Finite Group Databasebeta

← C59×#36902 #28449011

Subgroups — C59×#36902 #28449011

Order 15104.

2268 conjugacy classes of subgroups.

The subgroup lattice has 1018 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C59×#2847C212yesmaximal, complemented
2C59×#2781C212yesmaximal, complemented
3C59×#2748C211yesmaximal, characteristic, complemented
4C59×#2714C212yesmaximal, complemented
5C59×#2708C212yesmaximal, complemented
6C59×#2691C212yesmaximal, complemented
7C59×#2679C211yesmaximal, characteristic, complemented
8C59×#2678C212yesmaximal, complemented
9C59×#2669C211yesmaximal, characteristic, complemented
10C59×#2669C211yesmaximal, characteristic, complemented
11C59×#2668C212yesmaximal, complemented
12C59×#2648C212yesmaximal, complemented
13C59×#2531C212yesmaximal, complemented
14C59×#2467C212yesmaximal, complemented
15C59×#2464C212yesmaximal, complemented
16C59×#2424C212yesmaximal, complemented
17C59×#2328C211yesmaximal, characteristic, complemented
18C59×#2321C211yesmaximal, characteristic, complemented
19C4×#120×C59C211yesmaximal, characteristic, complemented
20C24×C4×C59C2211yescharacteristic, complemented
21C2×#127×C59C2211yescharacteristic
22C2×#126×C59C2212yescomplemented
23C2×#123×C59C2212yescomplemented
24C2×#121×C59C2212yes—
25C2×#121×C59C2212yes—
26C2×#121×C59C2212yes—
27C2×#121×C59C2212yes—
28C2×#121×C59C2212yes—
29C2×#120×C59C2211yescharacteristic
30C2×#120×C59C2211yescharacteristic
31C2×#120×C59C2212yes—
32C2×#120×C59C2212yes—
33C2×#120×C59C2212yescomplemented
34C2×#120×C59C2212yescomplemented
35C2×C4×D4×C59C2211yescharacteristic
36C2×C4×D4×C59C2212yes—
37C2×C4×D4×C59C2211yescharacteristic, complemented
38C22×C22⋊C4×C59C2211yescharacteristic, complemented
39C59×#400C2212yescomplemented
40C59×#399C2212yescomplemented
41C59×#398C2212yescomplemented
42C59×#398C2212yescomplemented
43C59×#397C2212yescomplemented
44C59×#397C2212yescomplemented
45C59×#397C2212yescomplemented
46C59×#397C2212yescomplemented
47C59×#396C2212yescomplemented
48C59×#396C2212yescomplemented
49C59×#394C2212yes—
50C59×#394C2212yes—
51C59×#394C2212yes—
52C59×#394C2212yes—
53C59×#394C2212yes—
54C59×#394C2212yescomplemented
55C59×#394C2212yescomplemented
56C59×#394C2212yescomplemented
57C59×#394C2212yescomplemented
58C59×#392C2212yes—
59C59×#392C2212yes—
60C59×#392C2212yes—
61C59×#392C2212yescomplemented
62C59×#392C2212yescomplemented
63C59×#390C2211yescharacteristic
64C59×#390C2212yes—
65C59×#390C2212yes—
66C59×#390C2211yescharacteristic, complemented
67C59×#390C2212yescomplemented
68C59×#390C2212yescomplemented
69C59×#388C2212yescomplemented
70C59×#388C2212yescomplemented
71C59×#388C2212yescomplemented
72C59×#388C2212yescomplemented
73C59×#388C2212yescomplemented
74C59×#388C2212yescomplemented
75C59×#388C2212yescomplemented
76C59×#387C2212yescomplemented
77C59×#387C2212yescomplemented
78C59×#387C2212yescomplemented
79C59×#386C2211yescharacteristic
80C59×#386C2211yescharacteristic
81C59×#386C2212yes—
82C59×#386C2212yes—
83C59×#386C2212yes—
84C59×#386C2212yes—
85C59×#386C2212yescomplemented
86C59×#386C2212yescomplemented
87C59×#386C2212yescomplemented
88C59×#386C2212yescomplemented
89C59×#386C2212yescomplemented
90C59×#386C2212yescomplemented
91C59×#386C2212yescomplemented
92C59×#385C2212yescomplemented
93C59×#385C2212yescomplemented
94C59×#385C2211yescharacteristic, complemented
95C59×#385C2211yescharacteristic, complemented
96C59×#385C2212yescomplemented
97C59×#382C2211yescharacteristic, complemented
98C59×#380C2212yescomplemented
99C59×#380C2212yescomplemented
100C59×#380C2212yescomplemented
101C59×#379C2211yescharacteristic, complemented
102C59×#379C2211yescharacteristic, complemented
103C4×C22⋊C4×C59C2212yescomplemented
104C4×C22⋊C4×C59C2211yescharacteristic, complemented
105C4×C22⋊C4×C59C2211yescharacteristic, complemented
106C59×#376C2211yescharacteristic, complemented
107C25×C59C2311yescharacteristic
108C25×C59C2311yescharacteristic
109C22×D4×C59C2312yes—
110C22×D4×C59C2312yes—
111C22×D4×C59C2312yes—
112C22×D4×C59C2312yes—
113C22×D4×C59C2312yes—
114C22×D4×C59C2312yes—
115C22×D4×C59C2312yes—
116C22×D4×C59C2312yes—
117C22×D4×C59C2312yes—
118C22×D4×C59C2311yescharacteristic
119C22×D4×C59C2312yes—
120C22×D4×C59C2311yescharacteristic
121C23×C4×C59—44no—
122C23×C4×C59—42no—
123C23×C4×C59C2312yes—
124C23×C4×C59C2311yescharacteristic
125C23×C4×C59C2311yescharacteristic
126C23×C4×C59C2311yescharacteristic
127C23×C4×C59C2312yes—
128C23×C4×C59C2311yescharacteristic
129C23×C4×C59C2312yes—
130#127×C59—24no—
131#126×C59—44no—
132#123×C59—44no—
133#121×C59—44no—
134#121×C59—44no—
135#121×C59—44no—
136#121×C59—44no—
137#121×C59—44no—
138#120×C59—24no—
139#120×C59—24no—
140#120×C59—44no—
141#120×C59—44no—
142#120×C59—44no—
143#120×C59—44no—
144C4×D4×C59—42no—
145C4×D4×C59—42no—
146C4×D4×C59—44no—
147C2×C4⋊C4×C59C2312yes—
148C2×C4⋊C4×C59C2312yes—
149C2×C4⋊C4×C59C2312yes—
150C2×C4⋊C4×C59C2312yes—
151C2×C4⋊C4×C59C2311yescharacteristic
152C2×C4⋊C4×C59C2311yescharacteristic
153C2×C4⋊C4×C59C2312yes—
154C2×C4⋊C4×C59C2312yes—
155C2×C4⋊C4×C59C2312yes—
156C2×C4⋊C4×C59C2312yes—
157C2×C4⋊C4×C59C2312yes—
158C2×C4⋊C4×C59C2312yes—
159C2×C22⋊C4×C59—42no—
160C2×C22⋊C4×C59C2312yes—
161C2×C22⋊C4×C59C2312yes—
162C2×C22⋊C4×C59C2311yescharacteristic
163C2×C22⋊C4×C59C2311yescharacteristic
164C2×C22⋊C4×C59C2312yes—
165C2×C22⋊C4×C59C2312yes—
166C2×C22⋊C4×C59C2312yes—
167C2×C22⋊C4×C59C2312yes—
168C2×C22⋊C4×C59C2312yes—
169C2×C22⋊C4×C59C2312yes—
170C2×C22⋊C4×C59C2312yes—
171C2×C22⋊C4×C59C2312yes—
172C2×C22⋊C4×C59C2311yescharacteristic
173C2×C22⋊C4×C59C2311yescharacteristic
174C2×C22⋊C4×C59C2311yescharacteristic
175C2×C22⋊C4×C59C2311yescharacteristic
176C2×C22⋊C4×C59C2312yes—
177C2×C22⋊C4×C59C2312yes—
178C2×C22⋊C4×C59C2312yes—
179C2×C22⋊C4×C59C2312yes—
180C2×C22⋊C4×C59C2312yes—
181C2×C22⋊C4×C59C2312yes—
182C2×C22⋊C4×C59C2312yes—
183C2×C22⋊C4×C59C2312yes—
184C2×C22⋊C4×C59C2312yes—
185C2×C22⋊C4×C59C2312yes—
186C2×C22⋊C4×C59C2312yes—
187C2×C22⋊C4×C59C2312yes—
188C2×C22⋊C4×C59C2312yes—
189C2×C22⋊C4×C59C2312yes—
190C2×C22⋊C4×C59C2312yes—
191C2×C22⋊C4×C59C2312yes—
192C2×C22⋊C4×C59C2312yes—
193C2×C42×C59C2311yescharacteristic
194C2×C42×C59C2311yescharacteristic
195C2×C42×C59C2311yescharacteristic
196C2×C42×C59C2312yes—
197C2×C42×C59C2312yes—
198#95×C59C2312yes—
199#95×C59C2312yes—
200#95×C59C2312yes—
201#95×C59C2312yes—
202#95×C59C2312yes—
203#95×C59C2312yes—
204#95×C59C2312yes—
205#95×C59C2312yes—
206#95×C59C2312yes—
207#95×C59C2312yes—
208#95×C59C2312yes—
209#95×C59C2312yes—
210#95×C59C2312yes—
211#95×C59C2312yes—
212#95×C59C2312yes—
213#95×C59C2312yes—
214C24×C59—22no—
215C24×C59—24no—
216C24×C59—22no—
217C24×C59—41no—
218C24×C59—42no—
219C24×C59—41no—
220C24×C59—41no—
221C24×C59—41no—
222C24×C59—42no—
223C24×C59—42no—
224C24×C59C2412yes—
225C24×C59C2412yes—
226C24×C59C2411yescharacteristic
227C24×C59C2411yescharacteristic
228C24×C59C2412yes—
229C2×D4×C59—24no—
230C2×D4×C59—24no—
231C2×D4×C59—24no—
232C2×D4×C59—24no—
233C2×D4×C59—24no—
234C2×D4×C59—24no—
235C2×D4×C59—24no—
236C2×D4×C59—24no—
237C2×D4×C59—24no—
238C2×D4×C59—22no—
239C2×D4×C59—24no—
240C2×D4×C59—41no—
241C2×D4×C59—41no—
242C2×D4×C59—42no—
243C2×D4×C59—41no—
244C2×D4×C59—41no—
245C2×D4×C59—42no—
246C2×D4×C59—42no—
247C2×D4×C59—42no—
248C2×D4×C59—42no—
249C2×D4×C59—42no—
250C2×D4×C59—42no—
251C2×D4×C59—42no—
252C2×D4×C59—42no—
253C2×D4×C59—42no—
254C2×D4×C59—42no—
255C2×D4×C59—42no—
256C2×D4×C59—42no—
257C2×D4×C59—42no—
258C2×D4×C59—42no—
259C2×D4×C59—42no—
260C2×D4×C59—42no—
261C2×D4×C59—42no—
262C2×D4×C59—42no—
263C2×D4×C59—42no—
264C2×D4×C59#4114yes—
265C22×C4×C59—24no—
266C22×C4×C59—22no—
267C22×C4×C59—24no—
268C22×C4×C59—24no—
269C22×C4×C59—24no—
270C22×C4×C59—22no—
271C22×C4×C59—42no—
272C22×C4×C59—42no—
273C22×C4×C59—41no—
274C22×C4×C59—42no—
275C22×C4×C59—42no—
276C22×C4×C59—41no—
277C22×C4×C59—42no—
278C22×C4×C59—42no—
279C22×C4×C59—42no—
280C22×C4×C59—42no—
281C22×C4×C59—42no—
282C22×C4×C59—416no—
283C22×C4×C59C2412yes—
284C22×C4×C59C2411yescharacteristic
285C22×C4×C59C2412yes—
286C22×C4×C59C2412yes—
287C22×C4×C59C2412yes—
288C22×C4×C59C2412yes—
289C22×C4×C59C2412yes—
290C22×C4×C59C2411yescharacteristic
291C22×C4×C59C2412yes—
292C22×C4×C59C2412yes—
293C22×C4×C59C2411yescharacteristic
294C22×C4×C59C2411yescharacteristic
295C22×C4×C59C2411yescharacteristic
296C22×C4×C59C2412yes—
297C4⋊C4×C59—24no—
298C4⋊C4×C59—24no—
299C4⋊C4×C59—42no—
300C4⋊C4×C59—41no—
301C4⋊C4×C59—41no—
302C4⋊C4×C59—42no—
303C4⋊C4×C59—42no—
304C4⋊C4×C59—42no—
305C4⋊C4×C59—42no—
306C4⋊C4×C59—42no—
307C4⋊C4×C59—42no—
308C4⋊C4×C59—42no—
309C22⋊C4×C59—22no—
310C22⋊C4×C59—22no—
311C22⋊C4×C59—24no—
312C22⋊C4×C59—24no—
313C22⋊C4×C59—24no—
314C22⋊C4×C59—24no—
315C22⋊C4×C59—24no—
316C22⋊C4×C59—24no—
317C22⋊C4×C59—24no—
318C22⋊C4×C59—24no—
319C22⋊C4×C59—24no—
320C22⋊C4×C59—24no—
321C22⋊C4×C59—42no—
322C22⋊C4×C59—41no—
323C22⋊C4×C59—41no—
324C22⋊C4×C59—41no—
325C22⋊C4×C59—41no—
326C22⋊C4×C59—42no—
327C22⋊C4×C59—42no—
328C22⋊C4×C59—42no—
329C22⋊C4×C59—42no—
330C22⋊C4×C59—42no—
331C22⋊C4×C59—42no—
332C22⋊C4×C59—42no—
333C22⋊C4×C59—42no—
334C22⋊C4×C59—42no—
335C22⋊C4×C59—42no—
336C22⋊C4×C59—42no—
337C22⋊C4×C59—42no—
338C22⋊C4×C59—42no—
339C22⋊C4×C59—42no—
340C22⋊C4×C59—42no—
341C22⋊C4×C59—42no—
342C42×C59—22no—
343C42×C59—22no—
344C42×C59—41no—
345C42×C59—42no—
346C42×C59—42no—
347C23×C59—22no—
348C23×C59—22no—
349C23×C59—22no—
350C23×C59—22no—
351C23×C59—21no—
352C23×C59—21no—
353C23×C59—22no—
354C23×C59—22no—
355C23×C59—22no—
356C23×C59—22no—
357C23×C59—22no—
358C23×C59—21no—
359C23×C59—21no—
360C23×C59—22no—
361C23×C59—22no—
362C23×C59—22no—
363C23×C59—22no—
364C23×C59—22no—
365C23×C59—22no—
366C23×C59—22no—
367C23×C59—22no—
368C23×C59—22no—
369C23×C59—22no—
370C23×C59—22no—
371C23×C59—22no—
372C23×C59—22no—
373C23×C59—22no—
374C23×C59—22no—
375C23×C59—48no—
376C23×C59—44no—
377C23×C59—44no—
378C23×C59—48no—
379C23×C59—44no—
380C23×C59—44no—
381C23×C59—84no—
382C23×C59—82no—
383C23×C59—82no—
384C23×C59—84no—
385C23×C59C2×#4112yes—
386C23×C59C2×#4112yes—
387C23×C59H(5,𝔽2)14yes—
388C23×C59C2511yescharacteristic
389D4×C59—44no—
390D4×C59—44no—
391D4×C59—48no—
392D4×C59—84no—
393D4×C59—84no—
394D4×C59—84no—
395D4×C59—84no—
396D4×C59—84no—
397D4×C59—84no—
398D4×C59—84no—
399D4×C59—84no—
400D4×C59—84no—
401C2×C4×C59—21no—
402C2×C4×C59—22no—
403C2×C4×C59—22no—
404C2×C4×C59—22no—
405C2×C4×C59—21no—
406C2×C4×C59—22no—
407C2×C4×C59—22no—
408C2×C4×C59—22no—
409C2×C4×C59—21no—
410C2×C4×C59—22no—
411C2×C4×C59—22no—
412C2×C4×C59—22no—
413C2×C4×C59—22no—
414C2×C4×C59—22no—
415C2×C4×C59—22no—
416C2×C4×C59—22no—
417C2×C4×C59—22no—
418C2×C4×C59—22no—
419C2×C4×C59—22no—
420C2×C4×C59—22no—
421C2×C4×C59—22no—
422C2×C4×C59—22no—
423C2×C4×C59—22no—
424C2×C4×C59—22no—
425C2×C4×C59—21no—
426C2×C4×C59—22no—
427C2×C4×C59—22no—
428C2×C4×C59—22no—
429C2×C4×C59—22no—
430C2×C4×C59—22no—
431C2×C4×C59—21no—
432C2×C4×C59—22no—
433C2×C4×C59—22no—
434C2×C4×C59—22no—
435C2×C4×C59—22no—
436C2×C4×C59—48no—
437C2×C4×C59—44no—
438C2×C4×C59—44no—
439C2×C4×C59—48no—
440C2×C4×C59—82no—
441C2×C4×C59—84no—
442C2×C4×C59—82no—
443C2×C4×C59C2×#4112yes—
444C2×C4×C59H(5,𝔽2)12yes—
445C2×C4×C59H(5,𝔽2)14yes—
446#36902C5911yesmaximal, characteristic, direct product factor, Sylow
447C22×C59—22no—
448C22×C59—22no—
449C22×C59—24no—
450C22×C59—24no—
451C22×C59—24no—
452C22×C59—24no—
453C22×C59—24no—
454C22×C59—416no—
455C22×C59—42no—
456C22×C59—42no—
457C22×C59—41no—
458C22×C59—42no—
459C22×C59—41no—
460C22×C59—41no—
461C22×C59—41no—
462C22×C59—42no—
463C22×C59—42no—
464C22×C59—42no—
465C22×C59—42no—
466C22×C59—42no—
467C22×C59—42no—
468C22×C59—42no—
469C22×C59—42no—
470C22×C59—42no—
471C22×C59—42no—
472C22×C59—42no—
473C22×C59—42no—
474C22×C59—42no—
475C22×C59—42no—
476C22×C59—42no—
477C22×C59—42no—
478C22×C59—42no—
479C22×C59—88no—
480C22×C59C22×#4111yescharacteristic
481C22×C59C2×H(5,𝔽2)11yescharacteristic
482C22×C59C2×H(5,𝔽2)12yes—
483C22×C59C2×H(5,𝔽2)12yes—
484C22×C59#58511yescharacteristic
485C4×C59—22no—
486C4×C59—22no—
487C4×C59—24no—
488C4×C59—42no—
489C4×C59—42no—
490C4×C59—42no—
491C4×C59—41no—
492C4×C59—41no—
493C4×C59—41no—
494C4×C59—42no—
495C4×C59—42no—
496C4×C59—42no—
497C4×C59—42no—
498C4×C59—42no—
499#2847C2×C5912yescomplemented
500#2781C2×C5912yescomplemented
501#2748C2×C5911yescharacteristic, complemented
502#2714C2×C5912yescomplemented
503#2708C2×C5912yescomplemented
504#2691C2×C5912yescomplemented
505#2679C2×C5911yescharacteristic, complemented
506#2678C2×C5912yescomplemented
507#2669C2×C5911yescharacteristic, complemented
508#2669C2×C5911yescharacteristic, complemented
509#2668C2×C5912yescomplemented
510#2648C2×C5912yescomplemented
511#2531C2×C5912yescomplemented
512#2467C2×C5912yescomplemented
513#2464C2×C5912yescomplemented
514#2424C2×C5912yescomplemented
515#2328C2×C5911yescharacteristic, complemented
516#2321C2×C5911yescharacteristic, complemented
517C4×#120C2×C5911yescharacteristic, complemented
518C2×C59—42no—
519C2×C59—44no—
520C2×C59—42no—
521C2×C59—82no—
522C2×C59—82no—
523C2×C59#345911yescharacteristic
524C2×C59#351912yes—
525C2×C59#353211yescharacteristic
526C2×C59#353711yescharacteristic
527C2×C59#354212yes—
528C24×C4C22×C5911yescharacteristic, complemented
529C2×#127C22×C5911yescharacteristic
530C2×#126C22×C5912yescomplemented
531C2×#123C22×C5912yescomplemented
532C2×#121C22×C5912yes—
533C2×#121C22×C5912yes—
534C2×#121C22×C5912yes—
535C2×#121C22×C5912yes—
536C2×#121C22×C5912yes—
537C2×#120C22×C5911yescharacteristic
538C2×#120C22×C5911yescharacteristic
539C2×#120C22×C5912yes—
540C2×#120C22×C5912yes—
541C2×#120C22×C5912yescomplemented
542C2×#120C22×C5912yescomplemented
543C2×C4×D4C22×C5911yescharacteristic
544C2×C4×D4C22×C5912yes—
545C2×C4×D4C22×C5911yescharacteristic, complemented
546C22×C22⋊C4C22×C5911yescharacteristic, complemented
547#400C22×C5912yescomplemented
548#399C22×C5912yescomplemented
549#398C22×C5912yescomplemented
550#398C22×C5912yescomplemented
551#397C22×C5912yescomplemented
552#397C22×C5912yescomplemented
553#397C22×C5912yescomplemented
554#397C22×C5912yescomplemented
555#396C22×C5912yescomplemented
556#396C22×C5912yescomplemented
557#394C22×C5912yes—
558#394C22×C5912yes—
559#394C22×C5912yes—
560#394C22×C5912yes—
561#394C22×C5912yes—
562#394C22×C5912yescomplemented
563#394C22×C5912yescomplemented
564#394C22×C5912yescomplemented
565#394C22×C5912yescomplemented
566#392C22×C5912yes—
567#392C22×C5912yes—
568#392C22×C5912yes—
569#392C22×C5912yescomplemented
570#392C22×C5912yescomplemented
571#390C22×C5912yes—
572#390C22×C5911yescharacteristic
573#390C22×C5912yes—
574#390C22×C5911yescharacteristic, complemented
575#390C22×C5912yescomplemented
576#390C22×C5912yescomplemented
577#388C22×C5912yescomplemented
578#388C22×C5912yescomplemented
579#388C22×C5912yescomplemented
580#388C22×C5912yescomplemented
581#388C22×C5912yescomplemented
582#388C22×C5912yescomplemented
583#388C22×C5912yescomplemented
584#387C22×C5912yescomplemented
585#387C22×C5912yescomplemented
586#387C22×C5912yescomplemented
587#386C22×C5912yes—
588#386C22×C5911yescharacteristic
589#386C22×C5912yes—
590#386C22×C5912yes—
591#386C22×C5912yes—
592#386C22×C5911yescharacteristic
593#386C22×C5912yescomplemented
594#386C22×C5912yescomplemented
595#386C22×C5912yescomplemented
596#386C22×C5912yescomplemented
597#386C22×C5912yescomplemented
598#386C22×C5912yescomplemented
599#386C22×C5912yescomplemented
600#385C22×C5911yescharacteristic, complemented
601#385C22×C5912yescomplemented
602#385C22×C5911yescharacteristic, complemented
603#385C22×C5912yescomplemented
604#385C22×C5912yescomplemented
605#382C22×C5911yescharacteristic, complemented
606#380C22×C5912yescomplemented
607#380C22×C5912yescomplemented
608#380C22×C5912yescomplemented
609#379C22×C5911yescharacteristic, complemented
610#379C22×C5911yescharacteristic, complemented
611C4×C22⋊C4C22×C5911yescharacteristic, complemented
612C4×C22⋊C4C22×C5911yescharacteristic, complemented
613C4×C22⋊C4C22×C5912yescomplemented
614#376C22×C5911yescharacteristic, complemented
615C59#3690211yescharacteristic, direct product factor, Sylow
616C25C23×C5911yescharacteristic
617C25C23×C5911yescharacteristic
618C22×D4C23×C5912yes—
619C22×D4C23×C5911yescharacteristic
620C22×D4C23×C5912yes—
621C22×D4C23×C5912yes—
622C22×D4C23×C5912yes—
623C22×D4C23×C5912yes—
624C22×D4C23×C5912yes—
625C22×D4C23×C5912yes—
626C22×D4C23×C5912yes—
627C22×D4C23×C5912yes—
628C22×D4C23×C5912yes—
629C22×D4C23×C5911yescharacteristic
630C23×C4—44no—
631C23×C4—42no—
632C23×C4C23×C5912yes—
633C23×C4C23×C5911yescharacteristic
634C23×C4C23×C5911yescharacteristic
635C23×C4C23×C5911yescharacteristic
636C23×C4C23×C5912yes—
637C23×C4C23×C5911yescharacteristic
638C23×C4C23×C5912yes—
639#127—24no—
640#126—44no—
641#123—44no—
642#121—44no—
643#121—44no—
644#121—44no—
645#121—44no—
646#121—44no—
647#120—24no—
648#120—24no—
649#120—44no—
650#120—44no—
651#120—44no—
652#120—44no—
653C4×D4—42no—
654C4×D4—42no—
655C4×D4—44no—
656C2×C4⋊C4C23×C5912yes—
657C2×C4⋊C4C23×C5912yes—
658C2×C4⋊C4C23×C5911yescharacteristic
659C2×C4⋊C4C23×C5911yescharacteristic
660C2×C4⋊C4C23×C5912yes—
661C2×C4⋊C4C23×C5912yes—
662C2×C4⋊C4C23×C5912yes—
663C2×C4⋊C4C23×C5912yes—
664C2×C4⋊C4C23×C5912yes—
665C2×C4⋊C4C23×C5912yes—
666C2×C4⋊C4C23×C5912yes—
667C2×C4⋊C4C23×C5912yes—
668C2×C22⋊C4—42no—
669C2×C22⋊C4C23×C5912yes—
670C2×C22⋊C4C23×C5912yes—
671C2×C22⋊C4C23×C5912yes—
672C2×C22⋊C4C23×C5912yes—
673C2×C22⋊C4C23×C5912yes—
674C2×C22⋊C4C23×C5911yescharacteristic
675C2×C22⋊C4C23×C5911yescharacteristic
676C2×C22⋊C4C23×C5912yes—
677C2×C22⋊C4C23×C5912yes—
678C2×C22⋊C4C23×C5912yes—
679C2×C22⋊C4C23×C5912yes—
680C2×C22⋊C4C23×C5912yes—
681C2×C22⋊C4C23×C5912yes—
682C2×C22⋊C4C23×C5911yescharacteristic
683C2×C22⋊C4C23×C5911yescharacteristic
684C2×C22⋊C4C23×C5912yes—
685C2×C22⋊C4C23×C5912yes—
686C2×C22⋊C4C23×C5912yes—
687C2×C22⋊C4C23×C5912yes—
688C2×C22⋊C4C23×C5912yes—
689C2×C22⋊C4C23×C5912yes—
690C2×C22⋊C4C23×C5912yes—
691C2×C22⋊C4C23×C5912yes—
692C2×C22⋊C4C23×C5912yes—
693C2×C22⋊C4C23×C5912yes—
694C2×C22⋊C4C23×C5912yes—
695C2×C22⋊C4C23×C5912yes—
696C2×C22⋊C4C23×C5912yes—
697C2×C22⋊C4C23×C5912yes—
698C2×C22⋊C4C23×C5912yes—
699C2×C22⋊C4C23×C5912yes—
700C2×C22⋊C4C23×C5911yescharacteristic
701C2×C22⋊C4C23×C5911yescharacteristic
702C2×C42C23×C5911yescharacteristic
703C2×C42C23×C5911yescharacteristic
704C2×C42C23×C5912yes—
705C2×C42C23×C5912yes—
706C2×C42C23×C5911yescharacteristic
707#95C23×C5912yes—
708#95C23×C5912yes—
709#95C23×C5912yes—
710#95C23×C5912yes—
711#95C23×C5912yes—
712#95C23×C5912yes—
713#95C23×C5912yes—
714#95C23×C5912yes—
715#95C23×C5912yes—
716#95C23×C5912yes—
717#95C23×C5912yes—
718#95C23×C5912yes—
719#95C23×C5912yes—
720#95C23×C5912yes—
721#95C23×C5912yes—
722#95C23×C5912yes—
723C24—22no—
724C24—24no—
725C24—22no—
726C24—42no—
727C24—41no—
728C24—41no—
729C24—41no—
730C24—41no—
731C24—42no—
732C24—42no—
733C24C24×C5912yes—
734C24C24×C5912yes—
735C24C24×C5911yescharacteristic
736C24C24×C5911yescharacteristic
737C24C24×C5912yes—
738C2×D4—24no—
739C2×D4—24no—
740C2×D4—24no—
741C2×D4—24no—
742C2×D4—24no—
743C2×D4—24no—
744C2×D4—24no—
745C2×D4—24no—
746C2×D4—24no—
747C2×D4—22no—
748C2×D4—24no—
749C2×D4—41no—
750C2×D4—41no—
751C2×D4—42no—
752C2×D4—41no—
753C2×D4—41no—
754C2×D4—42no—
755C2×D4—42no—
756C2×D4—42no—
757C2×D4—42no—
758C2×D4—42no—
759C2×D4—42no—
760C2×D4—42no—
761C2×D4—42no—
762C2×D4—42no—
763C2×D4—42no—
764C2×D4—42no—
765C2×D4—42no—
766C2×D4—42no—
767C2×D4—42no—
768C2×D4—42no—
769C2×D4—42no—
770C2×D4—42no—
771C2×D4—42no—
772C2×D4—42no—
773C2×D4#41×C5914yes—
774C22×C4—24no—
775C22×C4—22no—
776C22×C4—24no—
777C22×C4—24no—
778C22×C4—24no—
779C22×C4—22no—
780C22×C4—42no—
781C22×C4—42no—
782C22×C4—41no—
783C22×C4—42no—
784C22×C4—42no—
785C22×C4—41no—
786C22×C4—42no—
787C22×C4—42no—
788C22×C4—42no—
789C22×C4—42no—
790C22×C4—42no—
791C22×C4—416no—
792C22×C4C24×C5912yes—
793C22×C4C24×C5911yescharacteristic
794C22×C4C24×C5912yes—
795C22×C4C24×C5912yes—
796C22×C4C24×C5912yes—
797C22×C4C24×C5912yes—
798C22×C4C24×C5912yes—
799C22×C4C24×C5911yescharacteristic
800C22×C4C24×C5912yes—
801C22×C4C24×C5912yes—
802C22×C4C24×C5911yescharacteristic
803C22×C4C24×C5911yescharacteristic
804C22×C4C24×C5911yescharacteristic
805C22×C4C24×C5912yes—
806C4⋊C4—24no—
807C4⋊C4—24no—
808C4⋊C4—41no—
809C4⋊C4—41no—
810C4⋊C4—42no—
811C4⋊C4—42no—
812C4⋊C4—42no—
813C4⋊C4—42no—
814C4⋊C4—42no—
815C4⋊C4—42no—
816C4⋊C4—42no—
817C4⋊C4—42no—
818C22⋊C4—22no—
819C22⋊C4—22no—
820C22⋊C4—24no—
821C22⋊C4—24no—
822C22⋊C4—24no—
823C22⋊C4—24no—
824C22⋊C4—24no—
825C22⋊C4—24no—
826C22⋊C4—24no—
827C22⋊C4—24no—
828C22⋊C4—24no—
829C22⋊C4—24no—
830C22⋊C4—42no—
831C22⋊C4—41no—
832C22⋊C4—41no—
833C22⋊C4—42no—
834C22⋊C4—42no—
835C22⋊C4—42no—
836C22⋊C4—42no—
837C22⋊C4—42no—
838C22⋊C4—42no—
839C22⋊C4—42no—
840C22⋊C4—42no—
841C22⋊C4—42no—
842C22⋊C4—42no—
843C22⋊C4—42no—
844C22⋊C4—42no—
845C22⋊C4—42no—
846C22⋊C4—42no—
847C22⋊C4—42no—
848C22⋊C4—42no—
849C22⋊C4—41no—
850C22⋊C4—41no—
851C42—22no—
852C42—22no—
853C42—42no—
854C42—42no—
855C42—41no—
856C23—22no—
857C23—22no—
858C23—22no—
859C23—22no—
860C23—22no—
861C23—21no—
862C23—21no—
863C23—22no—
864C23—22no—
865C23—22no—
866C23—22no—
867C23—21no—
868C23—21no—
869C23—22no—
870C23—22no—
871C23—22no—
872C23—22no—
873C23—22no—
874C23—22no—
875C23—22no—
876C23—22no—
877C23—22no—
878C23—22no—
879C23—22no—
880C23—22no—
881C23—22no—
882C23—22no—
883C23—22no—
884C23—48no—
885C23—44no—
886C23—48no—
887C23—44no—
888C23—44no—
889C23—44no—
890C23—84no—
891C23—82no—
892C23—82no—
893C23—84no—
894C23C2×#41×C5912yes—
895C23C2×#41×C5912yes—
896C23H(5,𝔽2)×C5914yes—
897C23C25×C5911yescharacteristic
898D4—44no—
899D4—44no—
900D4—48no—
901D4—84no—
902D4—84no—
903D4—84no—
904D4—84no—
905D4—84no—
906D4—84no—
907D4—84no—
908D4—84no—
909D4—84no—
910C2×C4—21no—
911C2×C4—22no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—21no—
915C2×C4—22no—
916C2×C4—22no—
917C2×C4—22no—
918C2×C4—21no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—22no—
923C2×C4—22no—
924C2×C4—22no—
925C2×C4—22no—
926C2×C4—22no—
927C2×C4—22no—
928C2×C4—22no—
929C2×C4—22no—
930C2×C4—22no—
931C2×C4—22no—
932C2×C4—22no—
933C2×C4—22no—
934C2×C4—21no—
935C2×C4—22no—
936C2×C4—22no—
937C2×C4—22no—
938C2×C4—22no—
939C2×C4—22no—
940C2×C4—21no—
941C2×C4—22no—
942C2×C4—22no—
943C2×C4—22no—
944C2×C4—22no—
945C2×C4—48no—
946C2×C4—44no—
947C2×C4—44no—
948C2×C4—48no—
949C2×C4—82no—
950C2×C4—84no—
951C2×C4—82no—
952C2×C4C2×#41×C5912yes—
953C2×C4H(5,𝔽2)×C5912yes—
954C2×C4H(5,𝔽2)×C5914yes—
955C22—24no—
956C22—24no—
957C22—24no—
958C22—24no—
959C22—24no—
960C22—22no—
961C22—22no—
962C22—416no—
963C22—42no—
964C22—42no—
965C22—41no—
966C22—41no—
967C22—41no—
968C22—41no—
969C22—42no—
970C22—42no—
971C22—42no—
972C22—42no—
973C22—42no—
974C22—42no—
975C22—42no—
976C22—42no—
977C22—42no—
978C22—42no—
979C22—42no—
980C22—42no—
981C22—42no—
982C22—42no—
983C22—42no—
984C22—42no—
985C22—42no—
986C22—42no—
987C22—88no—
988C22C22×#41×C5911yescharacteristic
989C22C2×H(5,𝔽2)×C5912yes—
990C22C2×H(5,𝔽2)×C5912yes—
991C22C2×H(5,𝔽2)×C5911yescharacteristic
992C22C59×#58511yescharacteristic
993C4—22no—
994C4—24no—
995C4—22no—
996C4—42no—
997C4—42no—
998C4—42no—
999C4—41no—
1000C4—41no—
1001C4—41no—
1002C4—42no—
1003C4—42no—
1004C4—42no—
1005C4—42no—
1006C4—42no—
1007C2—44no—
1008C2—42no—
1009C2—42no—
1010C2—82no—
1011C2—82no—
1012C2C59×#345911yescharacteristic
1013C2C59×#351912yes—
1014C2C59×#353211yescharacteristic
1015C2C59×#353711yescharacteristic
1016C2C59×#354212yes—
subgroupG/H
center, socleC23×C59C25
commutator, Frattini, cosocleC23C25×C59
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C59 ◁ G

Complements

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

NH ≅ G/Ntype
1. C59×#2847C2semidirect
2. C59×#2781C2semidirect
3. C59×#2748C2semidirect
4. C59×#2714C2semidirect
5. C59×#2708C2semidirect
6. C59×#2691C2semidirect
7. C59×#2679C2semidirect
8. C59×#2678C2semidirect
9. C59×#2669C2semidirect
10. C59×#2669C2semidirect
11. C59×#2668C2semidirect
12. C59×#2648C2semidirect
13. C59×#2531C2semidirect
14. C59×#2467C2semidirect
15. C59×#2464C2semidirect
16. C59×#2424C2semidirect
17. C59×#2328C2semidirect
18. C59×#2321C2semidirect
19. C4×#120×C59C2semidirect
20. C24×C4×C59C22semidirect
22. C2×#126×C59C22semidirect
23. C2×#123×C59C22semidirect
33. C2×#120×C59C22semidirect
34. C2×#120×C59C22semidirect
37. C2×C4×D4×C59C22semidirect
38. C22×C22⋊C4×C59C22semidirect
39. C59×#400C22semidirect
40. C59×#399C22semidirect
41. C59×#398C22semidirect
42. C59×#398C22semidirect
43. C59×#397C22semidirect
44. C59×#397C22semidirect
45. C59×#397C22semidirect
46. C59×#397C22semidirect
47. C59×#396C22semidirect
48. C59×#396C22semidirect
54. C59×#394C22semidirect
55. C59×#394C22semidirect
56. C59×#394C22semidirect
57. C59×#394C22semidirect
61. C59×#392C22semidirect
62. C59×#392C22semidirect
66. C59×#390C22semidirect
67. C59×#390C22semidirect
68. C59×#390C22semidirect
69. C59×#388C22semidirect
70. C59×#388C22semidirect
71. C59×#388C22semidirect
72. C59×#388C22semidirect
73. C59×#388C22semidirect
74. C59×#388C22semidirect
75. C59×#388C22semidirect
76. C59×#387C22semidirect
77. C59×#387C22semidirect
78. C59×#387C22semidirect
85. C59×#386C22semidirect
86. C59×#386C22semidirect
87. C59×#386C22semidirect
88. C59×#386C22semidirect
89. C59×#386C22semidirect
90. C59×#386C22semidirect
91. C59×#386C22semidirect
92. C59×#385C22semidirect
93. C59×#385C22semidirect
94. C59×#385C22semidirect
95. C59×#385C22semidirect
96. C59×#385C22semidirect
97. C59×#382C22semidirect
98. C59×#380C22semidirect
99. C59×#380C22semidirect
100. C59×#380C22semidirect
101. C59×#379C22semidirect
102. C59×#379C22semidirect
103. C4×C22⋊C4×C59C22semidirect
104. C4×C22⋊C4×C59C22semidirect
105. C4×C22⋊C4×C59C22semidirect
106. C59×#376C22semidirect
446. #36902C59direct (N × H)
499. #2847C2×C59semidirect
500. #2781C2×C59semidirect
501. #2748C2×C59semidirect
502. #2714C2×C59semidirect
503. #2708C2×C59semidirect
504. #2691C2×C59semidirect
505. #2679C2×C59semidirect
506. #2678C2×C59semidirect
507. #2669C2×C59semidirect
508. #2669C2×C59semidirect
509. #2668C2×C59semidirect
510. #2648C2×C59semidirect
511. #2531C2×C59semidirect
512. #2467C2×C59semidirect
513. #2464C2×C59semidirect
514. #2424C2×C59semidirect
515. #2328C2×C59semidirect
516. #2321C2×C59semidirect
517. C4×#120C2×C59semidirect
528. C24×C4C22×C59semidirect
530. C2×#126C22×C59semidirect
531. C2×#123C22×C59semidirect
541. C2×#120C22×C59semidirect
542. C2×#120C22×C59semidirect
545. C2×C4×D4C22×C59semidirect
546. C22×C22⋊C4C22×C59semidirect
547. #400C22×C59semidirect
548. #399C22×C59semidirect
549. #398C22×C59semidirect
550. #398C22×C59semidirect
551. #397C22×C59semidirect
552. #397C22×C59semidirect
553. #397C22×C59semidirect
554. #397C22×C59semidirect
555. #396C22×C59semidirect
556. #396C22×C59semidirect
562. #394C22×C59semidirect
563. #394C22×C59semidirect
564. #394C22×C59semidirect
565. #394C22×C59semidirect
569. #392C22×C59semidirect
570. #392C22×C59semidirect
574. #390C22×C59semidirect
575. #390C22×C59semidirect
576. #390C22×C59semidirect
577. #388C22×C59semidirect
578. #388C22×C59semidirect
579. #388C22×C59semidirect
580. #388C22×C59semidirect
581. #388C22×C59semidirect
582. #388C22×C59semidirect
583. #388C22×C59semidirect
584. #387C22×C59semidirect
585. #387C22×C59semidirect
586. #387C22×C59semidirect
593. #386C22×C59semidirect
594. #386C22×C59semidirect
595. #386C22×C59semidirect
596. #386C22×C59semidirect
597. #386C22×C59semidirect
598. #386C22×C59semidirect
599. #386C22×C59semidirect
600. #385C22×C59semidirect
601. #385C22×C59semidirect
602. #385C22×C59semidirect
603. #385C22×C59semidirect
604. #385C22×C59semidirect
605. #382C22×C59semidirect
606. #380C22×C59semidirect
607. #380C22×C59semidirect
608. #380C22×C59semidirect
609. #379C22×C59semidirect
610. #379C22×C59semidirect
611. C4×C22⋊C4C22×C59semidirect
612. C4×C22⋊C4C22×C59semidirect
613. C4×C22⋊C4C22×C59semidirect
614. #376C22×C59semidirect
615. C59#36902direct (N × H)

Maximal subgroups

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

subgroupindex
C59×#28472
C59×#27812
C59×#27482
C59×#27142
C59×#27082
C59×#26912
C59×#26792
C59×#26782
C59×#26692
C59×#26682
C59×#26482
C59×#25312
C59×#24672
C59×#24642
C59×#24242
C59×#23282
C59×#23212
C4×#120×C592
#3690259