Finite Group Databasebeta

← C59×#14114 #28426223

Subgroups — C59×#14114 #28426223

Order 15104.

1630 conjugacy classes of subgroups.

The subgroup lattice has 1006 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C59×#388C211yesmaximal, characteristic
2C2×C59×#388C211yesmaximal, characteristic
3C2×C4×C22⋊C4×C59C211yesmaximal, characteristic
4C59×#1442C211yesmaximal, characteristic, complemented
5C59×#1441C211yesmaximal, characteristic, complemented
6C59×#1439C211yesmaximal, characteristic
7C59×#1439C211yesmaximal, characteristic
8C59×#1436C211yesmaximal, characteristic, complemented
9C59×#1436C211yesmaximal, characteristic, complemented
10C59×#1436C211yesmaximal, characteristic, complemented
11C59×C4⋊#95C211yesmaximal, characteristic, complemented
12C59×#1434C211yesmaximal, characteristic, complemented
13C59×C22⋊#95C211yesmaximal, characteristic
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×C22⋊C4×C59C2211yescharacteristic
22C22×C22⋊C4×C59C2211yescharacteristic
23C22×C22⋊C4×C59C2211yescharacteristic
24C22×C22⋊C4×C59C2211yescharacteristic
25C22×C22⋊C4×C59C2211yescharacteristic
26C22×C22⋊C4×C59C2211yescharacteristic
27C22×C42×C59C2211yescharacteristic
28C22×C42×C59C2211yescharacteristic
29C22×C42×C59C2211yescharacteristic
30C22×C42×C59C2211yescharacteristic
31C59×#388—24no—
32C59×#388C418yescomplemented
33C4×C22⋊C4×C59—24no—
34C2×#95×C59C2211yescharacteristic
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
53C2×#95×C59C2211yescharacteristic
54C25×C59C2311yescharacteristic
55C23×C4×C59—22no—
56C23×C4×C59—22no—
57C23×C4×C59—22no—
58C23×C4×C59—22no—
59C23×C4×C59—22no—
60C23×C4×C59—41no—
61C23×C4×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
75C23×C4×C59C2311yescharacteristic
76C2×C4⋊C4×C59—22no—
77C2×C4⋊C4×C59—22no—
78C2×C4⋊C4×C59—22no—
79C2×C4⋊C4×C59—22no—
80C2×C4⋊C4×C59—22no—
81C2×C4⋊C4×C59—41no—
82C2×C4⋊C4×C59—41no—
83C2×C4⋊C4×C59—41no—
84C2×C4⋊C4×C59—41no—
85C2×C4⋊C4×C59—41no—
86C2×C4⋊C4×C59—41no—
87C2×C4⋊C4×C59C2×C414yescomplemented
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—41no—
96C2×C22⋊C4×C59—41no—
97C2×C22⋊C4×C59—41no—
98C2×C22⋊C4×C59—41no—
99C2×C22⋊C4×C59—41no—
100C2×C22⋊C4×C59—41no—
101C2×C22⋊C4×C59C2×C414yes—
102C2×C22⋊C4×C59C2×C414yes—
103C2×C22⋊C4×C59C2×C414yes—
104C2×C22⋊C4×C59D414yes—
105C2×C22⋊C4×C59Q814yes—
106C2×C42×C59—22no—
107C2×C42×C59—22no—
108C2×C42×C59—22no—
109C2×C42×C59—22no—
110C2×C42×C59—22no—
111C2×C42×C59—22no—
112C2×C42×C59—41no—
113C2×C42×C59—41no—
114C2×C42×C59—41no—
115C2×C42×C59—41no—
116C2×C42×C59—41no—
117C2×C42×C59C2×C414yescomplemented
118#95×C59—22no—
119#95×C59—22no—
120#95×C59—22no—
121#95×C59—22no—
122#95×C59—22no—
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—22no—
130#95×C59—22no—
131#95×C59—41no—
132#95×C59—41no—
133#95×C59—41no—
134#95×C59—41no—
135#95×C59—41no—
136#95×C59C2×C414yescomplemented
137#95×C59C2×C414yescomplemented
138C24×C59—21no—
139C24×C59—21no—
140C24×C59—21no—
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×C59C22×C412yes—
151C24×C59C2×D412yes—
152C24×C59C2×Q812yes—
153C24×C59C2411yescharacteristic
154C22×C4×C59—21no—
155C22×C4×C59—21no—
156C22×C4×C59—21no—
157C22×C4×C59—21no—
158C22×C4×C59—21no—
159C22×C4×C59—21no—
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—28no—
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—21no—
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—44no—
236C22×C4×C59—44no—
237C22×C4×C59—44no—
238C22×C4×C59—44no—
239C22×C4×C59—44no—
240C22×C4×C59—44no—
241C22×C4×C59C22×C412yes—
242C22×C4×C59C22×C412yes—
243C22×C4×C59C22×C412yes—
244C22×C4×C59C22×C412yes—
245C22×C4×C59C22×C412yes—
246C22×C4×C59C22×C412yes—
247C22×C4×C59C2×D412yes—
248C22×C4×C59C2×D412yes—
249C22×C4×C59C2×Q812yes—
250C22×C4×C59C2×Q812yes—
251C22×C4×C59#4112yes—
252C22×C4×C59#4112yes—
253C22×C4×C59#4112yes—
254C22×C4×C59#4112yes—
255C22×C4×C59#4112yes—
256C22×C4×C59#4112yes—
257C22×C4×C59#4112yes—
258C22×C4×C59#4112yes—
259C4⋊C4×C59—44no—
260C4⋊C4×C59—44no—
261C4⋊C4×C59—44no—
262C4⋊C4×C59—44no—
263C22⋊C4×C59—28no—
264C22⋊C4×C59—44no—
265C22⋊C4×C59—44no—
266C22⋊C4×C59—44no—
267C22⋊C4×C59—44no—
268C22⋊C4×C59C4⋊C4116yescomplemented
269C42×C59—44no—
270C42×C59—44no—
271C42×C59—44no—
272C42×C59—44no—
273C23×C59—22no—
274C23×C59—22no—
275C23×C59—22no—
276C23×C59—22no—
277C23×C59—22no—
278C23×C59—22no—
279C23×C59—22no—
280C23×C59—22no—
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—41no—
292C23×C59—41no—
293C23×C59—41no—
294C23×C59—41no—
295C23×C59—41no—
296C23×C59—41no—
297C23×C59—41no—
298C23×C59—41no—
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×C59C2×C4⋊C414yes—
308C23×C59C23×C411yescharacteristic
309C23×C59C22×D411yescharacteristic
310C23×C59C22×Q811yescharacteristic
311C23×C59C2×#4111yescharacteristic
312C23×C59C2×#4111yescharacteristic
313C23×C59C2×#4111yescharacteristic
314C23×C59C2×#4111yescharacteristic
315C23×C59C2×#4111yescharacteristic
316C23×C59C2×#4111yescharacteristic
317C23×C59C2×#4111yescharacteristic
318C23×C59C2×#4111yescharacteristic
319C23×C59H(5,𝔽2)11yescharacteristic
320C23×C59H(5,𝔽2)11yescharacteristic
321C23×C59H(5,𝔽2)11yescharacteristic
322C23×C59H(5,𝔽2)11yescharacteristic
323C2×C4×C59—22no—
324C2×C4×C59—22no—
325C2×C4×C59—22no—
326C2×C4×C59—22no—
327C2×C4×C59—22no—
328C2×C4×C59—22no—
329C2×C4×C59—22no—
330C2×C4×C59—22no—
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—416no—
369C2×C4×C59—41no—
370C2×C4×C59—41no—
371C2×C4×C59—41no—
372C2×C4×C59—41no—
373C2×C4×C59—41no—
374C2×C4×C59—41no—
375C2×C4×C59—41no—
376C2×C4×C59—41no—
377C2×C4×C59—41no—
378C2×C4×C59—41no—
379C2×C4×C59—41no—
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×C59C2×C4⋊C414yes—
420C2×C4×C59C2×C4⋊C414yes—
421C2×C4×C59#12614yes—
422#14114C5911yesmaximal, characteristic, direct product factor, Sylow
423C22×C59—24no—
424C22×C59—24no—
425C22×C59—24no—
426C22×C59—42no—
427C22×C59—42no—
428C22×C59—42no—
429C22×C59—42no—
430C22×C59—42no—
431C22×C59—42no—
432C22×C59—42no—
433C22×C59—42no—
434C22×C59—42no—
435C22×C59—42no—
436C22×C59—42no—
437C22×C59—42no—
438C22×C59C22×C4⋊C411yescharacteristic
439C22×C59C4×#4111yescharacteristic
440C22×C59C4×#4111yescharacteristic
441C22×C59C4×#4111yescharacteristic
442C22×C59C4×#4111yescharacteristic
443C22×C59#51811yescharacteristic
444C22×C59#51811yescharacteristic
445C22×C59#52511yescharacteristic
446C22×C59#52511yescharacteristic
447C22×C59C2×#12611yescharacteristic
448C22×C59#52911yescharacteristic
449C22×C59#52911yescharacteristic
450C22×C59#52911yescharacteristic
451C22×C59#53311yescharacteristic
452C22×C59#53311yescharacteristic
453C22×C59#53811yescharacteristic
454C22×C59#53811yescharacteristic
455C22×C59#54011yescharacteristic
456C22×C59#54011yescharacteristic
457C22×C59#54611yescharacteristic
458C22×C59#54611yescharacteristic
459C22×C59#54611yescharacteristic
460C22×C59#54611yescharacteristic
461C22×C59#55111yescharacteristic
462C22×C59#55111yescharacteristic
463C22×C59#55111yescharacteristic
464C22×C59#55311yescharacteristic
465C22×C59#55311yescharacteristic
466C22×C59#55411yescharacteristic
467C22×C59#55411yescharacteristic
468C22×C59#55411yescharacteristic
469C22×C59#55411yescharacteristic
470C22×C59#55511yescharacteristic
471C22×C59#55511yescharacteristic
472C22×C59#55911yescharacteristic
473C4×C59—24no—
474C4×C59—24no—
475C4×C59—24no—
476C4×C59—42no—
477C4×C59—42no—
478C4×C59—42no—
479C4×C59—42no—
480C4×C59—42no—
481C4×C59—42no—
482C4×C59—42no—
483C4×C59—42no—
484C4×C59—42no—
485C4×C59—81no—
486C4×C59—81no—
487C2×#388C2×C5911yescharacteristic
488C2×#388C2×C5911yescharacteristic
489C2×C4×C22⋊C4C2×C5911yescharacteristic
490#1442C2×C5911yescharacteristic, complemented
491#1441C2×C5911yescharacteristic, complemented
492#1439C2×C5911yescharacteristic
493#1439C2×C5911yescharacteristic
494#1436C2×C5911yescharacteristic, complemented
495#1436C2×C5911yescharacteristic, complemented
496#1436C2×C5911yescharacteristic, complemented
497C4⋊#95C2×C5911yescharacteristic, complemented
498#1434C2×C5911yescharacteristic, complemented
499C22⋊#95C2×C5911yescharacteristic
500C22⋊#95C2×C5911yescharacteristic
501C4×#95C2×C5911yescharacteristic, complemented
502C2×C59—44no—
503C2×C59#229611yescharacteristic
504C2×C59C4×#12611yescharacteristic
505C2×C59#233311yescharacteristic
506C2×C59#234911yescharacteristic
507C2×C59#234911yescharacteristic
508C2×C59#237211yescharacteristic
509C2×C59#237411yescharacteristic
510C2×C59#245711yescharacteristic
511C2×C59#245911yescharacteristic
512C2×C59#247611yescharacteristic
513C2×C59#248011yescharacteristic
514C2×C59#249711yescharacteristic
515C2×C59#252211yescharacteristic
516C2×C59#257411yescharacteristic
517C2×C59#258911yescharacteristic
518C24×C4C22×C5911yescharacteristic
519C22×C4⋊C4C22×C5911yescharacteristic
520C22×C4⋊C4C22×C5911yescharacteristic
521C22×C4⋊C4C22×C5911yescharacteristic
522C22×C4⋊C4C22×C5911yescharacteristic
523C22×C22⋊C4C22×C5911yescharacteristic
524C22×C22⋊C4C22×C5911yescharacteristic
525C22×C22⋊C4C22×C5911yescharacteristic
526C22×C22⋊C4C22×C5911yescharacteristic
527C22×C22⋊C4C22×C5911yescharacteristic
528C22×C22⋊C4C22×C5911yescharacteristic
529C22×C42C22×C5911yescharacteristic
530C22×C42C22×C5911yescharacteristic
531C22×C42C22×C5911yescharacteristic
532C22×C42C22×C5911yescharacteristic
533#388—24no—
534#388C4×C5918yescomplemented
535C4×C22⋊C4—24no—
536C2×#95C22×C5911yescharacteristic
537C2×#95C22×C5911yescharacteristic
538C2×#95C22×C5911yescharacteristic
539C2×#95C22×C5911yescharacteristic
540C2×#95C22×C5911yescharacteristic
541C2×#95C22×C5911yescharacteristic
542C2×#95C22×C5911yescharacteristic
543C2×#95C22×C5911yescharacteristic
544C2×#95C22×C5911yescharacteristic
545C2×#95C22×C5911yescharacteristic
546C2×#95C22×C5911yescharacteristic
547C2×#95C22×C5911yescharacteristic
548C2×#95C22×C5911yescharacteristic
549C2×#95C22×C5911yescharacteristic
550C2×#95C22×C5911yescharacteristic
551C2×#95C22×C5911yescharacteristic
552C2×#95C22×C5911yescharacteristic
553C2×#95C22×C5911yescharacteristic
554C2×#95C22×C5911yescharacteristic
555C2×#95C22×C5911yescharacteristic
556C59#1411411yescharacteristic, direct product factor, Sylow
557C25C23×C5911yescharacteristic
558C23×C4—22no—
559C23×C4—22no—
560C23×C4—22no—
561C23×C4—22no—
562C23×C4—22no—
563C23×C4—41no—
564C23×C4—41no—
565C23×C4C23×C5911yescharacteristic
566C23×C4C23×C5911yescharacteristic
567C23×C4C23×C5911yescharacteristic
568C23×C4C23×C5911yescharacteristic
569C23×C4C23×C5911yescharacteristic
570C23×C4C23×C5911yescharacteristic
571C23×C4C23×C5911yescharacteristic
572C23×C4C23×C5911yescharacteristic
573C23×C4C23×C5911yescharacteristic
574C23×C4C23×C5911yescharacteristic
575C23×C4C23×C5911yescharacteristic
576C23×C4C23×C5911yescharacteristic
577C23×C4C23×C5911yescharacteristic
578C23×C4C23×C5911yescharacteristic
579C2×C4⋊C4—22no—
580C2×C4⋊C4—22no—
581C2×C4⋊C4—22no—
582C2×C4⋊C4—22no—
583C2×C4⋊C4—22no—
584C2×C4⋊C4—41no—
585C2×C4⋊C4—41no—
586C2×C4⋊C4—41no—
587C2×C4⋊C4—41no—
588C2×C4⋊C4—41no—
589C2×C4⋊C4—41no—
590C2×C4⋊C4C2×C4×C5914yescomplemented
591C2×C22⋊C4—22no—
592C2×C22⋊C4—22no—
593C2×C22⋊C4—22no—
594C2×C22⋊C4—22no—
595C2×C22⋊C4—22no—
596C2×C22⋊C4—22no—
597C2×C22⋊C4—22no—
598C2×C22⋊C4—41no—
599C2×C22⋊C4—41no—
600C2×C22⋊C4—41no—
601C2×C22⋊C4—41no—
602C2×C22⋊C4—41no—
603C2×C22⋊C4—41no—
604C2×C22⋊C4C2×C4×C5914yes—
605C2×C22⋊C4C2×C4×C5914yes—
606C2×C22⋊C4C2×C4×C5914yes—
607C2×C22⋊C4D4×C5914yes—
608C2×C22⋊C4Q8×C5914yes—
609C2×C42—22no—
610C2×C42—22no—
611C2×C42—22no—
612C2×C42—22no—
613C2×C42—22no—
614C2×C42—22no—
615C2×C42—41no—
616C2×C42—41no—
617C2×C42—41no—
618C2×C42—41no—
619C2×C42—41no—
620C2×C42C2×C4×C5914yescomplemented
621#95—22no—
622#95—22no—
623#95—22no—
624#95—22no—
625#95—22no—
626#95—22no—
627#95—22no—
628#95—22no—
629#95—22no—
630#95—22no—
631#95—22no—
632#95—22no—
633#95—22no—
634#95—41no—
635#95—41no—
636#95—41no—
637#95—41no—
638#95—41no—
639#95C2×C4×C5914yescomplemented
640#95C2×C4×C5914yescomplemented
641C24—21no—
642C24—21no—
643C24—21no—
644C24—21no—
645C24—21no—
646C24—21no—
647C24—21no—
648C24—21no—
649C24—21no—
650C24—21no—
651C24—21no—
652C24—21no—
653C24C22×C4×C5912yes—
654C24C2×D4×C5912yes—
655C24C2×Q8×C5912yes—
656C24C24×C5911yescharacteristic
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—28no—
670C22×C4—21no—
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—21no—
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—44no—
739C22×C4—44no—
740C22×C4—44no—
741C22×C4—44no—
742C22×C4—44no—
743C22×C4—44no—
744C22×C4C22×C4×C5912yes—
745C22×C4C22×C4×C5912yes—
746C22×C4C22×C4×C5912yes—
747C22×C4C22×C4×C5912yes—
748C22×C4C22×C4×C5912yes—
749C22×C4C22×C4×C5912yes—
750C22×C4C2×D4×C5912yes—
751C22×C4C2×D4×C5912yes—
752C22×C4C2×Q8×C5912yes—
753C22×C4C2×Q8×C5912yes—
754C22×C4#41×C5912yes—
755C22×C4#41×C5912yes—
756C22×C4#41×C5912yes—
757C22×C4#41×C5912yes—
758C22×C4#41×C5912yes—
759C22×C4#41×C5912yes—
760C22×C4#41×C5912yes—
761C22×C4#41×C5912yes—
762C4⋊C4—44no—
763C4⋊C4—44no—
764C4⋊C4—44no—
765C4⋊C4—44no—
766C22⋊C4—28no—
767C22⋊C4—44no—
768C22⋊C4—44no—
769C22⋊C4—44no—
770C22⋊C4—44no—
771C22⋊C4C4⋊C4×C59116yescomplemented
772C42—44no—
773C42—44no—
774C42—44no—
775C42—44no—
776C23—22no—
777C23—22no—
778C23—22no—
779C23—22no—
780C23—22no—
781C23—22no—
782C23—22no—
783C23—22no—
784C23—22no—
785C23—22no—
786C23—22no—
787C23—22no—
788C23—22no—
789C23—22no—
790C23—22no—
791C23—22no—
792C23—22no—
793C23—22no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23C2×C4⋊C4×C5914yes—
811C23C23×C4×C5911yescharacteristic
812C23C22×D4×C5911yescharacteristic
813C23C22×Q8×C5911yescharacteristic
814C23C2×#41×C5911yescharacteristic
815C23C2×#41×C5911yescharacteristic
816C23C2×#41×C5911yescharacteristic
817C23C2×#41×C5911yescharacteristic
818C23C2×#41×C5911yescharacteristic
819C23C2×#41×C5911yescharacteristic
820C23C2×#41×C5911yescharacteristic
821C23C2×#41×C5911yescharacteristic
822C23H(5,𝔽2)×C5911yescharacteristic
823C23H(5,𝔽2)×C5911yescharacteristic
824C23H(5,𝔽2)×C5911yescharacteristic
825C23H(5,𝔽2)×C5911yescharacteristic
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
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—416no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
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×C4C2×C4⋊C4×C5914yes—
923C2×C4C2×C4⋊C4×C5914yes—
924C2×C4#126×C5914yes—
925C22—24no—
926C22—24no—
927C22—24no—
928C22—42no—
929C22—42no—
930C22—42no—
931C22—42no—
932C22—42no—
933C22—42no—
934C22—42no—
935C22—42no—
936C22—42no—
937C22—42no—
938C22—42no—
939C22—42no—
940C22C22×C4⋊C4×C5911yescharacteristic
941C22C4×#41×C5911yescharacteristic
942C22C4×#41×C5911yescharacteristic
943C22C4×#41×C5911yescharacteristic
944C22C4×#41×C5911yescharacteristic
945C22C59×#51811yescharacteristic
946C22C59×#51811yescharacteristic
947C22C59×#52511yescharacteristic
948C22C59×#52511yescharacteristic
949C22C2×#126×C5911yescharacteristic
950C22C59×#52911yescharacteristic
951C22C59×#52911yescharacteristic
952C22C59×#52911yescharacteristic
953C22C59×#53311yescharacteristic
954C22C59×#53311yescharacteristic
955C22C59×#53811yescharacteristic
956C22C59×#53811yescharacteristic
957C22C59×#54011yescharacteristic
958C22C59×#54011yescharacteristic
959C22C59×#54611yescharacteristic
960C22C59×#54611yescharacteristic
961C22C59×#54611yescharacteristic
962C22C59×#54611yescharacteristic
963C22C59×#55111yescharacteristic
964C22C59×#55111yescharacteristic
965C22C59×#55111yescharacteristic
966C22C59×#55311yescharacteristic
967C22C59×#55311yescharacteristic
968C22C59×#55411yescharacteristic
969C22C59×#55411yescharacteristic
970C22C59×#55411yescharacteristic
971C22C59×#55411yescharacteristic
972C22C59×#55511yescharacteristic
973C22C59×#55511yescharacteristic
974C22C59×#55911yescharacteristic
975C4—24no—
976C4—24no—
977C4—24no—
978C4—42no—
979C4—42no—
980C4—42no—
981C4—42no—
982C4—42no—
983C4—42no—
984C4—42no—
985C4—42no—
986C4—42no—
987C4—81no—
988C4—81no—
989C2—44no—
990C2C59×#229611yescharacteristic
991C2C4×#126×C5911yescharacteristic
992C2C59×#233311yescharacteristic
993C2C59×#234911yescharacteristic
994C2C59×#234911yescharacteristic
995C2C59×#237211yescharacteristic
996C2C59×#237411yescharacteristic
997C2C59×#245711yescharacteristic
998C2C59×#245911yescharacteristic
999C2C59×#247611yescharacteristic
1000C2C59×#248011yescharacteristic
1001C2C59×#249711yescharacteristic
1002C2C59×#252211yescharacteristic
1003C2C59×#257411yescharacteristic
1004C2C59×#258911yescharacteristic
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
4. C59×#1442C2semidirect
5. C59×#1441C2semidirect
8. C59×#1436C2semidirect
9. C59×#1436C2semidirect
10. C59×#1436C2semidirect
11. C59×C4⋊#95C2semidirect
12. C59×#1434C2semidirect
15. C4×#95×C59C2semidirect
32. C59×#388C4semidirect
87. C2×C4⋊C4×C59C2×C4semidirect
117. C2×C42×C59C2×C4semidirect
136. #95×C59C2×C4semidirect
137. #95×C59C2×C4semidirect
268. C22⋊C4×C59C4⋊C4semidirect
422. #14114C59direct (N × H)
490. #1442C2×C59semidirect
491. #1441C2×C59semidirect
494. #1436C2×C59semidirect
495. #1436C2×C59semidirect
496. #1436C2×C59semidirect
497. C4⋊#95C2×C59semidirect
498. #1434C2×C59semidirect
501. C4×#95C2×C59semidirect
534. #388C4×C59semidirect
556. C59#14114direct (N × H)
590. C2×C4⋊C4C2×C4×C59semidirect
620. C2×C42C2×C4×C59semidirect
639. #95C2×C4×C59semidirect
640. #95C2×C4×C59semidirect
771. 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×#3882
C2×C4×C22⋊C4×C592
C59×#14422
C59×#14412
C59×#14392
C59×#14362
C59×C4⋊#952
C59×#14342
C59×C22⋊#952
C4×#95×C592
#1411459