C4×Q8×C59—28no—
106C4×Q8×C59—24no—
107C4×Q8×C59—24no—
108C4×D4×C59—24no—
109C4×D4×C59—28no—
110C4×D4×C59—28no—
111C4×D4×C59D418yes—
112#117×C59—28no—
113#117×C59—28no—
114#117×C59—24no—
115C2×C4⋊C4×C59—28no—
116C2×C4⋊C4×C59—24no—
117C2×C4⋊C4×C59C2312yes—
118C2×C4⋊C4×C59C2312yes—
119C2×C4⋊C4×C59C2314yes—
120C2×C4⋊C4×C59C2312yes—
121C2×C4⋊C4×C59C2314yes—
122C2×C4⋊C4×C59C2314yes—
123C2×C4⋊C4×C59C2314yes—
124C2×C4⋊C4×C59C2312yes—
125C2×C4⋊C4×C59C2312yes—
126C2×C4⋊C4×C59C2312yes—
127C2×C4⋊C4×C59C2311yescharacteristic
128C2×C4⋊C4×C59C2312yes—
129C2×C4⋊C4×C59C2311yescharacteristic
130C2×C4⋊C4×C59C2312yes—
131C2×C4⋊C4×C59C2312yes—
132C2×C4⋊C4×C59C2311yescharacteristic
133C2×C4⋊C4×C59C2311yescharacteristic
134C2×C4⋊C4×C59C2312yes—
135C2×C4⋊C4×C59C2314yes—
136C2×C4⋊C4×C59C2311yescharacteristic
137C2×C22⋊C4×C59C2312yes—
138C2×C22⋊C4×C59C2314yes—
139C2×C22⋊C4×C59C2314yes—
140C2×C22⋊C4×C59C2314yes—
141C2×C22⋊C4×C59C2314yes—
142C2×C22⋊C4×C59C2311yescharacteristic
143C2×C22⋊C4×C59C2311yescharacteristic
144C2×C22⋊C4×C59C2312yes—
145C2×C22⋊C4×C59C2312yes—
146C2×C22⋊C4×C59C2314yes—
147C2×C22⋊C4×C59C2312yes—
148C2×C42×C59C2312yes—
149C2×C42×C59C2314yes—
150C2×C42×C59C2312yes—
151C2×C42×C59C2312yes—
152C2×C42×C59C2311yescharacteristic
153C2×C42×C59C2312yes—
154C2×C42×C59C2314yes—
155C2×C42×C59C2311yescharacteristic
156#95×C59C2311yescharacteristic
157#95×C59C2312yes—
158#95×C59C2314yes—
159#95×C59C2312yes—
160#95×C59C2312yes—
161#95×C59C2314yes—
162#95×C59C2312yes—
163#95×C59C2311yescharacteristic
164#95×C59C2314yes—
165#95×C59C2314yes—
166#95×C59C2312yes—
167#95×C59C2314yes—
168#95×C59C2314yes—
169#95×C59C2314yes—
170#95×C59C2312yes—
171#95×C59C2314yes—
172C24×C59C2412yes—
173C24×C59C2411yescharacteristic
174#41×C59—232no—
175C2×Q8×C59—22no—
176C2×Q8×C59—22no—
177C2×Q8×C59—24no—
178C2×Q8×C59—22no—
179C2×Q8×C59—24no—
180C2×Q8×C59—24no—
181C2×Q8×C59—42no—
182C2×Q8×C59#4114yes—
183C2×D4×C59—24no—
184C2×D4×C59—24no—
185C2×D4×C59—24no—
186C2×D4×C59—22no—
187C2×D4×C59—22no—
188C2×D4×C59C2×D414yes—
189C22×C4×C59—24no—
190C22×C4×C59—22no—
191C22×C4×C59—24no—
192C22×C4×C59—24no—
193C22×C4×C59—22no—
194C22×C4×C59—24no—
195C22×C4×C59—24no—
196C22×C4×C59—44no—
197C22×C4×C59—44no—
198C22×C4×C59—44no—
199C22×C4×C59C2×D418yes—
200C22×C4×C59#4114yes—
201C22×C4×C59C2412yes—
202C22×C4×C59C2414yes—
203C22×C4×C59C2411yescharacteristic
204C22×C4×C59C2412yes—
205C22×C4×C59C2412yes—
206C22×C4×C59C2411yescharacteristic
207C22×C4×C59C2414yes—
208C22×C4×C59C2412yes—
209C22×C4×C59C2411yescharacteristic
210C22×C4×C59C2412yes—
211C22×C4×C59C2411yescharacteristic
212C22×C4×C59C2412yes—
213C22×C4×C59C2411yescharacteristic
214C22×C4×C59C2412yes—
215C22×C4×C59C2411yescharacteristic
216C4⋊C4×C59—24no—
217C4⋊C4×C59—22no—
218C4⋊C4×C59—24no—
219C4⋊C4×C59—24no—
220C4⋊C4×C59—22no—
221C4⋊C4×C59—22no—
222C4⋊C4×C59—22no—
223C4⋊C4×C59—24no—
224C4⋊C4×C59—28no—
225C4⋊C4×C59—24no—
226C4⋊C4×C59—24no—
227C4⋊C4×C59—24no—
228C4⋊C4×C59—28no—
229C4⋊C4×C59—28no—
230C4⋊C4×C59—28no—
231C4⋊C4×C59—24no—
232C4⋊C4×C59—24no—
233C4⋊C4×C59—42no—
234C4⋊C4×C59—44no—
235C4⋊C4×C59C2×D414yes—
236C22⋊C4×C59—24no—
237C22⋊C4×C59—28no—
238C22⋊C4×C59—28no—
239C22⋊C4×C59—28no—
240C22⋊C4×C59—22no—
241C22⋊C4×C59—22no—
242C22⋊C4×C59—24no—
243C22⋊C4×C59—28no—
244C22⋊C4×C59—44no—
245C22⋊C4×C59—42no—
246C22⋊C4×C59C2×D418yes—
247C42×C59—24no—
248C42×C59—24no—
249C42×C59—22no—
250C42×C59—28no—
251C42×C59—24no—
252C42×C59—24no—
253C42×C59—44no—
254C42×C59C2×D414yes—
255C23×C59—21no—
256C23×C59—22no—
257C23×C59—22no—
258C23×C59—21no—
259C23×C59—24no—
260C23×C59—22no—
261C23×C59—24no—
262C23×C59—22no—
263C23×C59C22×D414yes—
264C23×C59C2×#4112yes—
265C23×C59C2511yescharacteristic
266Q8×C59—28no—
267Q8×C59—44no—
268Q8×C59—48no—
269D4×C59—216no—
270D4×C59—28no—
271C2×C4×C59—216no—
272C2×C4×C59—22no—
273C2×C4×C59—21no—
274C2×C4×C59—22no—
275C2×C4×C59—21no—
276C2×C4×C59—22no—
277C2×C4×C59—22no—
278C2×C4×C59—22no—
279C2×C4×C59—24no—
280C2×C4×C59—22no—
281C2×C4×C59—28no—
282C2×C4×C59—21no—
283C2×C4×C59—22no—
284C2×C4×C59—24no—
285C2×C4×C59—22no—
286C2×C4×C59—22no—
287C2×C4×C59—21no—
288C2×C4×C59—22no—
289C2×C4×C59—24no—
290C2×C4×C59—24no—
291C2×C4×C59—24no—
292C2×C4×C59—22no—
293C2×C4×C59—24no—
294C2×C4×C59—22no—
295C2×C4×C59—22no—
296C2×C4×C59—22no—
297C2×C4×C59—24no—
298C2×C4×C59—22no—
299C2×C4×C59—22no—
300C2×C4×C59—22no—
301C2×C4×C59—24no—
302C2×C4×C59—22no—
303C2×C4×C59—48no—
304C2×C4×C59—84no—
305C2×C4×C59—84no—
306C2×C4×C59C22×D414yes—
307C2×C4×C59C22×D412yes—
308C2×C4×C59C22×D412yes—
309C2×C4×C59C22×D412yes—
310C2×C4×C59C2×#4112yes—
311C2×C4×C59C2×#4114yes—
312C2×C4×C59C2×#4112yes—
313C2×C4×C59C2×#4112yes—
314C2×C4×C592−1+414yes—
315#35846C5911yesmaximal, characteristic, direct product factor, Sylow
316C22×C59—24no—
317C22×C59—22no—
318C22×C59—24no—
319C22×C59—24no—
320C22×C59—24no—
321C22×C59—41no—
322C22×C59—41no—
323C22×C59—44no—
324C22×C59—44no—
325C22×C59—42no—
326C22×C59C23×D411yescharacteristic
327C22×C59C22×#4111yescharacteristic
328C22×C59C22×#4111yescharacteristic
329C22×C59C2×2−1+412yes—
330C22×C59#58512yes—
331C4×C59—22no—
332C4×C59—24no—
333C4×C59—22no—
334C4×C59—24no—
335C4×C59—22no—
336C4×C59—24no—
337C4×C59—44no—
338C4×C59—42no—
339C4×C59—41no—
340C4×C59—42no—
341C4×C59—41no—
342C4×C59—42no—
343C4×C59—44no—
344C4×C59—42no—
345C4×C59#52514yes—
346C2×#556C2×C5911yescharacteristic, complemented
347C2×#520C2×C5911yescharacteristic
348#2638C2×C5912yescomplemented
349#2621C2×C5911yescharacteristic, complemented
350#2583C2×C5912yescomplemented
351#2581C2×C5911yescharacteristic, complemented
352#2546C2×C5911yescharacteristic, complemented
353#2484C2×C5912yescomplemented
354#2478C2×C5914yescomplemented
355#2466C2×C5914yescomplemented
356#2447C2×C5912yescomplemented
357#2432C2×C5912yes—
358#2396C2×C5911yescharacteristic, complemented
359#2395C2×C5912yescomplemented
360#2365C2×C5912yescomplemented
361#2360C2×C5912yescomplemented
362#2357C2×C5911yescharacteristic, complemented
363C2×C59—44no—
364C2×C59—42no—
365C2×C59C2×#52511yescharacteristic
366C2×C59#348511yescharacteristic
367C2×C59#349911yescharacteristic
368C2×C59#350712yes—
369C2×C59#351612yes—
370C22×#41C22×C5911yescharacteristic
371#556—28no—
372C2×C4⋊Q8C22×C5912yes—
373C2×C4⋊Q8C22×C5911yescharacteristic
374C2×#126C22×C5914yes—
375C2×#124C22×C5912yes—
376C2×C22⋊Q8C22×C5912yes—
377C2×C22⋊Q8C22×C5912yes—
378#520—28no—
379C2×C4×Q8C22×C5911yescharacteristic
380C2×C4×Q8C22×C5911yescharacteristic
381C2×C4×Q8C22×C5912yes—
382C2×C4×Q8C22×C5911yescharacteristic
383C2×C4×D4C22×C5912yes—
384C2×C4×D4C22×C5911yescharacteristic
385C2×C4×D4C22×C5912yes—
386C2×C4×D4C22×C5911yescharacteristic
387C2×#117C22×C5911yescharacteristic
388C2×#117C22×C5912yes—
389C2×#117C22×C5912yes—
390C22×C4⋊C4C22×C5912yes—
391C22×C4⋊C4C22×C5911yescharacteristic
392#400C22×C5912yes—
393#400C22×C5911yescharacteristic
394#399C22×C5911yescharacteristic
395#398C22×C5912yes—
396#398C22×C5912yes—
397#398C22×C5912yes—
398#398C22×C5912yes—
399#398C22×C5912yes—
400#397C22×C5912yes—
401#397C22×C5912yes—
402#397C22×C5914yes—
403#397C22×C5914yes—
404#396C22×C5912yes—
405#395C22×C5912yes—
406#395C22×C5911yescharacteristic
407#394C22×C5914yes—
408#394C22×C5914yes—
409#393C22×C5911yescharacteristic
410#391C22×C5912yes—
411#391C22×C5912yes—
412#391C22×C5912yes—
413#390C22×C5912yes—
414#389C22×C5912yes—
415#389C22×C5914yes—
416#389C22×C5914yes—
417#389C22×C5914yes—
418#388C22×C5914yes—
419#387C22×C5914yes—
420#387C22×C5914yes—
421#387C22×C5914yes—
422#387C22×C5914yes—
423#385C22×C5914yes—
424#385C22×C5914yes—
425#385C22×C5914yes—
426#385C22×C5914yes—
427#382C22×C5911yescharacteristic
428#381C22×C5912yes—
429#381C22×C5914yes—
430C4×C4⋊C4C22×C5912yes—
431C4×C4⋊C4C22×C5911yescharacteristic
432C4×C4⋊C4C22×C5914yes—
433C4×C4⋊C4C22×C5912yes—
434C4×C22⋊C4C22×C5912yes—
435C4×C22⋊C4C22×C5914yes—
436C4×C22⋊C4C22×C5912yes—
437C59#3584611yescharacteristic, direct product factor, Sylow
438C2×#41—24no—
439C2×#41—24no—
440C2×#41—24no—
441C22×Q8C23×C5912yes—
442C22×Q8C23×C5911yescharacteristic
443C22×Q8C23×C5911yescharacteristic
444C22×D4C23×C5912yes—
445C22×D4C23×C5911yescharacteristic
446C23×C4C23×C5912yes—
447C23×C4C23×C5911yescharacteristic
448C23×C4C23×C5912yes—
449C23×C4C23×C5912yes—
450C23×C4C23×C5912yes—
451C4⋊Q8—28no—
452C4⋊Q8—24no—
453#126—216no—
454#124—28no—
455C22⋊Q8—28no—
456C22⋊Q8—28no—
457C4×Q8—24no—
458C4×Q8—28no—
459C4×Q8—24no—
460C4×Q8—24no—
461C4×D4—24no—
462C4×D4—28no—
463C4×D4—28no—
464C4×D4D4×C5918yes—
465#117—28no—
466#117—28no—
467#117—24no—
468C2×C4⋊C4—28no—
469C2×C4⋊C4—24no—
470C2×C4⋊C4C23×C5912yes—
471C2×C4⋊C4C23×C5911yescharacteristic
472C2×C4⋊C4C23×C5912yes—
473C2×C4⋊C4C23×C5911yescharacteristic
474C2×C4⋊C4C23×C5912yes—
475C2×C4⋊C4C23×C5911yescharacteristic
476C2×C4⋊C4C23×C5911yescharacteristic
477C2×C4⋊C4C23×C5912yes—
478C2×C4⋊C4C23×C5914yes—
479C2×C4⋊C4C23×C5912yes—
480C2×C4⋊C4C23×C5912yes—
481C2×C4⋊C4C23×C5914yes—
482C2×C4⋊C4C23×C5912yes—
483C2×C4⋊C4C23×C5914yes—
484C2×C4⋊C4C23×C5914yes—
485C2×C4⋊C4C23×C5912yes—
486C2×C4⋊C4C23×C5912yes—
487C2×C4⋊C4C23×C5912yes—
488C2×C4⋊C4C23×C5914yes—
489C2×C4⋊C4C23×C5911yescharacteristic
490C2×C22⋊C4C23×C5911yescharacteristic
491C2×C22⋊C4C23×C5911yescharacteristic
492C2×C22⋊C4C23×C5912yes—
493C2×C22⋊C4C23×C5914yes—
494C2×C22⋊C4C23×C5914yes—
495C2×C22⋊C4C23×C5914yes—
496C2×C22⋊C4C23×C5912yes—
497C2×C22⋊C4C23×C5914yes—
498C2×C22⋊C4C23×C5912yes—
499C2×C22⋊C4C23×C5914yes—
500C2×C22⋊C4C23×C5912yes—
501C2×C42C23×C5912yes—
502C2×C42C23×C5911yescharacteristic
503C2×C42C23×C5912yes—
504C2×C42C23×C5914yes—
505C2×C42C23×C5912yes—
506C2×C42C23×C5912yes—
507C2×C42C23×C5914yes—
508C2×C42C23×C5911yescharacteristic
509#95C23×C5911yescharacteristic
510#95C23×C5912yes—
511#95C23×C5914yes—
512#95C23×C5912yes—
513#95C23×C5912yes—
514#95C23×C5914yes—
515#95C23×C5912yes—
516#95C23×C5911yescharacteristic
517#95C23×C5914yes—
518#95C23×C5914yes—
519#95C23×C5912yes—
520#95C23×C5914yes—
521#95C23×C5914yes—
522#95C23×C5914yes—
523#95C23×C5912yes—
524#95C23×C5914yes—
525C24C24×C5912yes—
526C24C24×C5911yescharacteristic
527#41—232no—
528C2×Q8—22no—
529C2×Q8—22no—
530C2×Q8—24no—
531C2×Q8—22no—
532C2×Q8—24no—
533C2×Q8—24no—
534C2×Q8—42no—
535C2×Q8#41×C5914yes—
536C2×D4—24no—
537C2×D4—24no—
538C2×D4—24no—
539C2×D4—22no—
540C2×D4—22no—
541C2×D4C2×D4×C5914yes—
542C22×C4—24no—
543C22×C4—22no—
544C22×C4—24no—
545C22×C4—24no—
546C22×C4—22no—
547C22×C4—24no—
548C22×C4—24no—
549C22×C4—44no—
550C22×C4—44no—
551C22×C4—44no—
552C22×C4C2×D4×C5918yes—
553C22×C4#41×C5914yes—
554C22×C4C24×C5912yes—
555C22×C4C24×C5914yes—
556C22×C4C24×C5911yescharacteristic
557C22×C4C24×C5912yes—
558C22×C4C24×C5912yes—
559C22×C4C24×C5911yescharacteristic
560C22×C4C24×C5914yes—
561C22×C4C24×C5912yes—
562C22×C4C24×C5911yescharacteristic
563C22×C4C24×C5912yes—
564C22×C4C24×C5911yescharacteristic
565C22×C4C24×C5912yes—
566C22×C4C24×C5911yescharacteristic
567C22×C4C24×C5912yes—
568C22×C4C24×C5911yescharacteristic
569C4⋊C4—24no—
570C4⋊C4—22no—
571C4⋊C4—24no—
572C4⋊C4—24no—
573C4⋊C4—22no—
574C4⋊C4—22no—
575C4⋊C4—22no—
576C4⋊C4—24no—
577C4⋊C4—28no—
578C4⋊C4—24no—
579C4⋊C4—24no—
580C4⋊C4—24no—
581C4⋊C4—28no—
582C4⋊C4—28no—
583C4⋊C4—28no—
584C4⋊C4—24no—
585C4⋊C4—24no—
586C4⋊C4—42no—
587C4⋊C4—44no—
588C4⋊C4C2×D4×C5914yes—
589C22⋊C4—24no—
590C22⋊C4—28no—
591C22⋊C4—28no—
592C22⋊C4—28no—
593C22⋊C4—22no—
594C22⋊C4—22no—
595C22⋊C4—24no—
596C22⋊C4—28no—
597C22⋊C4—44no—
598C22⋊C4—42no—
599C22⋊C4C2×D4×C5918yes—
600C42—24no—
601C42—24no—
602C42—22no—
603C42—28no—
604C42—24no—
605C42—24no—
606C42—44no—
607C42C2×D4×C5914yes—
608C23—21no—
609C23—22no—
610C23—22no—
611C23—21no—
612C23—22no—
613C23—24no—
614C23—22no—
615C23—24no—
616C23C22×D4×C5914yes—
617C23C2×#41×C5912yes—
618C23C25×C5911yescharacteristic
619Q8—28no—
620Q8—44no—
621Q8—48no—
622D4—216no—
623D4—28no—
624C2×C4—216no—
625C2×C4—22no—
626C2×C4—21no—
627C2×C4—22no—
628C2×C4—21no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—24no—
633C2×C4—22no—
634C2×C4—28no—
635C2×C4—21no—
636C2×C4—22no—
637C2×C4—24no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—21no—
641C2×C4—22no—
642C2×C4—24no—
643C2×C4—24no—
644C2×C4—24no—
645C2×C4—24no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—24no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—24no—
655C2×C4—22no—
656C2×C4—48no—
657C2×C4—84no—
658C2×C4—84no—
659C2×C4C22×D4×C5914yes—
660C2×C4C22×D4×C5912yes—
661C2×C4C22×D4×C5912yes—
662C2×C4C22×D4×C5912yes—
663C2×C4C2×#41×C5912yes—
664C2×C4C2×#41×C5914yes—
665C2×C4C2×#41×C5912yes—
666C2×C4C2×#41×C5912yes—
667C2×C42−1+4×C5914yes—
668C22—24no—
669C22—24no—
670C22—22no—
671C22—24no—
672C22—24no—
673C22—44no—
674C22—42no—
675C22—44no—
676C22—41no—
677C22—41no—
678C22C23×D4×C5911yescharacteristic
679C22C22×#41×C5911yescharacteristic
680C22C22×#41×C5911yescharacteristic
681C22C2×2−1+4×C5912yes—
682C22C59×#58512yes—
683C4—24no—
684C4—22no—
685C4—24no—
686C4—22no—
687C4—24no—
688C4—22no—
689C4—44no—
690C4—42no—
691C4—44no—
692C4—42no—
693C4—41no—
694C4—42no—
695C4—41no—
696C4—42no—
697C4C59×#52514yes—
698C2—42no—
699C2—44no—
700C2C2×C59×#52511yescharacteristic
701C2C59×#348511yescharacteristic
702C2C59×#349911yescharacteristic
703C2C59×#350712yes—
704C2C59×#351612yes—
subgroupG/H
center, socleC23×C59C25
commutator, Frattini, cosocleC23C25×C59
prime radicalC22×#41×C59C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C59 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C59×#556C2semidirect
3. C59×#2638C2semidirect
4. C59×#2621C2semidirect
5. C59×#2583C2semidirect
6. C59×#2581C2semidirect
7. C59×#2546C2semidirect
8. C59×#2484C2semidirect
9. C59×#2478C2semidirect
10. C59×#2466C2semidirect
11. C59×#2447C2semidirect
13. C59×#2396C2semidirect
14. C59×#2395C2semidirect
15. C59×#2365C2semidirect
16. C59×#2360C2semidirect
17. C59×#2357C2semidirect
315. #35846C59direct (N × H)
346. C2×#556C2×C59semidirect
348. #2638C2×C59semidirect
349. #2621C2×C59semidirect
350. #2583C2×C59semidirect
351. #2581C2×C59semidirect
352. #2546C2×C59semidirect
353. #2484C2×C59semidirect
354. #2478C2×C59semidirect
355. #2466C2×C59semidirect
356. #2447C2×C59semidirect
358. #2396C2×C59semidirect
359. #2395C2×C59semidirect
360. #2365C2×C59semidirect
361. #2360C2×C59semidirect
362. #2357C2×C59semidirect
437. C59#35846direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C59×#5562
C2×C59×#5202
C59×#26382
C59×#26212
C59×#25832
C59×#25812
C59×#25462
C59×#24842
C59×#24782
C59×#24662
C59×#24472
C59×#24322
C59×#23962
C59×#23952
C59×#23652
C59×#23602
C59×#23572
#3584659