Finite Group Databasebeta

← C59×#16497 #28428606

Subgroups — C59×#16497 #28428606

Order 15104.

1506 conjugacy classes of subgroups.

The subgroup lattice has 1118 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C59×#396C211yesmaximal, characteristic, complemented
2C2×C59×#388C211yesmaximal, characteristic, complemented
3C59×#1445C211yesmaximal, characteristic, complemented
4C59×#1445C211yesmaximal, characteristic, complemented
5C59×#1442C211yesmaximal, characteristic, complemented
6C59×#1440C211yesmaximal, characteristic, complemented
7C59×#1440C211yesmaximal, characteristic, complemented
8C59×#1440C211yesmaximal, characteristic, complemented
9C59×#1439C211yesmaximal, characteristic, complemented
10C59×#1439C211yesmaximal, characteristic, complemented
11C59×#1438C211yesmaximal, characteristic
12C59×#1438C211yesmaximal, characteristic
13C59×#1438C211yesmaximal, characteristic
14C59×#1437C211yesmaximal, characteristic, complemented
15C59×#1434C211yesmaximal, characteristic, complemented
16C23×D4×C59C2211yescharacteristic
17C22×C4⋊C4×C59C2211yescharacteristic
18C22×C4⋊C4×C59C2211yescharacteristic
19C22×C4⋊C4×C59C2211yescharacteristic
20C22×C22⋊C4×C59C2211yescharacteristic
21C22×C22⋊C4×C59C2211yescharacteristic
22C22×C22⋊C4×C59C2211yescharacteristic
23C22×C22⋊C4×C59C2211yescharacteristic
24C22×C22⋊C4×C59C2211yescharacteristic
25C22×C22⋊C4×C59C2211yescharacteristic
26C22×C22⋊C4×C59C2211yescharacteristic
27C22×C22⋊C4×C59C2211yescharacteristic
28C22×C22⋊C4×C59C2211yescharacteristic
29C22×C22⋊C4×C59C2211yescharacteristic
30C22×C22⋊C4×C59C2211yescharacteristic
31C22×C22⋊C4×C59C2211yescharacteristic
32C22×C42×C59C2211yescharacteristic
33C59×#396—24no—
34C59×#388—24no—
35C2×#95×C59C2211yescharacteristic
36C2×#95×C59C2211yescharacteristic
37C2×#95×C59C2211yescharacteristic
38C2×#95×C59C2211yescharacteristic
39C2×#95×C59C2211yescharacteristic
40C2×#95×C59C2211yescharacteristic
41C2×#95×C59C2211yescharacteristic
42C2×#95×C59C2211yescharacteristic
43C2×#95×C59C2211yescharacteristic
44C2×#95×C59C2211yescharacteristic
45C2×#95×C59C2211yescharacteristic
46C2×#95×C59C2211yescharacteristic
47C2×#95×C59C2211yescharacteristic
48C2×#95×C59C2211yescharacteristic
49C2×#95×C59C2211yescharacteristic
50C2×#95×C59C2211yescharacteristic
51C2×#95×C59C2211yescharacteristic
52C2×#95×C59C2211yescharacteristic
53C25×C59C2311yescharacteristic
54C25×C59C2311yescharacteristic
55C22×D4×C59—22no—
56C22×D4×C59—22no—
57C22×D4×C59—22no—
58C22×D4×C59—41no—
59C22×D4×C59—41no—
60C22×D4×C59—41no—
61C22×D4×C59—41no—
62C23×C4×C59C2311yescharacteristic
63C23×C4×C59C2311yescharacteristic
64C23×C4×C59C2311yescharacteristic
65C23×C4×C59C2311yescharacteristic
66C23×C4×C59C2311yescharacteristic
67C23×C4×C59C2311yescharacteristic
68C23×C4×C59C2311yescharacteristic
69C23×C4×C59C2311yescharacteristic
70C23×C4×C59C2311yescharacteristic
71C23×C4×C59C2311yescharacteristic
72C23×C4×C59C2311yescharacteristic
73C23×C4×C59C2311yescharacteristic
74C23×C4×C59C2311yescharacteristic
75C2×C4⋊C4×C59—22no—
76C2×C4⋊C4×C59—22no—
77C2×C4⋊C4×C59—22no—
78C2×C4⋊C4×C59—41no—
79C2×C4⋊C4×C59—41no—
80C2×C4⋊C4×C59—41no—
81C2×C4⋊C4×C59—41no—
82C2×C4⋊C4×C59—41no—
83C2×C4⋊C4×C59D414yescomplemented
84C2×C22⋊C4×C59—22no—
85C2×C22⋊C4×C59—22no—
86C2×C22⋊C4×C59—22no—
87C2×C22⋊C4×C59—22no—
88C2×C22⋊C4×C59—22no—
89C2×C22⋊C4×C59—22no—
90C2×C22⋊C4×C59—22no—
91C2×C22⋊C4×C59—22no—
92C2×C22⋊C4×C59—22no—
93C2×C22⋊C4×C59—22no—
94C2×C22⋊C4×C59—22no—
95C2×C22⋊C4×C59—22no—
96C2×C22⋊C4×C59—22no—
97C2×C22⋊C4×C59—22no—
98C2×C22⋊C4×C59—22no—
99C2×C22⋊C4×C59—22no—
100C2×C22⋊C4×C59—41no—
101C2×C22⋊C4×C59—41no—
102C2×C22⋊C4×C59—41no—
103C2×C22⋊C4×C59—41no—
104C2×C22⋊C4×C59—41no—
105C2×C22⋊C4×C59—41no—
106C2×C22⋊C4×C59—41no—
107C2×C22⋊C4×C59—41no—
108C2×C22⋊C4×C59—41no—
109C2×C22⋊C4×C59—41no—
110C2×C22⋊C4×C59—41no—
111C2×C22⋊C4×C59—41no—
112C2×C22⋊C4×C59—41no—
113C2×C22⋊C4×C59—41no—
114C2×C22⋊C4×C59—41no—
115C2×C22⋊C4×C59—41no—
116C2×C22⋊C4×C59—41no—
117C2×C22⋊C4×C59—41no—
118C2×C22⋊C4×C59—41no—
119C2×C22⋊C4×C59—41no—
120C2×C42×C59—22no—
121C2×C42×C59—22no—
122C2×C42×C59—41no—
123#95×C59—22no—
124#95×C59—22no—
125#95×C59—22no—
126#95×C59—22no—
127#95×C59—22no—
128#95×C59—22no—
129#95×C59—41no—
130#95×C59—41no—
131#95×C59—41no—
132#95×C59—41no—
133#95×C59—41no—
134#95×C59—41no—
135#95×C59—41no—
136#95×C59—41no—
137#95×C59—41no—
138#95×C59—41no—
139#95×C59—41no—
140#95×C59—41no—
141C24×C59—21no—
142C24×C59—21no—
143C24×C59—21no—
144C24×C59—21no—
145C24×C59—21no—
146C24×C59—21no—
147C24×C59—21no—
148C24×C59—21no—
149C24×C59—21no—
150C24×C59—21no—
151C24×C59—21no—
152C24×C59—21no—
153C24×C59—21no—
154C24×C59—21no—
155C24×C59—21no—
156C24×C59—21no—
157C24×C59—21no—
158C24×C59—21no—
159C24×C59—21no—
160C24×C59—21no—
161C24×C59—21no—
162C24×C59—21no—
163C24×C59—21no—
164C24×C59—21no—
165C24×C59—21no—
166C24×C59—21no—
167C24×C59—21no—
168C24×C59—21no—
169C24×C59#4112yes—
170C24×C59#4112yes—
171C24×C59C2411yescharacteristic
172C2×D4×C59—44no—
173C2×D4×C59—44no—
174C2×D4×C59—44no—
175C2×D4×C59—44no—
176C2×D4×C59—44no—
177C2×D4×C59—44no—
178C2×D4×C59—44no—
179C22×C4×C59—21no—
180C22×C4×C59—21no—
181C22×C4×C59—21no—
182C22×C4×C59—21no—
183C22×C4×C59—21no—
184C22×C4×C59—21no—
185C22×C4×C59—21no—
186C22×C4×C59—21no—
187C22×C4×C59—21no—
188C22×C4×C59—21no—
189C22×C4×C59—21no—
190C22×C4×C59—21no—
191C22×C4×C59—21no—
192C22×C4×C59—21no—
193C22×C4×C59—21no—
194C22×C4×C59—21no—
195C22×C4×C59—21no—
196C22×C4×C59—21no—
197C22×C4×C59—21no—
198C22×C4×C59—21no—
199C22×C4×C59—21no—
200C22×C4×C59—21no—
201C22×C4×C59—21no—
202C22×C4×C59—21no—
203C22×C4×C59—21no—
204C22×C4×C59—21no—
205C22×C4×C59—21no—
206C22×C4×C59—21no—
207C22×C4×C59—21no—
208C22×C4×C59—21no—
209C22×C4×C59—21no—
210C22×C4×C59—21no—
211C22×C4×C59—21no—
212C22×C4×C59—21no—
213C22×C4×C59—21no—
214C22×C4×C59—21no—
215C22×C4×C59—21no—
216C22×C4×C59—21no—
217C22×C4×C59—21no—
218C22×C4×C59—21no—
219C22×C4×C59—21no—
220C22×C4×C59—21no—
221C22×C4×C59—21no—
222C22×C4×C59—21no—
223C22×C4×C59—21no—
224C22×C4×C59—21no—
225C22×C4×C59—21no—
226C22×C4×C59—21no—
227C22×C4×C59—21no—
228C22×C4×C59—21no—
229C22×C4×C59—21no—
230C22×C4×C59—21no—
231C22×C4×C59—21no—
232C22×C4×C59—21no—
233C22×C4×C59—21no—
234C22×C4×C59—21no—
235C22×C4×C59—21no—
236C22×C4×C59—21no—
237C22×C4×C59—21no—
238C22×C4×C59—21no—
239C22×C4×C59—21no—
240C22×C4×C59—21no—
241C22×C4×C59—21no—
242C22×C4×C59—21no—
243C22×C4×C59—21no—
244C22×C4×C59—21no—
245C22×C4×C59—21no—
246C22×C4×C59—21no—
247C22×C4×C59—21no—
248C22×C4×C59—21no—
249C22×C4×C59—21no—
250C22×C4×C59—21no—
251C22×C4×C59—21no—
252C22×C4×C59—21no—
253C22×C4×C59—21no—
254C22×C4×C59—21no—
255C22×C4×C59—21no—
256C22×C4×C59—21no—
257C22×C4×C59—21no—
258C22×C4×C59—21no—
259C22×C4×C59—21no—
260C22×C4×C59—21no—
261C22×C4×C59—21no—
262C22×C4×C59—21no—
263C22×C4×C59C2×D412yes—
264C22×C4×C59C2×D412yes—
265C22×C4×C59C2×D412yes—
266C22×C4×C59#4112yes—
267C22×C4×C59#4112yes—
268C22×C4×C59#4112yes—
269C22×C4×C59#4112yes—
270C4⋊C4×C59—44no—
271C4⋊C4×C59—44no—
272C4⋊C4×C59—44no—
273C22⋊C4×C59—28no—
274C22⋊C4×C59—44no—
275C22⋊C4×C59—44no—
276C22⋊C4×C59—44no—
277C22⋊C4×C59—44no—
278C22⋊C4×C59—44no—
279C22⋊C4×C59—44no—
280C22⋊C4×C59—44no—
281C22⋊C4×C59—44no—
282C22⋊C4×C59—44no—
283C22⋊C4×C59—44no—
284C22⋊C4×C59—44no—
285C42×C59—44no—
286C23×C59—22no—
287C23×C59—22no—
288C23×C59—22no—
289C23×C59—22no—
290C23×C59—22no—
291C23×C59—22no—
292C23×C59—22no—
293C23×C59—22no—
294C23×C59—22no—
295C23×C59—22no—
296C23×C59—22no—
297C23×C59—22no—
298C23×C59—22no—
299C23×C59—22no—
300C23×C59—41no—
301C23×C59—41no—
302C23×C59—41no—
303C23×C59—41no—
304C23×C59—41no—
305C23×C59—41no—
306C23×C59—41no—
307C23×C59—41no—
308C23×C59—41no—
309C23×C59—41no—
310C23×C59—41no—
311C23×C59—41no—
312C23×C59—41no—
313C23×C59—41no—
314C23×C59—41no—
315C23×C59—41no—
316C23×C59—41no—
317C23×C59—41no—
318C23×C59—41no—
319C23×C59—41no—
320C23×C59—41no—
321C23×C59—41no—
322C23×C59—41no—
323C23×C59—41no—
324C23×C59—41no—
325C23×C59—41no—
326C23×C59—41no—
327C23×C59—41no—
328C23×C59—41no—
329C23×C59—41no—
330C23×C59—41no—
331C23×C59—41no—
332C23×C59—41no—
333C23×C59—41no—
334C23×C59—41no—
335C23×C59—41no—
336C23×C59—41no—
337C23×C59—41no—
338C23×C59—41no—
339C23×C59—41no—
340C23×C59—41no—
341C23×C59—41no—
342C23×C59—41no—
343C23×C59—41no—
344C23×C59—41no—
345C23×C59—41no—
346C23×C59—41no—
347C23×C59—41no—
348C23×C59—41no—
349C23×C59—41no—
350C23×C59—41no—
351C23×C59—41no—
352C23×C59—41no—
353C23×C59—41no—
354C23×C59—41no—
355C23×C59—41no—
356C23×C59C22×D411yescharacteristic
357C23×C59C2×#4111yescharacteristic
358C23×C59C2×#4111yescharacteristic
359C23×C59C2×#4111yescharacteristic
360C23×C59C2×#4111yescharacteristic
361C23×C59C2×#4111yescharacteristic
362C23×C59C2×#4111yescharacteristic
363C23×C59H(5,𝔽2)11yescharacteristic
364C23×C59H(5,𝔽2)11yescharacteristic
365C23×C59H(5,𝔽2)11yescharacteristic
366C23×C59H(5,𝔽2)11yescharacteristic
367C23×C59H(5,𝔽2)11yescharacteristic
368C23×C59H(5,𝔽2)11yescharacteristic
369C23×C59H(5,𝔽2)11yescharacteristic
370C23×C592−1+411yescharacteristic
371D4×C59—416no—
372C2×C4×C59—22no—
373C2×C4×C59—22no—
374C2×C4×C59—22no—
375C2×C4×C59—22no—
376C2×C4×C59—22no—
377C2×C4×C59—22no—
378C2×C4×C59—22no—
379C2×C4×C59—22no—
380C2×C4×C59—22no—
381C2×C4×C59—22no—
382C2×C4×C59—22no—
383C2×C4×C59—22no—
384C2×C4×C59—22no—
385C2×C4×C59—22no—
386C2×C4×C59—22no—
387C2×C4×C59—22no—
388C2×C4×C59—22no—
389C2×C4×C59—22no—
390C2×C4×C59—22no—
391C2×C4×C59—22no—
392C2×C4×C59—22no—
393C2×C4×C59—41no—
394C2×C4×C59—41no—
395C2×C4×C59—41no—
396C2×C4×C59—41no—
397C2×C4×C59—41no—
398C2×C4×C59—41no—
399C2×C4×C59—41no—
400C2×C4×C59—41no—
401C2×C4×C59—41no—
402C2×C4×C59—41no—
403C2×C4×C59—41no—
404C2×C4×C59—41no—
405C2×C4×C59—41no—
406C2×C4×C59—41no—
407C2×C4×C59—41no—
408C2×C4×C59—41no—
409C2×C4×C59—41no—
410C2×C4×C59—41no—
411C2×C4×C59—41no—
412C2×C4×C59—41no—
413C2×C4×C59—41no—
414C2×C4×C59—41no—
415C2×C4×C59—41no—
416C2×C4×C59—41no—
417C2×C4×C59—41no—
418C2×C4×C59—41no—
419C2×C4×C59—41no—
420C2×C4×C59—41no—
421C2×C4×C59—41no—
422C2×C4×C59—41no—
423C2×C4×C59—41no—
424C2×C4×C59—41no—
425C2×C4×C59—41no—
426C2×C4×C59—41no—
427C2×C4×C59—41no—
428C2×C4×C59—41no—
429C2×C4×C59—41no—
430C2×C4×C59—41no—
431C2×C4×C59—41no—
432C2×C4×C59—41no—
433C2×C4×C59—41no—
434C2×C4×C59—41no—
435C2×C4×C59—41no—
436C2×C4×C59—41no—
437C2×C4×C59—41no—
438C2×C4×C59—41no—
439C2×C4×C59—41no—
440C2×C4×C59—41no—
441C2×C4×C59—41no—
442C2×C4×C59—41no—
443C2×C4×C59—41no—
444C2×C4×C59—41no—
445C2×C4×C59—41no—
446C2×C4×C59—41no—
447C2×C4×C59—41no—
448C2×C4×C59—41no—
449C2×C4×C59—41no—
450C2×C4×C59—41no—
451C2×C4×C59—41no—
452C2×C4×C59—41no—
453C2×C4×C59—41no—
454C2×C4×C59—41no—
455C2×C4×C59—41no—
456C2×C4×C59—41no—
457C2×C4×C59—41no—
458C2×C4×C59—41no—
459C2×C4×C59—41no—
460C2×C4×C59—41no—
461C2×C4×C59—41no—
462C2×C4×C59—41no—
463#16497C5911yesmaximal, characteristic, direct product factor, Sylow
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—81no—
479C22×C59—81no—
480C22×C59—81no—
481C22×C59—81no—
482C22×C59—81no—
483C22×C59—81no—
484C22×C59—81no—
485C22×C59—81no—
486C22×C59—81no—
487C22×C59—81no—
488C22×C59—81no—
489C22×C59—81no—
490C22×C59—81no—
491C22×C59—81no—
492C22×C59—81no—
493C22×C59—81no—
494C22×C59#52511yescharacteristic
495C22×C59#52911yescharacteristic
496C22×C59#52911yescharacteristic
497C22×C59#53411yescharacteristic
498C22×C59#53511yescharacteristic
499C22×C59#53811yescharacteristic
500C22×C59#53811yescharacteristic
501C22×C59#53811yescharacteristic
502C22×C59#53811yescharacteristic
503C22×C59#53811yescharacteristic
504C22×C59#53811yescharacteristic
505C22×C59#53811yescharacteristic
506C22×C59#53911yescharacteristic
507C22×C59#54011yescharacteristic
508C22×C59#54011yescharacteristic
509C22×C59#54011yescharacteristic
510C22×C59#54011yescharacteristic
511C22×C59#54211yescharacteristic
512C22×C59#54211yescharacteristic
513C22×C59#54611yescharacteristic
514C22×C59#54611yescharacteristic
515C22×C59#54811yescharacteristic
516C22×C59#55011yescharacteristic
517C22×C59#55111yescharacteristic
518C22×C59#55111yescharacteristic
519C22×C59#55111yescharacteristic
520C22×C59#55111yescharacteristic
521C22×C59#55211yescharacteristic
522C22×C59#55311yescharacteristic
523C22×C59#55311yescharacteristic
524C22×C59#55511yescharacteristic
525C22×C59#56011yescharacteristic
526C22×C59#56011yescharacteristic
527C22×C59#56211yescharacteristic
528C22×C59#56211yescharacteristic
529C4×C59—42no—
530C4×C59—42no—
531C4×C59—42no—
532C4×C59—42no—
533C4×C59—42no—
534C4×C59—42no—
535C4×C59—42no—
536C4×C59—81no—
537C4×C59—81no—
538C4×C59—81no—
539C4×C59—81no—
540C4×C59—81no—
541C4×C59—81no—
542C2×#396C2×C5911yescharacteristic, complemented
543C2×#388C2×C5911yescharacteristic, complemented
544#1445C2×C5911yescharacteristic, complemented
545#1445C2×C5911yescharacteristic, complemented
546#1442C2×C5911yescharacteristic, complemented
547#1440C2×C5911yescharacteristic, complemented
548#1440C2×C5911yescharacteristic, complemented
549#1440C2×C5911yescharacteristic, complemented
550#1439C2×C5911yescharacteristic, complemented
551#1439C2×C5911yescharacteristic, complemented
552#1438C2×C5911yescharacteristic
553#1438C2×C5911yescharacteristic
554#1438C2×C5911yescharacteristic
555#1437C2×C5911yescharacteristic, complemented
556#1434C2×C5911yescharacteristic, complemented
557C2×C59—82no—
558C2×C59—82no—
559C2×C59#246711yescharacteristic
560C2×C59#247711yescharacteristic
561C2×C59#252611yescharacteristic
562C2×C59#263511yescharacteristic
563C2×C59#264811yescharacteristic
564C2×C59#265111yescharacteristic
565C2×C59#269611yescharacteristic
566C2×C59#269911yescharacteristic
567C2×C59#271411yescharacteristic
568C2×C59#273011yescharacteristic
569C2×C59#273511yescharacteristic
570C2×C59#274911yescharacteristic
571C2×C59#276111yescharacteristic
572C2×C59#278111yescharacteristic
573C2×C59#282911yescharacteristic
574C23×D4C22×C5911yescharacteristic
575C22×C4⋊C4C22×C5911yescharacteristic
576C22×C4⋊C4C22×C5911yescharacteristic
577C22×C4⋊C4C22×C5911yescharacteristic
578C22×C22⋊C4C22×C5911yescharacteristic
579C22×C22⋊C4C22×C5911yescharacteristic
580C22×C22⋊C4C22×C5911yescharacteristic
581C22×C22⋊C4C22×C5911yescharacteristic
582C22×C22⋊C4C22×C5911yescharacteristic
583C22×C22⋊C4C22×C5911yescharacteristic
584C22×C22⋊C4C22×C5911yescharacteristic
585C22×C22⋊C4C22×C5911yescharacteristic
586C22×C22⋊C4C22×C5911yescharacteristic
587C22×C22⋊C4C22×C5911yescharacteristic
588C22×C22⋊C4C22×C5911yescharacteristic
589C22×C22⋊C4C22×C5911yescharacteristic
590C22×C42C22×C5911yescharacteristic
591#396—24no—
592#388—24no—
593C2×#95C22×C5911yescharacteristic
594C2×#95C22×C5911yescharacteristic
595C2×#95C22×C5911yescharacteristic
596C2×#95C22×C5911yescharacteristic
597C2×#95C22×C5911yescharacteristic
598C2×#95C22×C5911yescharacteristic
599C2×#95C22×C5911yescharacteristic
600C2×#95C22×C5911yescharacteristic
601C2×#95C22×C5911yescharacteristic
602C2×#95C22×C5911yescharacteristic
603C2×#95C22×C5911yescharacteristic
604C2×#95C22×C5911yescharacteristic
605C2×#95C22×C5911yescharacteristic
606C2×#95C22×C5911yescharacteristic
607C2×#95C22×C5911yescharacteristic
608C2×#95C22×C5911yescharacteristic
609C2×#95C22×C5911yescharacteristic
610C2×#95C22×C5911yescharacteristic
611C59#1649711yescharacteristic, direct product factor, Sylow
612C25C23×C5911yescharacteristic
613C25C23×C5911yescharacteristic
614C22×D4—22no—
615C22×D4—22no—
616C22×D4—22no—
617C22×D4—41no—
618C22×D4—41no—
619C22×D4—41no—
620C22×D4—41no—
621C23×C4C23×C5911yescharacteristic
622C23×C4C23×C5911yescharacteristic
623C23×C4C23×C5911yescharacteristic
624C23×C4C23×C5911yescharacteristic
625C23×C4C23×C5911yescharacteristic
626C23×C4C23×C5911yescharacteristic
627C23×C4C23×C5911yescharacteristic
628C23×C4C23×C5911yescharacteristic
629C23×C4C23×C5911yescharacteristic
630C23×C4C23×C5911yescharacteristic
631C23×C4C23×C5911yescharacteristic
632C23×C4C23×C5911yescharacteristic
633C23×C4C23×C5911yescharacteristic
634C2×C4⋊C4—22no—
635C2×C4⋊C4—22no—
636C2×C4⋊C4—22no—
637C2×C4⋊C4—41no—
638C2×C4⋊C4—41no—
639C2×C4⋊C4—41no—
640C2×C4⋊C4—41no—
641C2×C4⋊C4—41no—
642C2×C4⋊C4D4×C5914yescomplemented
643C2×C22⋊C4—22no—
644C2×C22⋊C4—22no—
645C2×C22⋊C4—22no—
646C2×C22⋊C4—22no—
647C2×C22⋊C4—22no—
648C2×C22⋊C4—22no—
649C2×C22⋊C4—22no—
650C2×C22⋊C4—22no—
651C2×C22⋊C4—22no—
652C2×C22⋊C4—22no—
653C2×C22⋊C4—22no—
654C2×C22⋊C4—22no—
655C2×C22⋊C4—22no—
656C2×C22⋊C4—22no—
657C2×C22⋊C4—22no—
658C2×C22⋊C4—22no—
659C2×C22⋊C4—41no—
660C2×C22⋊C4—41no—
661C2×C22⋊C4—41no—
662C2×C22⋊C4—41no—
663C2×C22⋊C4—41no—
664C2×C22⋊C4—41no—
665C2×C22⋊C4—41no—
666C2×C22⋊C4—41no—
667C2×C22⋊C4—41no—
668C2×C22⋊C4—41no—
669C2×C22⋊C4—41no—
670C2×C22⋊C4—41no—
671C2×C22⋊C4—41no—
672C2×C22⋊C4—41no—
673C2×C22⋊C4—41no—
674C2×C22⋊C4—41no—
675C2×C22⋊C4—41no—
676C2×C22⋊C4—41no—
677C2×C22⋊C4—41no—
678C2×C22⋊C4—41no—
679C2×C42—22no—
680C2×C42—22no—
681C2×C42—41no—
682#95—22no—
683#95—22no—
684#95—22no—
685#95—22no—
686#95—22no—
687#95—22no—
688#95—41no—
689#95—41no—
690#95—41no—
691#95—41no—
692#95—41no—
693#95—41no—
694#95—41no—
695#95—41no—
696#95—41no—
697#95—41no—
698#95—41no—
699#95—41no—
700C24—21no—
701C24—21no—
702C24—21no—
703C24—21no—
704C24—21no—
705C24—21no—
706C24—21no—
707C24—21no—
708C24—21no—
709C24—21no—
710C24—21no—
711C24—21no—
712C24—21no—
713C24—21no—
714C24—21no—
715C24—21no—
716C24—21no—
717C24—21no—
718C24—21no—
719C24—21no—
720C24—21no—
721C24—21no—
722C24—21no—
723C24—21no—
724C24—21no—
725C24—21no—
726C24—21no—
727C24—21no—
728C24#41×C5912yes—
729C24#41×C5912yes—
730C24C24×C5911yescharacteristic
731C2×D4—44no—
732C2×D4—44no—
733C2×D4—44no—
734C2×D4—44no—
735C2×D4—44no—
736C2×D4—44no—
737C2×D4—44no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4C2×D4×C5912yes—
823C22×C4C2×D4×C5912yes—
824C22×C4C2×D4×C5912yes—
825C22×C4#41×C5912yes—
826C22×C4#41×C5912yes—
827C22×C4#41×C5912yes—
828C22×C4#41×C5912yes—
829C4⋊C4—44no—
830C4⋊C4—44no—
831C4⋊C4—44no—
832C22⋊C4—28no—
833C22⋊C4—44no—
834C22⋊C4—44no—
835C22⋊C4—44no—
836C22⋊C4—44no—
837C22⋊C4—44no—
838C22⋊C4—44no—
839C22⋊C4—44no—
840C22⋊C4—44no—
841C22⋊C4—44no—
842C22⋊C4—44no—
843C22⋊C4—44no—
844C42—44no—
845C23—22no—
846C23—22no—
847C23—22no—
848C23—22no—
849C23—22no—
850C23—22no—
851C23—22no—
852C23—22no—
853C23—22no—
854C23—22no—
855C23—22no—
856C23—22no—
857C23—22no—
858C23—22no—
859C23—41no—
860C23—41no—
861C23—41no—
862C23—41no—
863C23—41no—
864C23—41no—
865C23—41no—
866C23—41no—
867C23—41no—
868C23—41no—
869C23—41no—
870C23—41no—
871C23—41no—
872C23—41no—
873C23—41no—
874C23—41no—
875C23—41no—
876C23—41no—
877C23—41no—
878C23—41no—
879C23—41no—
880C23—41no—
881C23—41no—
882C23—41no—
883C23—41no—
884C23—41no—
885C23—41no—
886C23—41no—
887C23—41no—
888C23—41no—
889C23—41no—
890C23—41no—
891C23—41no—
892C23—41no—
893C23—41no—
894C23—41no—
895C23—41no—
896C23—41no—
897C23—41no—
898C23—41no—
899C23—41no—
900C23—41no—
901C23—41no—
902C23—41no—
903C23—41no—
904C23—41no—
905C23—41no—
906C23—41no—
907C23—41no—
908C23—41no—
909C23—41no—
910C23—41no—
911C23—41no—
912C23—41no—
913C23—41no—
914C23—41no—
915C23C22×D4×C5911yescharacteristic
916C23C2×#41×C5911yescharacteristic
917C23C2×#41×C5911yescharacteristic
918C23C2×#41×C5911yescharacteristic
919C23C2×#41×C5911yescharacteristic
920C23C2×#41×C5911yescharacteristic
921C23C2×#41×C5911yescharacteristic
922C23H(5,𝔽2)×C5911yescharacteristic
923C23H(5,𝔽2)×C5911yescharacteristic
924C23H(5,𝔽2)×C5911yescharacteristic
925C23H(5,𝔽2)×C5911yescharacteristic
926C23H(5,𝔽2)×C5911yescharacteristic
927C23H(5,𝔽2)×C5911yescharacteristic
928C23H(5,𝔽2)×C5911yescharacteristic
929C232−1+4×C5911yescharacteristic
930D4—416no—
931C2×C4—22no—
932C2×C4—22no—
933C2×C4—22no—
934C2×C4—22no—
935C2×C4—22no—
936C2×C4—22no—
937C2×C4—22no—
938C2×C4—22no—
939C2×C4—22no—
940C2×C4—22no—
941C2×C4—22no—
942C2×C4—22no—
943C2×C4—22no—
944C2×C4—22no—
945C2×C4—22no—
946C2×C4—22no—
947C2×C4—22no—
948C2×C4—22no—
949C2×C4—22no—
950C2×C4—22no—
951C2×C4—22no—
952C2×C4—41no—
953C2×C4—41no—
954C2×C4—41no—
955C2×C4—41no—
956C2×C4—41no—
957C2×C4—41no—
958C2×C4—41no—
959C2×C4—41no—
960C2×C4—41no—
961C2×C4—41no—
962C2×C4—41no—
963C2×C4—41no—
964C2×C4—41no—
965C2×C4—41no—
966C2×C4—41no—
967C2×C4—41no—
968C2×C4—41no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—41no—
973C2×C4—41no—
974C2×C4—41no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—41no—
978C2×C4—41no—
979C2×C4—41no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—41no—
986C2×C4—41no—
987C2×C4—41no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—41no—
999C2×C4—41no—
1000C2×C4—41no—
1001C2×C4—41no—
1002C2×C4—41no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—41no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C22—42no—
1023C22—42no—
1024C22—42no—
1025C22—42no—
1026C22—42no—
1027C22—42no—
1028C22—42no—
1029C22—42no—
1030C22—42no—
1031C22—42no—
1032C22—42no—
1033C22—42no—
1034C22—42no—
1035C22—42no—
1036C22—81no—
1037C22—81no—
1038C22—81no—
1039C22—81no—
1040C22—81no—
1041C22—81no—
1042C22—81no—
1043C22—81no—
1044C22—81no—
1045C22—81no—
1046C22—81no—
1047C22—81no—
1048C22—81no—
1049C22—81no—
1050C22—81no—
1051C22—81no—
1052C22C59×#52511yescharacteristic
1053C22C59×#52911yescharacteristic
1054C22C59×#52911yescharacteristic
1055C22C59×#53411yescharacteristic
1056C22C59×#53511yescharacteristic
1057C22C59×#53811yescharacteristic
1058C22C59×#53811yescharacteristic
1059C22C59×#53811yescharacteristic
1060C22C59×#53811yescharacteristic
1061C22C59×#53811yescharacteristic
1062C22C59×#53811yescharacteristic
1063C22C59×#53811yescharacteristic
1064C22C59×#53911yescharacteristic
1065C22C59×#54011yescharacteristic
1066C22C59×#54011yescharacteristic
1067C22C59×#54011yescharacteristic
1068C22C59×#54011yescharacteristic
1069C22C59×#54211yescharacteristic
1070C22C59×#54211yescharacteristic
1071C22C59×#54611yescharacteristic
1072C22C59×#54611yescharacteristic
1073C22C59×#54811yescharacteristic
1074C22C59×#55011yescharacteristic
1075C22C59×#55111yescharacteristic
1076C22C59×#55111yescharacteristic
1077C22C59×#55111yescharacteristic
1078C22C59×#55111yescharacteristic
1079C22C59×#55211yescharacteristic
1080C22C59×#55311yescharacteristic
1081C22C59×#55311yescharacteristic
1082C22C59×#55511yescharacteristic
1083C22C59×#56011yescharacteristic
1084C22C59×#56011yescharacteristic
1085C22C59×#56211yescharacteristic
1086C22C59×#56211yescharacteristic
1087C4—42no—
1088C4—42no—
1089C4—42no—
1090C4—42no—
1091C4—42no—
1092C4—42no—
1093C4—42no—
1094C4—81no—
1095C4—81no—
1096C4—81no—
1097C4—81no—
1098C4—81no—
1099C4—81no—
1100C2—82no—
1101C2—82no—
1102C2C59×#246711yescharacteristic
1103C2C59×#247711yescharacteristic
1104C2C59×#252611yescharacteristic
1105C2C59×#263511yescharacteristic
1106C2C59×#264811yescharacteristic
1107C2C59×#265111yescharacteristic
1108C2C59×#269611yescharacteristic
1109C2C59×#269911yescharacteristic
1110C2C59×#271411yescharacteristic
1111C2C59×#273011yescharacteristic
1112C2C59×#273511yescharacteristic
1113C2C59×#274911yescharacteristic
1114C2C59×#276111yescharacteristic
1115C2C59×#278111yescharacteristic
1116C2C59×#282911yescharacteristic
subgroupG/H
center, socleC24×C59C24
commutator, Frattini, cosocleC24C24×C59
prime radicalC23×D4×C59C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C59 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C59×#396C2semidirect
2. C2×C59×#388C2semidirect
3. C59×#1445C2semidirect
4. C59×#1445C2semidirect
5. C59×#1442C2semidirect
6. C59×#1440C2semidirect
7. C59×#1440C2semidirect
8. C59×#1440C2semidirect
9. C59×#1439C2semidirect
10. C59×#1439C2semidirect
14. C59×#1437C2semidirect
15. C59×#1434C2semidirect
83. C2×C4⋊C4×C59D4semidirect
463. #16497C59direct (N × H)
542. C2×#396C2×C59semidirect
543. C2×#388C2×C59semidirect
544. #1445C2×C59semidirect
545. #1445C2×C59semidirect
546. #1442C2×C59semidirect
547. #1440C2×C59semidirect
548. #1440C2×C59semidirect
549. #1440C2×C59semidirect
550. #1439C2×C59semidirect
551. #1439C2×C59semidirect
555. #1437C2×C59semidirect
556. #1434C2×C59semidirect
611. C59#16497direct (N × H)
642. C2×C4⋊C4D4×C59semidirect

Maximal subgroups

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

subgroupindex
C2×C59×#3962
C2×C59×#3882
C59×#14452
C59×#14422
C59×#14402
C59×#14392
C59×#14382
C59×#14372
C59×#14342
#1649759