Finite Group Databasebeta

← C59×#35267 #28447376

Subgroups — C59×#35267 #28447376

Order 15104.

1806 conjugacy classes of subgroups.

The subgroup lattice has 714 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C59×#2863C212yesmaximal, complemented
2C59×#2860C212yesmaximal, complemented
3C59×#2645C212yesmaximal, complemented
4C59×#2644C212yesmaximal, complemented
5C59×#2510C214yesmaximal, complemented
6C59×#2497C212yesmaximal, complemented
7C59×#2496C212yesmaximal, complemented
8C59×#2495C212yesmaximal, complemented
9C59×#2494C212yesmaximal, complemented
10C59×#2481C214yesmaximal, complemented
11C59×#2317C211yesmaximal, characteristic, complemented
12C59×#2316C211yesmaximal, characteristic, complemented
13C59×#2311C211yesmaximal, characteristic
14C59×#2311C211yesmaximal, characteristic
15C59×#2297C211yesmaximal, characteristic
16C2×C59×#389C211yesmaximal, characteristic, complemented
17C4×#117×C59C211yesmaximal, characteristic, complemented
18C22×#41×C59C2211yescharacteristic
19C2×#126×C59C2214yes—
20C2×#117×C59C2211yescharacteristic
21C2×#117×C59C2211yescharacteristic
22C2×#117×C59C2211yescharacteristic
23C22×C4⋊C4×C59C2211yescharacteristic
24C22×C4⋊C4×C59C2211yescharacteristic
25C22×C4⋊C4×C59C2212yes—
26C22×C42×C59C2211yescharacteristic
27C59×#401C2214yes—
28C59×#400C2214yes—
29C59×#400C2214yes—
30C59×#400C2214yes—
31C59×#397C2214yes—
32C59×#397C2214yes—
33C59×#397C2214yes—
34C59×#396C2214yes—
35C59×#391C2211yescharacteristic
36C59×#391C2211yescharacteristic
37C59×#391C2212yes—
38C59×#391C2212yes—
39C59×#390C2211yescharacteristic
40C59×#390C2211yescharacteristic
41C59×#390C2212yes—
42C59×#390C2212yes—
43C59×#389C2212yes—
44C59×#389C2212yes—
45C59×#389C2212yes—
46C59×#389C2212yes—
47C59×#389C2212yes—
48C59×#389C2212yes—
49C59×#389C2212yes—
50C59×#389C2212yes—
51C59×#389C2212yes—
52C59×#389C2212yes—
53C59×#388C2214yes—
54C59×#388C2214yes—
55C59×#388C2214yes—
56C59×#387C2214yes—
57C59×#387C2214yes—
58C59×#387C2214yes—
59C59×#386C2212yes—
60C59×#386C2214yes—
61C59×#386C2214yes—
62C59×#386C2212yes—
63C59×#385C2214yes—
64C59×#384C2212yes—
65C59×#383C2214yes—
66C59×#382C2212yes—
67C59×#380C2212yes—
68C59×#380C2212yes—
69C59×#380C2212yes—
70C59×#380C2212yes—
71C59×#380C2214yes—
72C4×C4⋊C4×C59C2211yescharacteristic
73C4×C4⋊C4×C59C2211yescharacteristic
74C4×C4⋊C4×C59C2211yescharacteristic
75C4×C4⋊C4×C59C2211yescharacteristic
76C4×C22⋊C4×C59C2212yes—
77C4×C22⋊C4×C59C2212yes—
78C4×C22⋊C4×C59C2212yes—
79C4×C22⋊C4×C59C2212yes—
80C59×#376C2212yes—
81C2×#95×C59C2212yes—
82C43×C59C2212yes—
83C2×#41×C59—24no—
84C2×#41×C59—24no—
85C2×#41×C59—24no—
86C22×Q8×C59C2311yescharacteristic
87C22×D4×C59C2312yes—
88C22×D4×C59C2311yescharacteristic
89C23×C4×C59C2312yes—
90C23×C4×C59C2311yescharacteristic
91C23×C4×C59C2311yescharacteristic
92C23×C4×C59C2312yes—
93C23×C4×C59C2312yes—
94C23×C4×C59C2311yescharacteristic
95#126×C59—48no—
96#117×C59—24no—
97#117×C59—24no—
98#117×C59—24no—
99C2×C4⋊C4×C59—24no—
100C2×C4⋊C4×C59—24no—
101C2×C4⋊C4×C59—44no—
102C2×C4⋊C4×C59C2311yescharacteristic
103C2×C4⋊C4×C59C2311yescharacteristic
104C2×C4⋊C4×C59C2311yescharacteristic
105C2×C4⋊C4×C59C2311yescharacteristic
106C2×C4⋊C4×C59C2312yes—
107C2×C4⋊C4×C59C2312yes—
108C2×C4⋊C4×C59C2314yes—
109C2×C4⋊C4×C59C2312yes—
110C2×C4⋊C4×C59C2312yes—
111C2×C4⋊C4×C59C2311yescharacteristic
112C2×C4⋊C4×C59C2311yescharacteristic
113C2×C4⋊C4×C59C2314yes—
114C2×C4⋊C4×C59C2314yes—
115C2×C4⋊C4×C59C2314yes—
116C2×C4⋊C4×C59C2314yes—
117C2×C4⋊C4×C59C2314yes—
118C2×C22⋊C4×C59C2312yes—
119C2×C22⋊C4×C59C2312yes—
120C2×C22⋊C4×C59C2312yes—
121C2×C22⋊C4×C59C2312yes—
122C2×C22⋊C4×C59C2312yes—
123C2×C22⋊C4×C59C2312yes—
124C2×C22⋊C4×C59C2312yes—
125C2×C22⋊C4×C59C2314yes—
126C2×C22⋊C4×C59C2314yes—
127C2×C22⋊C4×C59C2314yes—
128C2×C22⋊C4×C59C2314yes—
129C2×C42×C59—24no—
130C2×C42×C59C2311yescharacteristic
131C2×C42×C59C2312yes—
132C2×C42×C59C2312yes—
133C2×C42×C59C2312yes—
134C2×C42×C59C2312yes—
135C2×C42×C59C2311yescharacteristic
136C2×C42×C59C2311yescharacteristic
137C2×C42×C59C2311yescharacteristic
138C2×C42×C59C2312yes—
139C2×C42×C59C2312yes—
140C2×C42×C59C2312yes—
141#95×C59C2314yes—
142#95×C59C2314yes—
143#95×C59C2312yes—
144#95×C59C2312yes—
145#95×C59C2312yes—
146#95×C59C2312yes—
147#95×C59C2312yes—
148#95×C59C2312yes—
149#95×C59C2312yes—
150#95×C59C2312yes—
151#95×C59C2314yes—
152#95×C59C2314yes—
153#95×C59C2314yes—
154#95×C59C2314yes—
155#95×C59C2314yes—
156#95×C59C2314yes—
157#95×C59C2314yes—
158#95×C59C2314yes—
159C24×C59C2412yes—
160C24×C59C2411yescharacteristic
161#41×C59—416no—
162C2×Q8×C59—22no—
163C2×Q8×C59—22no—
164C2×Q8×C59—22no—
165C2×D4×C59—24no—
166C2×D4×C59—24no—
167C2×D4×C59—24no—
168C2×D4×C59—22no—
169C2×D4×C59—22no—
170C2×D4×C59—22no—
171C22×C4×C59—22no—
172C22×C4×C59—22no—
173C22×C4×C59—24no—
174C22×C4×C59—24no—
175C22×C4×C59—24no—
176C22×C4×C59—24no—
177C22×C4×C59—24no—
178C22×C4×C59—22no—
179C22×C4×C59—22no—
180C22×C4×C59—42no—
181C22×C4×C59—41no—
182C22×C4×C59—41no—
183C22×C4×C59—42no—
184C22×C4×C59—42no—
185C22×C4×C59—42no—
186C22×C4×C59#4114yes—
187C22×C4×C59#4114yes—
188C22×C4×C59#4114yes—
189C22×C4×C59C2412yes—
190C22×C4×C59C2411yescharacteristic
191C22×C4×C59C2412yes—
192C22×C4×C59C2412yes—
193C22×C4×C59C2412yes—
194C22×C4×C59C2411yescharacteristic
195C22×C4×C59C2412yes—
196C22×C4×C59C2412yes—
197C22×C4×C59C2414yes—
198C22×C4×C59C2414yes—
199C22×C4×C59C2412yes—
200C22×C4×C59C2411yescharacteristic
201C22×C4×C59C2411yescharacteristic
202C22×C4×C59C2411yescharacteristic
203C22×C4×C59C2411yescharacteristic
204C4⋊C4×C59—24no—
205C4⋊C4×C59—24no—
206C4⋊C4×C59—24no—
207C4⋊C4×C59—24no—
208C4⋊C4×C59—22no—
209C4⋊C4×C59—22no—
210C4⋊C4×C59—22no—
211C4⋊C4×C59—22no—
212C4⋊C4×C59—22no—
213C4⋊C4×C59—22no—
214C4⋊C4×C59—28no—
215C4⋊C4×C59—44no—
216C4⋊C4×C59—44no—
217C4⋊C4×C59—44no—
218C4⋊C4×C59—44no—
219C4⋊C4×C59—44no—
220C22⋊C4×C59—24no—
221C22⋊C4×C59—24no—
222C22⋊C4×C59—24no—
223C22⋊C4×C59—24no—
224C22⋊C4×C59—24no—
225C22⋊C4×C59—44no—
226C22⋊C4×C59—44no—
227C22⋊C4×C59—42no—
228C22⋊C4×C59—42no—
229C22⋊C4×C59—44no—
230C22⋊C4×C59—44no—
231C42×C59—22no—
232C42×C59—22no—
233C42×C59—22no—
234C42×C59—22no—
235C42×C59—24no—
236C42×C59—24no—
237C42×C59—24no—
238C42×C59—24no—
239C42×C59—24no—
240C42×C59—42no—
241C42×C59—42no—
242C23×C59—21no—
243C23×C59—21no—
244C23×C59—21no—
245C23×C59—21no—
246C23×C59—22no—
247C23×C59—22no—
248C23×C59—22no—
249C23×C59—22no—
250C23×C59—22no—
251C23×C59—22no—
252C23×C59—22no—
253C23×C59C2×#4112yes—
254C23×C59C2×#4112yes—
255C23×C59C2×#4112yes—
256C23×C59C2511yescharacteristic
257Q8×C59—44no—
258D4×C59—48no—
259D4×C59—44no—
260C2×C4×C59—21no—
261C2×C4×C59—21no—
262C2×C4×C59—21no—
263C2×C4×C59—21no—
264C2×C4×C59—21no—
265C2×C4×C59—21no—
266C2×C4×C59—22no—
267C2×C4×C59—22no—
268C2×C4×C59—22no—
269C2×C4×C59—22no—
270C2×C4×C59—22no—
271C2×C4×C59—22no—
272C2×C4×C59—24no—
273C2×C4×C59—24no—
274C2×C4×C59—22no—
275C2×C4×C59—22no—
276C2×C4×C59—22no—
277C2×C4×C59—22no—
278C2×C4×C59—22no—
279C2×C4×C59—22no—
280C2×C4×C59—24no—
281C2×C4×C59—24no—
282C2×C4×C59—21no—
283C2×C4×C59—22no—
284C2×C4×C59—22no—
285C2×C4×C59—22no—
286C2×C4×C59—21no—
287C2×C4×C59—22no—
288C2×C4×C59—22no—
289C2×C4×C59—22no—
290C2×C4×C59—22no—
291C2×C4×C59—21no—
292C2×C4×C59—21no—
293C2×C4×C59—22no—
294C2×C4×C59—22no—
295C2×C4×C59—24no—
296C2×C4×C59—24no—
297C2×C4×C59—44no—
298C2×C4×C59—44no—
299C2×C4×C59—48no—
300C2×C4×C59—48no—
301C2×C4×C59—84no—
302C2×C4×C59#126116yescomplemented
303C2×C4×C59C2×#4112yes—
304C2×C4×C59C2×#4112yes—
305C2×C4×C59C2×#4112yes—
306C2×C4×C59C2×#4112yes—
307C2×C4×C59C2×#4112yes—
308C2×C4×C59C2×#4112yes—
309C2×C4×C59H(5,𝔽2)12yes—
310C2×C4×C592−1+412yes—
311#35267C5911yesmaximal, characteristic, direct product factor, Sylow
312C22×C59—22no—
313C22×C59—22no—
314C22×C59—22no—
315C22×C59—22no—
316C22×C59—22no—
317C22×C59—22no—
318C22×C59—42no—
319C22×C59—42no—
320C22×C59—42no—
321C22×C59—42no—
322C22×C59—42no—
323C22×C59—42no—
324C22×C59—42no—
325C22×C59C2×#12614yes—
326C22×C59C22×#4111yescharacteristic
327C22×C59C22×#4111yescharacteristic
328C22×C59C22×#4111yescharacteristic
329C22×C59C2×H(5,𝔽2)11yescharacteristic
330C22×C59C2×2−1+411yescharacteristic
331C22×C59#58511yescharacteristic
332C22×C59#58511yescharacteristic
333C4×C59—22no—
334C4×C59—22no—
335C4×C59—42no—
336C4×C59—42no—
337C4×C59—44no—
338C4×C59—42no—
339C4×C59—41no—
340C4×C59—44no—
341C4×C59—41no—
342C4×C59—42no—
343C4×C59—42no—
344C4×C59—42no—
345C4×C59—42no—
346C4×C59C2×#12614yes—
347C4×C59C2×#12614yes—
348#2863C2×C5912yescomplemented
349#2860C2×C5912yescomplemented
350#2645C2×C5912yescomplemented
351#2644C2×C5912yescomplemented
352#2510C2×C5914yescomplemented
353#2497C2×C5912yescomplemented
354#2496C2×C5912yescomplemented
355#2495C2×C5912yescomplemented
356#2494C2×C5912yescomplemented
357#2481C2×C5914yescomplemented
358#2317C2×C5911yescharacteristic, complemented
359#2316C2×C5911yescharacteristic, complemented
360#2311C2×C5911yescharacteristic
361#2311C2×C5911yescharacteristic
362#2297C2×C5911yescharacteristic
363C2×#389C2×C5911yescharacteristic, complemented
364C4×#117C2×C5911yescharacteristic, complemented
365C2×C59—24no—
366C2×C59—82no—
367C2×C59C22×#12611yescharacteristic
368C2×C59#346011yescharacteristic
369C2×C59#346111yescharacteristic
370C2×C59#349411yescharacteristic
371C2×C59#349511yescharacteristic
372C2×C59#351111yescharacteristic
373C2×C59#351211yescharacteristic
374C22×#41C22×C5911yescharacteristic
375C2×#126C22×C5914yes—
376C2×#117C22×C5911yescharacteristic
377C2×#117C22×C5911yescharacteristic
378C2×#117C22×C5911yescharacteristic
379C22×C4⋊C4C22×C5911yescharacteristic
380C22×C4⋊C4C22×C5911yescharacteristic
381C22×C4⋊C4C22×C5912yes—
382C22×C42C22×C5911yescharacteristic
383#401C22×C5914yes—
384#400C22×C5914yes—
385#400C22×C5914yes—
386#400C22×C5914yes—
387#397C22×C5914yes—
388#397C22×C5914yes—
389#397C22×C5914yes—
390#396C22×C5914yes—
391#391C22×C5912yes—
392#391C22×C5912yes—
393#391C22×C5911yescharacteristic
394#391C22×C5911yescharacteristic
395#390C22×C5912yes—
396#390C22×C5912yes—
397#390C22×C5911yescharacteristic
398#390C22×C5911yescharacteristic
399#389C22×C5912yes—
400#389C22×C5912yes—
401#389C22×C5912yes—
402#389C22×C5912yes—
403#389C22×C5912yes—
404#389C22×C5912yes—
405#389C22×C5912yes—
406#389C22×C5912yes—
407#389C22×C5912yes—
408#389C22×C5912yes—
409#388C22×C5914yes—
410#388C22×C5914yes—
411#388C22×C5914yes—
412#387C22×C5914yes—
413#387C22×C5914yes—
414#387C22×C5914yes—
415#386C22×C5914yes—
416#386C22×C5914yes—
417#386C22×C5912yes—
418#386C22×C5912yes—
419#385C22×C5914yes—
420#384C22×C5912yes—
421#383C22×C5914yes—
422#382C22×C5912yes—
423#380C22×C5912yes—
424#380C22×C5912yes—
425#380C22×C5912yes—
426#380C22×C5912yes—
427#380C22×C5914yes—
428C4×C4⋊C4C22×C5911yescharacteristic
429C4×C4⋊C4C22×C5911yescharacteristic
430C4×C4⋊C4C22×C5911yescharacteristic
431C4×C4⋊C4C22×C5911yescharacteristic
432C4×C22⋊C4C22×C5912yes—
433C4×C22⋊C4C22×C5912yes—
434C4×C22⋊C4C22×C5912yes—
435C4×C22⋊C4C22×C5912yes—
436#376C22×C5912yes—
437C2×#95C22×C5912yes—
438C43C22×C5912yes—
439C59#3526711yescharacteristic, direct product factor, Sylow
440C2×#41—24no—
441C2×#41—24no—
442C2×#41—24no—
443C22×Q8C23×C5911yescharacteristic
444C22×D4C23×C5912yes—
445C22×D4C23×C5911yescharacteristic
446C23×C4C23×C5912yes—
447C23×C4C23×C5911yescharacteristic
448C23×C4C23×C5911yescharacteristic
449C23×C4C23×C5912yes—
450C23×C4C23×C5912yes—
451C23×C4C23×C5911yescharacteristic
452#126—48no—
453#117—24no—
454#117—24no—
455#117—24no—
456C2×C4⋊C4—24no—
457C2×C4⋊C4—24no—
458C2×C4⋊C4—44no—
459C2×C4⋊C4C23×C5914yes—
460C2×C4⋊C4C23×C5912yes—
461C2×C4⋊C4C23×C5912yes—
462C2×C4⋊C4C23×C5912yes—
463C2×C4⋊C4C23×C5912yes—
464C2×C4⋊C4C23×C5911yescharacteristic
465C2×C4⋊C4C23×C5911yescharacteristic
466C2×C4⋊C4C23×C5911yescharacteristic
467C2×C4⋊C4C23×C5911yescharacteristic
468C2×C4⋊C4C23×C5911yescharacteristic
469C2×C4⋊C4C23×C5911yescharacteristic
470C2×C4⋊C4C23×C5914yes—
471C2×C4⋊C4C23×C5914yes—
472C2×C4⋊C4C23×C5914yes—
473C2×C4⋊C4C23×C5914yes—
474C2×C4⋊C4C23×C5914yes—
475C2×C22⋊C4C23×C5912yes—
476C2×C22⋊C4C23×C5912yes—
477C2×C22⋊C4C23×C5912yes—
478C2×C22⋊C4C23×C5912yes—
479C2×C22⋊C4C23×C5912yes—
480C2×C22⋊C4C23×C5914yes—
481C2×C22⋊C4C23×C5914yes—
482C2×C22⋊C4C23×C5912yes—
483C2×C22⋊C4C23×C5912yes—
484C2×C22⋊C4C23×C5914yes—
485C2×C22⋊C4C23×C5914yes—
486C2×C42—24no—
487C2×C42C23×C5912yes—
488C2×C42C23×C5912yes—
489C2×C42C23×C5912yes—
490C2×C42C23×C5912yes—
491C2×C42C23×C5911yescharacteristic
492C2×C42C23×C5912yes—
493C2×C42C23×C5911yescharacteristic
494C2×C42C23×C5911yescharacteristic
495C2×C42C23×C5911yescharacteristic
496C2×C42C23×C5912yes—
497C2×C42C23×C5912yes—
498#95C23×C5914yes—
499#95C23×C5914yes—
500#95C23×C5912yes—
501#95C23×C5912yes—
502#95C23×C5912yes—
503#95C23×C5912yes—
504#95C23×C5912yes—
505#95C23×C5912yes—
506#95C23×C5912yes—
507#95C23×C5912yes—
508#95C23×C5914yes—
509#95C23×C5914yes—
510#95C23×C5914yes—
511#95C23×C5914yes—
512#95C23×C5914yes—
513#95C23×C5914yes—
514#95C23×C5914yes—
515#95C23×C5914yes—
516C24C24×C5912yes—
517C24C24×C5911yescharacteristic
518#41—416no—
519C2×Q8—22no—
520C2×Q8—22no—
521C2×Q8—22no—
522C2×D4—24no—
523C2×D4—24no—
524C2×D4—24no—
525C2×D4—22no—
526C2×D4—22no—
527C2×D4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—24no—
531C22×C4—24no—
532C22×C4—24no—
533C22×C4—24no—
534C22×C4—24no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—42no—
538C22×C4—41no—
539C22×C4—41no—
540C22×C4—42no—
541C22×C4—42no—
542C22×C4—42no—
543C22×C4#41×C5914yes—
544C22×C4#41×C5914yes—
545C22×C4#41×C5914yes—
546C22×C4C24×C5912yes—
547C22×C4C24×C5911yescharacteristic
548C22×C4C24×C5912yes—
549C22×C4C24×C5912yes—
550C22×C4C24×C5912yes—
551C22×C4C24×C5911yescharacteristic
552C22×C4C24×C5912yes—
553C22×C4C24×C5912yes—
554C22×C4C24×C5914yes—
555C22×C4C24×C5914yes—
556C22×C4C24×C5912yes—
557C22×C4C24×C5911yescharacteristic
558C22×C4C24×C5911yescharacteristic
559C22×C4C24×C5911yescharacteristic
560C22×C4C24×C5911yescharacteristic
561C4⋊C4—24no—
562C4⋊C4—24no—
563C4⋊C4—24no—
564C4⋊C4—24no—
565C4⋊C4—22no—
566C4⋊C4—22no—
567C4⋊C4—22no—
568C4⋊C4—22no—
569C4⋊C4—22no—
570C4⋊C4—22no—
571C4⋊C4—28no—
572C4⋊C4—44no—
573C4⋊C4—44no—
574C4⋊C4—44no—
575C4⋊C4—44no—
576C4⋊C4—44no—
577C22⋊C4—24no—
578C22⋊C4—24no—
579C22⋊C4—24no—
580C22⋊C4—24no—
581C22⋊C4—24no—
582C22⋊C4—44no—
583C22⋊C4—44no—
584C22⋊C4—44no—
585C22⋊C4—44no—
586C22⋊C4—42no—
587C22⋊C4—42no—
588C42—22no—
589C42—22no—
590C42—22no—
591C42—22no—
592C42—24no—
593C42—24no—
594C42—24no—
595C42—24no—
596C42—24no—
597C42—42no—
598C42—42no—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—22no—
604C23—22no—
605C23—22no—
606C23—22no—
607C23—22no—
608C23—22no—
609C23—22no—
610C23C2×#41×C5912yes—
611C23C2×#41×C5912yes—
612C23C2×#41×C5912yes—
613C23C25×C5911yescharacteristic
614Q8—44no—
615D4—48no—
616D4—44no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—24no—
630C2×C4—24no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—24no—
638C2×C4—24no—
639C2×C4—21no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—21no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—24no—
653C2×C4—24no—
654C2×C4—44no—
655C2×C4—44no—
656C2×C4—48no—
657C2×C4—48no—
658C2×C4—84no—
659C2×C4#126×C59116yescomplemented
660C2×C4C2×#41×C5912yes—
661C2×C4C2×#41×C5912yes—
662C2×C4C2×#41×C5912yes—
663C2×C4C2×#41×C5912yes—
664C2×C4C2×#41×C5912yes—
665C2×C4C2×#41×C5912yes—
666C2×C4H(5,𝔽2)×C5912yes—
667C2×C42−1+4×C5912yes—
668C22—22no—
669C22—22no—
670C22—22no—
671C22—22no—
672C22—22no—
673C22—22no—
674C22—42no—
675C22—42no—
676C22—42no—
677C22—42no—
678C22—42no—
679C22—42no—
680C22—42no—
681C22C2×#126×C5914yes—
682C22C22×#41×C5911yescharacteristic
683C22C22×#41×C5911yescharacteristic
684C22C22×#41×C5911yescharacteristic
685C22C2×H(5,𝔽2)×C5911yescharacteristic
686C22C2×2−1+4×C5911yescharacteristic
687C22C59×#58511yescharacteristic
688C22C59×#58511yescharacteristic
689C4—22no—
690C4—22no—
691C4—42no—
692C4—42no—
693C4—42no—
694C4—42no—
695C4—42no—
696C4—44no—
697C4—42no—
698C4—42no—
699C4—41no—
700C4—44no—
701C4—41no—
702C4C2×#126×C5914yes—
703C4C2×#126×C5914yes—
704C2—24no—
705C2—82no—
706C2C22×#126×C5911yescharacteristic
707C2C59×#346011yescharacteristic
708C2C59×#346111yescharacteristic
709C2C59×#349411yescharacteristic
710C2C59×#349511yescharacteristic
711C2C59×#351111yescharacteristic
712C2C59×#351211yescharacteristic
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. C59×#2863C2semidirect
2. C59×#2860C2semidirect
3. C59×#2645C2semidirect
4. C59×#2644C2semidirect
5. C59×#2510C2semidirect
6. C59×#2497C2semidirect
7. C59×#2496C2semidirect
8. C59×#2495C2semidirect
9. C59×#2494C2semidirect
10. C59×#2481C2semidirect
11. C59×#2317C2semidirect
12. C59×#2316C2semidirect
16. C2×C59×#389C2semidirect
17. C4×#117×C59C2semidirect
302. C2×C4×C59#126semidirect
311. #35267C59direct (N × H)
348. #2863C2×C59semidirect
349. #2860C2×C59semidirect
350. #2645C2×C59semidirect
351. #2644C2×C59semidirect
352. #2510C2×C59semidirect
353. #2497C2×C59semidirect
354. #2496C2×C59semidirect
355. #2495C2×C59semidirect
356. #2494C2×C59semidirect
357. #2481C2×C59semidirect
358. #2317C2×C59semidirect
359. #2316C2×C59semidirect
363. C2×#389C2×C59semidirect
364. C4×#117C2×C59semidirect
439. C59#35267direct (N × H)
659. C2×C4#126×C59semidirect

Maximal subgroups

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

subgroupindex
C59×#28632
C59×#28602
C59×#26452
C59×#26442
C59×#25102
C59×#24972
C59×#24962
C59×#24952
C59×#24942
C59×#24812
C59×#23172
C59×#23162
C59×#23112
C59×#22972
C2×C59×#3892
C4×#117×C592
#3526759