Finite Group Databasebeta

← C59×#14116 #28426225

Subgroups — C59×#14116 #28426225

Order 15104.

1730 conjugacy classes of subgroups.

The subgroup lattice has 1022 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C59×#389C211yesmaximal, characteristic, complemented
2C2×C59×#388C211yesmaximal, characteristic
3C2×C59×#388C211yesmaximal, characteristic
4C2×C59×#385C211yesmaximal, characteristic
5C2×C4×C22⋊C4×C59C211yesmaximal, characteristic
6C59×#1442C211yesmaximal, characteristic, complemented
7C59×#1441C211yesmaximal, characteristic, complemented
8C59×#1439C211yesmaximal, characteristic
9C59×#1439C211yesmaximal, characteristic
10C59×#1436C211yesmaximal, characteristic, complemented
11C59×#1436C211yesmaximal, characteristic, complemented
12C59×#1436C211yesmaximal, characteristic, complemented
13C59×C4⋊#95C211yesmaximal, characteristic, complemented
14C59×C22⋊#95C211yesmaximal, characteristic
15C4×#95×C59C211yesmaximal, characteristic, complemented
16C24×C4×C59C2211yescharacteristic
17C22×C4⋊C4×C59C2211yescharacteristic
18C22×C4⋊C4×C59C2211yescharacteristic
19C22×C4⋊C4×C59C2211yescharacteristic
20C22×C4⋊C4×C59C2211yescharacteristic
21C22×C4⋊C4×C59C2211yescharacteristic
22C22×C4⋊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×C42×C59C2211yescharacteristic
30C22×C42×C59C2211yescharacteristic
31C22×C42×C59C2211yescharacteristic
32C22×C42×C59C2211yescharacteristic
33C59×#389—24no—
34C59×#388—24no—
35C59×#388C418yescomplemented
36C59×#385—24no—
37C4×C22⋊C4×C59—24no—
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
53C2×#95×C59C2211yescharacteristic
54C2×#95×C59C2211yescharacteristic
55C2×#95×C59C2211yescharacteristic
56C25×C59C2311yescharacteristic
57C23×C4×C59—22no—
58C23×C4×C59—22no—
59C23×C4×C59—22no—
60C23×C4×C59—22no—
61C23×C4×C59—22no—
62C23×C4×C59—41no—
63C23×C4×C59—41no—
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
75C23×C4×C59C2311yescharacteristic
76C23×C4×C59C2311yescharacteristic
77C23×C4×C59C2311yescharacteristic
78C2×C4⋊C4×C59—22no—
79C2×C4⋊C4×C59—22no—
80C2×C4⋊C4×C59—22no—
81C2×C4⋊C4×C59—22no—
82C2×C4⋊C4×C59—22no—
83C2×C4⋊C4×C59—22no—
84C2×C4⋊C4×C59—22no—
85C2×C4⋊C4×C59—22no—
86C2×C4⋊C4×C59—22no—
87C2×C4⋊C4×C59—22no—
88C2×C4⋊C4×C59—22no—
89C2×C4⋊C4×C59—22no—
90C2×C4⋊C4×C59—22no—
91C2×C4⋊C4×C59—41no—
92C2×C4⋊C4×C59—41no—
93C2×C4⋊C4×C59—41no—
94C2×C4⋊C4×C59—41no—
95C2×C4⋊C4×C59C2×C414yescomplemented
96C2×C22⋊C4×C59—22no—
97C2×C22⋊C4×C59—22no—
98C2×C22⋊C4×C59—22no—
99C2×C22⋊C4×C59—22no—
100C2×C22⋊C4×C59—22no—
101C2×C22⋊C4×C59—22no—
102C2×C22⋊C4×C59—22no—
103C2×C22⋊C4×C59—22no—
104C2×C22⋊C4×C59—22no—
105C2×C22⋊C4×C59—41no—
106C2×C22⋊C4×C59—41no—
107C2×C22⋊C4×C59—41no—
108C2×C22⋊C4×C59—41no—
109C2×C22⋊C4×C59C2×C414yes—
110C2×C22⋊C4×C59C2×C414yes—
111C2×C22⋊C4×C59C2×C414yes—
112C2×C22⋊C4×C59D414yes—
113C2×C22⋊C4×C59Q814yes—
114C2×C42×C59—22no—
115C2×C42×C59—22no—
116C2×C42×C59—22no—
117C2×C42×C59—22no—
118C2×C42×C59—22no—
119C2×C42×C59—22no—
120C2×C42×C59—41no—
121C2×C42×C59—41no—
122C2×C42×C59—41no—
123C2×C42×C59—41no—
124C2×C42×C59—41no—
125C2×C42×C59C2×C414yescomplemented
126#95×C59—22no—
127#95×C59—22no—
128#95×C59—22no—
129#95×C59—22no—
130#95×C59—22no—
131#95×C59—22no—
132#95×C59—22no—
133#95×C59—22no—
134#95×C59—22no—
135#95×C59—22no—
136#95×C59—22no—
137#95×C59—22no—
138#95×C59—41no—
139#95×C59—41no—
140#95×C59—41no—
141#95×C59C2×C414yescomplemented
142#95×C59C2×C414yescomplemented
143#95×C59D414yes—
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×C59C22×C412yes—
157C24×C59C2×D412yes—
158C24×C59C2×Q812yes—
159C24×C59C2411yescharacteristic
160C22×C4×C59—21no—
161C22×C4×C59—21no—
162C22×C4×C59—21no—
163C22×C4×C59—21no—
164C22×C4×C59—21no—
165C22×C4×C59—21no—
166C22×C4×C59—21no—
167C22×C4×C59—21no—
168C22×C4×C59—21no—
169C22×C4×C59—21no—
170C22×C4×C59—21no—
171C22×C4×C59—21no—
172C22×C4×C59—21no—
173C22×C4×C59—21no—
174C22×C4×C59—21no—
175C22×C4×C59—21no—
176C22×C4×C59—28no—
177C22×C4×C59—21no—
178C22×C4×C59—21no—
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—44no—
240C22×C4×C59—44no—
241C22×C4×C59—44no—
242C22×C4×C59—44no—
243C22×C4×C59—44no—
244C22×C4×C59—44no—
245C22×C4×C59C22×C412yes—
246C22×C4×C59C22×C412yes—
247C22×C4×C59C22×C412yes—
248C22×C4×C59C22×C412yes—
249C22×C4×C59C22×C412yes—
250C22×C4×C59C22×C412yes—
251C22×C4×C59C2×D412yes—
252C22×C4×C59C2×D412yes—
253C22×C4×C59C2×D412yes—
254C22×C4×C59C2×D412yes—
255C22×C4×C59C2×D412yes—
256C22×C4×C59C2×Q812yes—
257C22×C4×C59C2×Q812yes—
258C22×C4×C59#4112yes—
259C22×C4×C59#4112yes—
260C22×C4×C59#4112yes—
261C22×C4×C59#4112yes—
262C22×C4×C59#4112yes—
263C22×C4×C59#4112yes—
264C22×C4×C59#4112yes—
265C4⋊C4×C59—28no—
266C4⋊C4×C59—44no—
267C4⋊C4×C59—44no—
268C4⋊C4×C59—44no—
269C4⋊C4×C59—44no—
270C4⋊C4×C59—44no—
271C22⋊C4×C59—28no—
272C22⋊C4×C59—28no—
273C22⋊C4×C59—44no—
274C22⋊C4×C59—44no—
275C22⋊C4×C59—44no—
276C22⋊C4×C59C4⋊C4116yescomplemented
277C42×C59—44no—
278C42×C59—44no—
279C42×C59—44no—
280C42×C59—44no—
281C23×C59—22no—
282C23×C59—22no—
283C23×C59—22no—
284C23×C59—22no—
285C23×C59—22no—
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—41no—
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×C59C2×C4⋊C414yes—
316C23×C59C23×C411yescharacteristic
317C23×C59C22×D411yescharacteristic
318C23×C59C22×D411yescharacteristic
319C23×C59C22×Q811yescharacteristic
320C23×C59C2×#4111yescharacteristic
321C23×C59C2×#4111yescharacteristic
322C23×C59C2×#4111yescharacteristic
323C23×C59C2×#4111yescharacteristic
324C23×C59C2×#4111yescharacteristic
325C23×C59C2×#4111yescharacteristic
326C23×C59C2×#4111yescharacteristic
327C23×C59H(5,𝔽2)11yescharacteristic
328C23×C59H(5,𝔽2)11yescharacteristic
329C23×C59H(5,𝔽2)11yescharacteristic
330C23×C592−1+411yescharacteristic
331C2×C4×C59—22no—
332C2×C4×C59—22no—
333C2×C4×C59—22no—
334C2×C4×C59—22no—
335C2×C4×C59—22no—
336C2×C4×C59—22no—
337C2×C4×C59—22no—
338C2×C4×C59—22no—
339C2×C4×C59—22no—
340C2×C4×C59—22no—
341C2×C4×C59—22no—
342C2×C4×C59—22no—
343C2×C4×C59—22no—
344C2×C4×C59—22no—
345C2×C4×C59—22no—
346C2×C4×C59—22no—
347C2×C4×C59—22no—
348C2×C4×C59—22no—
349C2×C4×C59—22no—
350C2×C4×C59—22no—
351C2×C4×C59—22no—
352C2×C4×C59—22no—
353C2×C4×C59—22no—
354C2×C4×C59—22no—
355C2×C4×C59—22no—
356C2×C4×C59—22no—
357C2×C4×C59—22no—
358C2×C4×C59—22no—
359C2×C4×C59—22no—
360C2×C4×C59—22no—
361C2×C4×C59—22no—
362C2×C4×C59—22no—
363C2×C4×C59—22no—
364C2×C4×C59—22no—
365C2×C4×C59—22no—
366C2×C4×C59—22no—
367C2×C4×C59—22no—
368C2×C4×C59—22no—
369C2×C4×C59—22no—
370C2×C4×C59—22no—
371C2×C4×C59—22no—
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—416no—
380C2×C4×C59—41no—
381C2×C4×C59—41no—
382C2×C4×C59—41no—
383C2×C4×C59—41no—
384C2×C4×C59—41no—
385C2×C4×C59—41no—
386C2×C4×C59—41no—
387C2×C4×C59—41no—
388C2×C4×C59—41no—
389C2×C4×C59—41no—
390C2×C4×C59—41no—
391C2×C4×C59—41no—
392C2×C4×C59—41no—
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×C59C2×C4⋊C414yes—
427C2×C4×C59C2×C4⋊C414yes—
428C2×C4×C59C4×D414yes—
429C2×C4×C59#12414yes—
430#14116C5911yesmaximal, characteristic, direct product factor, Sylow
431C22×C59—24no—
432C22×C59—24no—
433C22×C59—24no—
434C22×C59—42no—
435C22×C59—42no—
436C22×C59—42no—
437C22×C59—42no—
438C22×C59—42no—
439C22×C59—42no—
440C22×C59—42no—
441C22×C59—42no—
442C22×C59—42no—
443C22×C59—42no—
444C22×C59—42no—
445C22×C59—42no—
446C22×C59C22×C4⋊C411yescharacteristic
447C22×C59C2×C4×D411yescharacteristic
448C22×C59C4×#4111yescharacteristic
449C22×C59C4×#4111yescharacteristic
450C22×C59C4×#4111yescharacteristic
451C22×C59#51811yescharacteristic
452C22×C59#52011yescharacteristic
453C22×C59#52511yescharacteristic
454C22×C59#52511yescharacteristic
455C22×C59C2×#12411yescharacteristic
456C22×C59#52911yescharacteristic
457C22×C59#52911yescharacteristic
458C22×C59#53211yescharacteristic
459C22×C59#53311yescharacteristic
460C22×C59#53311yescharacteristic
461C22×C59#53811yescharacteristic
462C22×C59#53911yescharacteristic
463C22×C59#54011yescharacteristic
464C22×C59#54211yescharacteristic
465C22×C59D4211yescharacteristic
466C22×C59#54611yescharacteristic
467C22×C59#54611yescharacteristic
468C22×C59#54611yescharacteristic
469C22×C59#54611yescharacteristic
470C22×C59#54711yescharacteristic
471C22×C59D4×Q811yescharacteristic
472C22×C59#55111yescharacteristic
473C22×C59#55211yescharacteristic
474C22×C59#55311yescharacteristic
475C22×C59#55311yescharacteristic
476C22×C59#55311yescharacteristic
477C22×C59#55411yescharacteristic
478C22×C59#55411yescharacteristic
479C22×C59#55411yescharacteristic
480C22×C59#55611yescharacteristic
481C4×C59—24no—
482C4×C59—24no—
483C4×C59—24no—
484C4×C59—24no—
485C4×C59—42no—
486C4×C59—42no—
487C4×C59—42no—
488C4×C59—42no—
489C4×C59—42no—
490C4×C59—42no—
491C4×C59—42no—
492C4×C59—42no—
493C4×C59—81no—
494C4×C59—81no—
495C2×#389C2×C5911yescharacteristic, complemented
496C2×#388C2×C5911yescharacteristic
497C2×#388C2×C5911yescharacteristic
498C2×#385C2×C5911yescharacteristic
499C2×C4×C22⋊C4C2×C5911yescharacteristic
500#1442C2×C5911yescharacteristic, complemented
501#1441C2×C5911yescharacteristic, complemented
502#1439C2×C5911yescharacteristic
503#1439C2×C5911yescharacteristic
504#1436C2×C5911yescharacteristic, complemented
505#1436C2×C5911yescharacteristic, complemented
506#1436C2×C5911yescharacteristic, complemented
507C4⋊#95C2×C5911yescharacteristic, complemented
508C22⋊#95C2×C5911yescharacteristic
509C4×#95C2×C5911yescharacteristic, complemented
510C2×C59—44no—
511C2×C59#229611yescharacteristic
512C2×C59C4×#12411yescharacteristic
513C2×C59#233511yescharacteristic
514C2×C59D4×C4⋊C411yescharacteristic
515C2×C59#234911yescharacteristic
516C2×C59#236411yescharacteristic
517C2×C59#237311yescharacteristic
518C2×C59#246411yescharacteristic
519C2×C59#246611yescharacteristic
520C2×C59#247011yescharacteristic
521C2×C59#247211yescharacteristic
522C2×C59#249211yescharacteristic
523C2×C59#252211yescharacteristic
524C2×C59#255611yescharacteristic
525C2×C59#258711yescharacteristic
526C24×C4C22×C5911yescharacteristic
527C22×C4⋊C4C22×C5911yescharacteristic
528C22×C4⋊C4C22×C5911yescharacteristic
529C22×C4⋊C4C22×C5911yescharacteristic
530C22×C4⋊C4C22×C5911yescharacteristic
531C22×C4⋊C4C22×C5911yescharacteristic
532C22×C4⋊C4C22×C5911yescharacteristic
533C22×C22⋊C4C22×C5911yescharacteristic
534C22×C22⋊C4C22×C5911yescharacteristic
535C22×C22⋊C4C22×C5911yescharacteristic
536C22×C22⋊C4C22×C5911yescharacteristic
537C22×C22⋊C4C22×C5911yescharacteristic
538C22×C22⋊C4C22×C5911yescharacteristic
539C22×C42C22×C5911yescharacteristic
540C22×C42C22×C5911yescharacteristic
541C22×C42C22×C5911yescharacteristic
542C22×C42C22×C5911yescharacteristic
543#389—24no—
544#388—24no—
545#388C4×C5918yescomplemented
546#385—24no—
547C4×C22⋊C4—24no—
548C2×#95C22×C5911yescharacteristic
549C2×#95C22×C5911yescharacteristic
550C2×#95C22×C5911yescharacteristic
551C2×#95C22×C5911yescharacteristic
552C2×#95C22×C5911yescharacteristic
553C2×#95C22×C5911yescharacteristic
554C2×#95C22×C5911yescharacteristic
555C2×#95C22×C5911yescharacteristic
556C2×#95C22×C5911yescharacteristic
557C2×#95C22×C5911yescharacteristic
558C2×#95C22×C5911yescharacteristic
559C2×#95C22×C5911yescharacteristic
560C2×#95C22×C5911yescharacteristic
561C2×#95C22×C5911yescharacteristic
562C2×#95C22×C5911yescharacteristic
563C2×#95C22×C5911yescharacteristic
564C2×#95C22×C5911yescharacteristic
565C2×#95C22×C5911yescharacteristic
566C59#1411611yescharacteristic, direct product factor, Sylow
567C25C23×C5911yescharacteristic
568C23×C4—22no—
569C23×C4—22no—
570C23×C4—22no—
571C23×C4—22no—
572C23×C4—22no—
573C23×C4—41no—
574C23×C4—41no—
575C23×C4C23×C5911yescharacteristic
576C23×C4C23×C5911yescharacteristic
577C23×C4C23×C5911yescharacteristic
578C23×C4C23×C5911yescharacteristic
579C23×C4C23×C5911yescharacteristic
580C23×C4C23×C5911yescharacteristic
581C23×C4C23×C5911yescharacteristic
582C23×C4C23×C5911yescharacteristic
583C23×C4C23×C5911yescharacteristic
584C23×C4C23×C5911yescharacteristic
585C23×C4C23×C5911yescharacteristic
586C23×C4C23×C5911yescharacteristic
587C23×C4C23×C5911yescharacteristic
588C23×C4C23×C5911yescharacteristic
589C2×C4⋊C4—22no—
590C2×C4⋊C4—22no—
591C2×C4⋊C4—22no—
592C2×C4⋊C4—22no—
593C2×C4⋊C4—22no—
594C2×C4⋊C4—22no—
595C2×C4⋊C4—22no—
596C2×C4⋊C4—22no—
597C2×C4⋊C4—22no—
598C2×C4⋊C4—22no—
599C2×C4⋊C4—22no—
600C2×C4⋊C4—22no—
601C2×C4⋊C4—22no—
602C2×C4⋊C4—41no—
603C2×C4⋊C4—41no—
604C2×C4⋊C4—41no—
605C2×C4⋊C4—41no—
606C2×C4⋊C4C2×C4×C5914yescomplemented
607C2×C22⋊C4—22no—
608C2×C22⋊C4—22no—
609C2×C22⋊C4—22no—
610C2×C22⋊C4—22no—
611C2×C22⋊C4—22no—
612C2×C22⋊C4—22no—
613C2×C22⋊C4—22no—
614C2×C22⋊C4—22no—
615C2×C22⋊C4—22no—
616C2×C22⋊C4—41no—
617C2×C22⋊C4—41no—
618C2×C22⋊C4—41no—
619C2×C22⋊C4—41no—
620C2×C22⋊C4C2×C4×C5914yes—
621C2×C22⋊C4C2×C4×C5914yes—
622C2×C22⋊C4C2×C4×C5914yes—
623C2×C22⋊C4D4×C5914yes—
624C2×C22⋊C4Q8×C5914yes—
625C2×C42—22no—
626C2×C42—22no—
627C2×C42—22no—
628C2×C42—22no—
629C2×C42—22no—
630C2×C42—22no—
631C2×C42—41no—
632C2×C42—41no—
633C2×C42—41no—
634C2×C42—41no—
635C2×C42—41no—
636C2×C42C2×C4×C5914yescomplemented
637#95—22no—
638#95—22no—
639#95—22no—
640#95—22no—
641#95—22no—
642#95—22no—
643#95—22no—
644#95—22no—
645#95—22no—
646#95—22no—
647#95—22no—
648#95—22no—
649#95—41no—
650#95—41no—
651#95—41no—
652#95C2×C4×C5914yescomplemented
653#95C2×C4×C5914yescomplemented
654#95D4×C5914yes—
655C24—21no—
656C24—21no—
657C24—21no—
658C24—21no—
659C24—21no—
660C24—21no—
661C24—21no—
662C24—21no—
663C24—21no—
664C24—21no—
665C24—21no—
666C24—21no—
667C24C22×C4×C5912yes—
668C24C2×D4×C5912yes—
669C24C2×Q8×C5912yes—
670C24C24×C5911yescharacteristic
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—28no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
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—44no—
751C22×C4—44no—
752C22×C4—44no—
753C22×C4—44no—
754C22×C4—44no—
755C22×C4—44no—
756C22×C4C22×C4×C5912yes—
757C22×C4C22×C4×C5912yes—
758C22×C4C22×C4×C5912yes—
759C22×C4C22×C4×C5912yes—
760C22×C4C22×C4×C5912yes—
761C22×C4C22×C4×C5912yes—
762C22×C4C2×D4×C5912yes—
763C22×C4C2×D4×C5912yes—
764C22×C4C2×D4×C5912yes—
765C22×C4C2×D4×C5912yes—
766C22×C4C2×D4×C5912yes—
767C22×C4C2×Q8×C5912yes—
768C22×C4C2×Q8×C5912yes—
769C22×C4#41×C5912yes—
770C22×C4#41×C5912yes—
771C22×C4#41×C5912yes—
772C22×C4#41×C5912yes—
773C22×C4#41×C5912yes—
774C22×C4#41×C5912yes—
775C22×C4#41×C5912yes—
776C4⋊C4—28no—
777C4⋊C4—44no—
778C4⋊C4—44no—
779C4⋊C4—44no—
780C4⋊C4—44no—
781C4⋊C4—44no—
782C22⋊C4—28no—
783C22⋊C4—28no—
784C22⋊C4—44no—
785C22⋊C4—44no—
786C22⋊C4—44no—
787C22⋊C4C4⋊C4×C59116yescomplemented
788C42—44no—
789C42—44no—
790C42—44no—
791C42—44no—
792C23—22no—
793C23—22no—
794C23—22no—
795C23—22no—
796C23—22no—
797C23—22no—
798C23—22no—
799C23—22no—
800C23—22no—
801C23—22no—
802C23—22no—
803C23—22no—
804C23—22no—
805C23—22no—
806C23—22no—
807C23—22no—
808C23—22no—
809C23—22no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23C2×C4⋊C4×C5914yes—
827C23C23×C4×C5911yescharacteristic
828C23C22×D4×C5911yescharacteristic
829C23C22×D4×C5911yescharacteristic
830C23C22×Q8×C5911yescharacteristic
831C23C2×#41×C5911yescharacteristic
832C23C2×#41×C5911yescharacteristic
833C23C2×#41×C5911yescharacteristic
834C23C2×#41×C5911yescharacteristic
835C23C2×#41×C5911yescharacteristic
836C23C2×#41×C5911yescharacteristic
837C23C2×#41×C5911yescharacteristic
838C23H(5,𝔽2)×C5911yescharacteristic
839C23H(5,𝔽2)×C5911yescharacteristic
840C23H(5,𝔽2)×C5911yescharacteristic
841C232−1+4×C5911yescharacteristic
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—416no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4C2×C4⋊C4×C5914yes—
938C2×C4C2×C4⋊C4×C5914yes—
939C2×C4C4×D4×C5914yes—
940C2×C4#124×C5914yes—
941C22—24no—
942C22—24no—
943C22—24no—
944C22—42no—
945C22—42no—
946C22—42no—
947C22—42no—
948C22—42no—
949C22—42no—
950C22—42no—
951C22—42no—
952C22—42no—
953C22—42no—
954C22—42no—
955C22—42no—
956C22C22×C4⋊C4×C5911yescharacteristic
957C22C2×C4×D4×C5911yescharacteristic
958C22C4×#41×C5911yescharacteristic
959C22C4×#41×C5911yescharacteristic
960C22C4×#41×C5911yescharacteristic
961C22C59×#51811yescharacteristic
962C22C59×#52011yescharacteristic
963C22C59×#52511yescharacteristic
964C22C59×#52511yescharacteristic
965C22C2×#124×C5911yescharacteristic
966C22C59×#52911yescharacteristic
967C22C59×#52911yescharacteristic
968C22C59×#53211yescharacteristic
969C22C59×#53311yescharacteristic
970C22C59×#53311yescharacteristic
971C22C59×#53811yescharacteristic
972C22C59×#53911yescharacteristic
973C22C59×#54011yescharacteristic
974C22C59×#54211yescharacteristic
975C22D42×C5911yescharacteristic
976C22C59×#54611yescharacteristic
977C22C59×#54611yescharacteristic
978C22C59×#54611yescharacteristic
979C22C59×#54611yescharacteristic
980C22C59×#54711yescharacteristic
981C22D4×Q8×C5911yescharacteristic
982C22C59×#55111yescharacteristic
983C22C59×#55211yescharacteristic
984C22C59×#55311yescharacteristic
985C22C59×#55311yescharacteristic
986C22C59×#55311yescharacteristic
987C22C59×#55411yescharacteristic
988C22C59×#55411yescharacteristic
989C22C59×#55411yescharacteristic
990C22C59×#55611yescharacteristic
991C4—24no—
992C4—24no—
993C4—24no—
994C4—24no—
995C4—42no—
996C4—42no—
997C4—42no—
998C4—42no—
999C4—42no—
1000C4—42no—
1001C4—42no—
1002C4—42no—
1003C4—81no—
1004C4—81no—
1005C2—44no—
1006C2C59×#229611yescharacteristic
1007C2C4×#124×C5911yescharacteristic
1008C2C59×#233511yescharacteristic
1009C2D4×C4⋊C4×C5911yescharacteristic
1010C2C59×#234911yescharacteristic
1011C2C59×#236411yescharacteristic
1012C2C59×#237311yescharacteristic
1013C2C59×#246411yescharacteristic
1014C2C59×#246611yescharacteristic
1015C2C59×#247011yescharacteristic
1016C2C59×#247211yescharacteristic
1017C2C59×#249211yescharacteristic
1018C2C59×#252211yescharacteristic
1019C2C59×#255611yescharacteristic
1020C2C59×#258711yescharacteristic
subgroupG/H
center, socleC24×C59C24
commutatorC23C23×C4×C59
Frattini, cosocleC24C24×C59
prime radicalC25×C59C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C59 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C59×#389C2semidirect
6. C59×#1442C2semidirect
7. C59×#1441C2semidirect
10. C59×#1436C2semidirect
11. C59×#1436C2semidirect
12. C59×#1436C2semidirect
13. C59×C4⋊#95C2semidirect
15. C4×#95×C59C2semidirect
35. C59×#388C4semidirect
95. C2×C4⋊C4×C59C2×C4semidirect
125. C2×C42×C59C2×C4semidirect
141. #95×C59C2×C4semidirect
142. #95×C59C2×C4semidirect
276. C22⋊C4×C59C4⋊C4semidirect
430. #14116C59direct (N × H)
495. C2×#389C2×C59semidirect
500. #1442C2×C59semidirect
501. #1441C2×C59semidirect
504. #1436C2×C59semidirect
505. #1436C2×C59semidirect
506. #1436C2×C59semidirect
507. C4⋊#95C2×C59semidirect
509. C4×#95C2×C59semidirect
545. #388C4×C59semidirect
566. C59#14116direct (N × H)
606. C2×C4⋊C4C2×C4×C59semidirect
636. C2×C42C2×C4×C59semidirect
652. #95C2×C4×C59semidirect
653. #95C2×C4×C59semidirect
787. C22⋊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×C59×#3882
C2×C59×#3852
C2×C4×C22⋊C4×C592
C59×#14422
C59×#14412
C59×#14392
C59×#14362
C59×C4⋊#952
C59×C22⋊#952
C4×#95×C592
#1411659