Finite Group Databasebeta

← C59×#22005 #28434114

Subgroups — C59×#22005 #28434114

Order 15104.

752 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C59×#2293C211yesmaximal, characteristic
2C59×#1924C211yesmaximal, characteristic, complemented
3C59×#1923C211yesmaximal, characteristic, complemented
4C59×#1917C211yesmaximal, characteristic, complemented
5C59×#1916C211yesmaximal, characteristic, complemented
6C59×#1870C211yesmaximal, characteristic
7C59×#1869C211yesmaximal, characteristic
8C59×#1851C211yesmaximal, characteristic, complemented
9C59×#1850C211yesmaximal, characteristic, complemented
10C59×#1839C211yesmaximal, characteristic, complemented
11C59×#1831C211yesmaximal, characteristic, complemented
12C59×#1818C211yesmaximal, characteristic, complemented
13C59×#1798C211yesmaximal, characteristic, complemented
14C59×#1750C211yesmaximal, characteristic, complemented
15C59×#1729C211yesmaximal, characteristic, complemented
16C22×M16×C59C2211yescharacteristic
17C23×C8×C59C2211yescharacteristic
18C2×C4×D4×C59C2211yescharacteristic
19C2×#117×C59C2211yescharacteristic
20C2×#117×C59C2211yescharacteristic
21C2×C4⋊C8×C59C2211yescharacteristic
22C2×C4⋊C8×C59C2211yescharacteristic
23C2×C4⋊C8×C59C2211yescharacteristic
24C2×C4⋊C8×C59C2211yescharacteristic
25C2×C22⋊C8×C59C2211yescharacteristic
26C2×C22⋊C8×C59C2211yescharacteristic
27C2×C22⋊C8×C59C2211yescharacteristic
28C2×C22⋊C8×C59C2211yescharacteristic
29C2×C22⋊C8×C59C2211yescharacteristic
30C2×C22⋊C8×C59C2211yescharacteristic
31C2×#97×C59C2211yescharacteristic
32C2×C4×C8×C59C2211yescharacteristic
33C59×#390C411yescharacteristic
34C59×#390C411yescharacteristic
35C59×#389C411yescharacteristic
36C59×#389C411yescharacteristic
37C59×#388C411yescharacteristic
38C59×#388C411yescharacteristic
39C59×#388C411yescharacteristic
40C59×#388C411yescharacteristic
41C4×C4⋊C4×C59C2211yescharacteristic
42C4×C22⋊C4×C59C2211yescharacteristic
43C4×C22⋊C4×C59C2211yescharacteristic
44C43×C59C2211yescharacteristic
45C59×#336C2211yescharacteristic
46C59×#336C2211yescharacteristic
47C59×#336C2211yescharacteristic
48C59×#336C2211yescharacteristic
49C59×#336C2211yescharacteristic
50C59×#336C2211yescharacteristic
51C59×#336C2211yescharacteristic
52C59×#336C2211yescharacteristic
53C59×#336C2211yescharacteristic
54C59×#336C2211yescharacteristic
55C59×#336C2211yescharacteristic
56C59×#336C2211yescharacteristic
57C59×#336C2211yescharacteristic
58C59×#336C2211yescharacteristic
59C22×D4×C59C2×C411yescharacteristic
60C23×C4×C59C2311yescharacteristic
61C23×C4×C59C2311yescharacteristic
62C2×M16×C59—22no—
63C2×M16×C59—41no—
64C2×M16×C59—41no—
65C22×C8×C59—22no—
66C22×C8×C59—41no—
67C22×C8×C59—41no—
68C22×C8×C59C2311yescharacteristic
69C22×C8×C59C2311yescharacteristic
70C22×C8×C59C2311yescharacteristic
71C22×C8×C59C2311yescharacteristic
72C22×C8×C59C2311yescharacteristic
73C22×C8×C59C2311yescharacteristic
74C22×C8×C59C2311yescharacteristic
75C22×C8×C59C2311yescharacteristic
76C4×D4×C59—22no—
77C4×D4×C59—22no—
78#117×C59—41no—
79#117×C59—41no—
80#117×C59—41no—
81#117×C59—41no—
82C2×C4⋊C4×C59C2×C411yescharacteristic
83C2×C4⋊C4×C59C2×C411yescharacteristic
84C2×C4⋊C4×C59C2×C411yescharacteristic
85C2×C4⋊C4×C59C2×C411yescharacteristic
86C2×C4⋊C4×C59C2×C411yescharacteristic
87C2×C4⋊C4×C59C2×C411yescharacteristic
88C2×C4⋊C4×C59C2×C411yescharacteristic
89C2×C22⋊C4×C59C2×C411yescharacteristic
90C2×C22⋊C4×C59C2×C411yescharacteristic
91C2×C22⋊C4×C59C2×C411yescharacteristic
92C2×C22⋊C4×C59C2×C411yescharacteristic
93C2×C22⋊C4×C59C2×C411yescharacteristic
94C2×C22⋊C4×C59C2×C411yescharacteristic
95C2×C22⋊C4×C59C2×C411yescharacteristic
96C2×C22⋊C4×C59C2×C411yescharacteristic
97C2×C22⋊C4×C59C2×C411yescharacteristic
98C2×C22⋊C4×C59C2×C411yescharacteristic
99C2×C42×C59C2×C411yescharacteristic
100C2×C42×C59C2×C411yescharacteristic
101C2×C42×C59C2×C411yescharacteristic
102C2×C42×C59C2×C411yescharacteristic
103C2×C42×C59C2311yescharacteristic
104C2×C42×C59C2311yescharacteristic
105C2×C42×C59C2311yescharacteristic
106C2×C42×C59C2311yescharacteristic
107C2×C42×C59C2311yescharacteristic
108C4⋊C8×C59—41no—
109C4⋊C8×C59—41no—
110C4⋊C8×C59—41no—
111C4⋊C8×C59—41no—
112C22⋊C8×C59—22no—
113C22⋊C8×C59—22no—
114C22⋊C8×C59—41no—
115C22⋊C8×C59—41no—
116C22⋊C8×C59—41no—
117C22⋊C8×C59—41no—
118#97×C59—41no—
119C4×C8×C59—41no—
120#95×C59C2×C411yescharacteristic
121#95×C59C2×C411yescharacteristic
122#95×C59C2×C411yescharacteristic
123#95×C59C2×C411yescharacteristic
124#95×C59C2×C411yescharacteristic
125#95×C59C2×C411yescharacteristic
126C24×C59C22×C411yescharacteristic
127C24×C59C22×C411yescharacteristic
128C2×D4×C59—22no—
129C2×D4×C59—22no—
130C2×D4×C59—41no—
131C22×C4×C59—21no—
132C22×C4×C59—21no—
133C22×C4×C59—21no—
134C22×C4×C59—21no—
135C22×C4×C59—21no—
136C22×C4×C59—21no—
137C22×C4×C59—21no—
138C22×C4×C59—21no—
139C22×C4×C59—21no—
140C22×C4×C59—21no—
141C22×C4×C59C22×C411yescharacteristic
142C22×C4×C59C22×C411yescharacteristic
143C22×C4×C59C22×C411yescharacteristic
144C22×C4×C59C22×C411yescharacteristic
145C22×C4×C59C22×C411yescharacteristic
146C22×C4×C59C22×C411yescharacteristic
147C22×C4×C59C22×C411yescharacteristic
148C22×C4×C59C22×C411yescharacteristic
149C22×C4×C59C22×C411yescharacteristic
150C22×C4×C59C22×C411yescharacteristic
151C22×C4×C59C22×C411yescharacteristic
152C22×C4×C59C22×C411yescharacteristic
153C22×C4×C59#4112yes—
154C22×C4×C59#4112yes—
155C22×C4×C59C2411yescharacteristic
156M16×C59—44no—
157C2×C8×C59—21no—
158C2×C8×C59—21no—
159C2×C8×C59—21no—
160C2×C8×C59—21no—
161C2×C8×C59—21no—
162C2×C8×C59—21no—
163C2×C8×C59—21no—
164C2×C8×C59—21no—
165C2×C8×C59—21no—
166C2×C8×C59—21no—
167C2×C8×C59—21no—
168C2×C8×C59—21no—
169C2×C8×C59—21no—
170C2×C8×C59—21no—
171C2×C8×C59—21no—
172C2×C8×C59—21no—
173C2×C8×C59—21no—
174C2×C8×C59—21no—
175C2×C8×C59—21no—
176C2×C8×C59—21no—
177C2×C8×C59—21no—
178C2×C8×C59—21no—
179C2×C8×C59—21no—
180C2×C8×C59—21no—
181C2×C8×C59—44no—
182C4⋊C4×C59—22no—
183C4⋊C4×C59—22no—
184C4⋊C4×C59—41no—
185C4⋊C4×C59—41no—
186C4⋊C4×C59—41no—
187C4⋊C4×C59—41no—
188C4⋊C4×C59—41no—
189C22⋊C4×C59—22no—
190C22⋊C4×C59—22no—
191C22⋊C4×C59—22no—
192C22⋊C4×C59—22no—
193C22⋊C4×C59—41no—
194C22⋊C4×C59—41no—
195C22⋊C4×C59—41no—
196C22⋊C4×C59—41no—
197C22⋊C4×C59—41no—
198C22⋊C4×C59—41no—
199C42×C59—22no—
200C42×C59—22no—
201C42×C59—21no—
202C42×C59—21no—
203C42×C59—21no—
204C42×C59—21no—
205C42×C59—21no—
206C42×C59—21no—
207C42×C59—21no—
208C42×C59—21no—
209C42×C59—21no—
210C42×C59—21no—
211C42×C59—41no—
212C42×C59—41no—
213C23×C59—21no—
214C23×C59—21no—
215C23×C59—21no—
216C23×C59—21no—
217C23×C59—21no—
218C23×C59—21no—
219C23×C59—21no—
220C23×C59—21no—
221C23×C59—21no—
222C23×C59—21no—
223C23×C59—21no—
224C23×C59—21no—
225C23×C59—21no—
226C23×C59#11712yes—
227C23×C59C23×C411yescharacteristic
228D4×C59—44no—
229C2×C4×C59—21no—
230C2×C4×C59—21no—
231C2×C4×C59—21no—
232C2×C4×C59—21no—
233C2×C4×C59—21no—
234C2×C4×C59—21no—
235C2×C4×C59—22no—
236C2×C4×C59—22no—
237C2×C4×C59—22no—
238C2×C4×C59—22no—
239C2×C4×C59—21no—
240C2×C4×C59—21no—
241C2×C4×C59—21no—
242C2×C4×C59—21no—
243C2×C4×C59—21no—
244C2×C4×C59—21no—
245C2×C4×C59—21no—
246C2×C4×C59—21no—
247C2×C4×C59—21no—
248C2×C4×C59—21no—
249C2×C4×C59—21no—
250C2×C4×C59—21no—
251C2×C4×C59—21no—
252C2×C4×C59—21no—
253C2×C4×C59—21no—
254C2×C4×C59—21no—
255C2×C4×C59—21no—
256C2×C4×C59—21no—
257C2×C4×C59—21no—
258C2×C4×C59—21no—
259C2×C4×C59—21no—
260C2×C4×C59—21no—
261C2×C4×C59—21no—
262C2×C4×C59—21no—
263C2×C4×C59—21no—
264C2×C4×C59—21no—
265C2×C4×C59—21no—
266C2×C4×C59—41no—
267C2×C4×C59—41no—
268C2×C4×C59—41no—
269C2×C4×C59—41no—
270C2×C4×C59#11712yes—
271C2×C4×C59#13112yes—
272C2×C4×C59#13112yes—
273C2×C4×C59C2×#4111yescharacteristic
274C2×C4×C59C2×#4111yescharacteristic
275C2×C4×C59H(5,𝔽2)11yescharacteristic
276C2×C4×C59H(5,𝔽2)11yescharacteristic
277C2×C4×C59H(5,𝔽2)11yescharacteristic
278C2×C4×C592−1+411yescharacteristic
279C8×C59—41no—
280C8×C59—41no—
281C8×C59—41no—
282C8×C59—41no—
283C8×C59—41no—
284C8×C59—41no—
285C8×C59—41no—
286C8×C59—41no—
287#22005C5911yesmaximal, characteristic, direct product factor, Sylow
288C22×C59—22no—
289C22×C59—22no—
290C22×C59—22no—
291C22×C59—41no—
292C22×C59—41no—
293C22×C59—41no—
294C22×C59—41no—
295C22×C59—41no—
296C22×C59—41no—
297C22×C59—41no—
298C22×C59—41no—
299C22×C59—41no—
300C22×C59—41no—
301C22×C59—41no—
302C22×C59C2×#11711yescharacteristic
303C22×C59#51811yescharacteristic
304C22×C59#52011yescharacteristic
305C22×C59C2×#13111yescharacteristic
306C22×C59C2×#13111yescharacteristic
307C22×C59#56811yescharacteristic
308C22×C59#56811yescharacteristic
309C4×C59—22no—
310C4×C59—22no—
311C4×C59—22no—
312C4×C59—41no—
313C4×C59—41no—
314C4×C59—41no—
315C4×C59—41no—
316C4×C59—41no—
317C4×C59—41no—
318C4×C59—41no—
319C4×C59—41no—
320C4×C59—41no—
321C4×C59#53811yescharacteristic
322C4×C59#53811yescharacteristic
323C4×C59#53911yescharacteristic
324C4×C59#53911yescharacteristic
325#2293C2×C5911yescharacteristic
326#1924C2×C5911yescharacteristic, complemented
327#1923C2×C5911yescharacteristic, complemented
328#1917C2×C5911yescharacteristic, complemented
329#1916C2×C5911yescharacteristic, complemented
330#1870C2×C5911yescharacteristic
331#1869C2×C5911yescharacteristic
332#1851C2×C5911yescharacteristic, complemented
333#1850C2×C5911yescharacteristic, complemented
334#1839C2×C5911yescharacteristic, complemented
335#1831C2×C5911yescharacteristic, complemented
336#1818C2×C5911yescharacteristic, complemented
337#1798C2×C5911yescharacteristic, complemented
338#1750C2×C5911yescharacteristic, complemented
339#1729C2×C5911yescharacteristic, complemented
340C2×C59—42no—
341C2×C59—81no—
342C2×C59#231811yescharacteristic
343C2×C59#292411yescharacteristic
344C2×C59#292511yescharacteristic
345C2×C59#297911yescharacteristic
346C2×C59#298011yescharacteristic
347C2×C59#299211yescharacteristic
348C2×C59#299311yescharacteristic
349C22×M16C22×C5911yescharacteristic
350C23×C8C22×C5911yescharacteristic
351C2×C4×D4C22×C5911yescharacteristic
352C2×#117C22×C5911yescharacteristic
353C2×#117C22×C5911yescharacteristic
354C2×C4⋊C8C22×C5911yescharacteristic
355C2×C4⋊C8C22×C5911yescharacteristic
356C2×C4⋊C8C22×C5911yescharacteristic
357C2×C4⋊C8C22×C5911yescharacteristic
358C2×C22⋊C8C22×C5911yescharacteristic
359C2×C22⋊C8C22×C5911yescharacteristic
360C2×C22⋊C8C22×C5911yescharacteristic
361C2×C22⋊C8C22×C5911yescharacteristic
362C2×C22⋊C8C22×C5911yescharacteristic
363C2×C22⋊C8C22×C5911yescharacteristic
364C2×#97C22×C5911yescharacteristic
365C2×C4×C8C22×C5911yescharacteristic
366#390C4×C5911yescharacteristic
367#390C4×C5911yescharacteristic
368#389C4×C5911yescharacteristic
369#389C4×C5911yescharacteristic
370#388C4×C5911yescharacteristic
371#388C4×C5911yescharacteristic
372#388C4×C5911yescharacteristic
373#388C4×C5911yescharacteristic
374C4×C4⋊C4C22×C5911yescharacteristic
375C4×C22⋊C4C22×C5911yescharacteristic
376C4×C22⋊C4C22×C5911yescharacteristic
377C43C22×C5911yescharacteristic
378#336C22×C5911yescharacteristic
379#336C22×C5911yescharacteristic
380#336C22×C5911yescharacteristic
381#336C22×C5911yescharacteristic
382#336C22×C5911yescharacteristic
383#336C22×C5911yescharacteristic
384#336C22×C5911yescharacteristic
385#336C22×C5911yescharacteristic
386#336C22×C5911yescharacteristic
387#336C22×C5911yescharacteristic
388#336C22×C5911yescharacteristic
389#336C22×C5911yescharacteristic
390#336C22×C5911yescharacteristic
391#336C22×C5911yescharacteristic
392C59#2200511yescharacteristic, direct product factor, Sylow
393C22×D4C2×C4×C5911yescharacteristic
394C23×C4C23×C5911yescharacteristic
395C23×C4C23×C5911yescharacteristic
396C2×M16—22no—
397C2×M16—41no—
398C2×M16—41no—
399C22×C8—22no—
400C22×C8—41no—
401C22×C8—41no—
402C22×C8C23×C5911yescharacteristic
403C22×C8C23×C5911yescharacteristic
404C22×C8C23×C5911yescharacteristic
405C22×C8C23×C5911yescharacteristic
406C22×C8C23×C5911yescharacteristic
407C22×C8C23×C5911yescharacteristic
408C22×C8C23×C5911yescharacteristic
409C22×C8C23×C5911yescharacteristic
410C4×D4—22no—
411C4×D4—22no—
412#117—41no—
413#117—41no—
414#117—41no—
415#117—41no—
416C2×C4⋊C4C2×C4×C5911yescharacteristic
417C2×C4⋊C4C2×C4×C5911yescharacteristic
418C2×C4⋊C4C2×C4×C5911yescharacteristic
419C2×C4⋊C4C2×C4×C5911yescharacteristic
420C2×C4⋊C4C2×C4×C5911yescharacteristic
421C2×C4⋊C4C2×C4×C5911yescharacteristic
422C2×C4⋊C4C2×C4×C5911yescharacteristic
423C2×C22⋊C4C2×C4×C5911yescharacteristic
424C2×C22⋊C4C2×C4×C5911yescharacteristic
425C2×C22⋊C4C2×C4×C5911yescharacteristic
426C2×C22⋊C4C2×C4×C5911yescharacteristic
427C2×C22⋊C4C2×C4×C5911yescharacteristic
428C2×C22⋊C4C2×C4×C5911yescharacteristic
429C2×C22⋊C4C2×C4×C5911yescharacteristic
430C2×C22⋊C4C2×C4×C5911yescharacteristic
431C2×C22⋊C4C2×C4×C5911yescharacteristic
432C2×C22⋊C4C2×C4×C5911yescharacteristic
433C2×C42C2×C4×C5911yescharacteristic
434C2×C42C2×C4×C5911yescharacteristic
435C2×C42C2×C4×C5911yescharacteristic
436C2×C42C2×C4×C5911yescharacteristic
437C2×C42C23×C5911yescharacteristic
438C2×C42C23×C5911yescharacteristic
439C2×C42C23×C5911yescharacteristic
440C2×C42C23×C5911yescharacteristic
441C2×C42C23×C5911yescharacteristic
442C4⋊C8—41no—
443C4⋊C8—41no—
444C4⋊C8—41no—
445C4⋊C8—41no—
446C22⋊C8—22no—
447C22⋊C8—22no—
448C22⋊C8—41no—
449C22⋊C8—41no—
450C22⋊C8—41no—
451C22⋊C8—41no—
452#97—41no—
453C4×C8—41no—
454#95C2×C4×C5911yescharacteristic
455#95C2×C4×C5911yescharacteristic
456#95C2×C4×C5911yescharacteristic
457#95C2×C4×C5911yescharacteristic
458#95C2×C4×C5911yescharacteristic
459#95C2×C4×C5911yescharacteristic
460C24C22×C4×C5911yescharacteristic
461C24C22×C4×C5911yescharacteristic
462C2×D4—22no—
463C2×D4—22no—
464C2×D4—41no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4C22×C4×C5911yescharacteristic
476C22×C4C22×C4×C5911yescharacteristic
477C22×C4C22×C4×C5911yescharacteristic
478C22×C4C22×C4×C5911yescharacteristic
479C22×C4C22×C4×C5911yescharacteristic
480C22×C4C22×C4×C5911yescharacteristic
481C22×C4C22×C4×C5911yescharacteristic
482C22×C4C22×C4×C5911yescharacteristic
483C22×C4C22×C4×C5911yescharacteristic
484C22×C4C22×C4×C5911yescharacteristic
485C22×C4C22×C4×C5911yescharacteristic
486C22×C4C22×C4×C5911yescharacteristic
487C22×C4#41×C5912yes—
488C22×C4#41×C5912yes—
489C22×C4C24×C5911yescharacteristic
490M16—44no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—44no—
516C4⋊C4—22no—
517C4⋊C4—22no—
518C4⋊C4—41no—
519C4⋊C4—41no—
520C4⋊C4—41no—
521C4⋊C4—41no—
522C4⋊C4—41no—
523C22⋊C4—22no—
524C22⋊C4—22no—
525C22⋊C4—22no—
526C22⋊C4—22no—
527C22⋊C4—41no—
528C22⋊C4—41no—
529C22⋊C4—41no—
530C22⋊C4—41no—
531C22⋊C4—41no—
532C22⋊C4—41no—
533C42—22no—
534C42—22no—
535C42—21no—
536C42—21no—
537C42—21no—
538C42—21no—
539C42—21no—
540C42—21no—
541C42—21no—
542C42—21no—
543C42—21no—
544C42—21no—
545C42—41no—
546C42—41no—
547C23—21no—
548C23—21no—
549C23—21no—
550C23—21no—
551C23—21no—
552C23—21no—
553C23—21no—
554C23—21no—
555C23—21no—
556C23—21no—
557C23—21no—
558C23—21no—
559C23—21no—
560C23#117×C5912yes—
561C23C23×C4×C5911yescharacteristic
562D4—44no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4#117×C5912yes—
605C2×C4#131×C5912yes—
606C2×C4#131×C5912yes—
607C2×C4C2×#41×C5911yescharacteristic
608C2×C4C2×#41×C5911yescharacteristic
609C2×C4H(5,𝔽2)×C5911yescharacteristic
610C2×C4H(5,𝔽2)×C5911yescharacteristic
611C2×C4H(5,𝔽2)×C5911yescharacteristic
612C2×C42−1+4×C5911yescharacteristic
613C8—41no—
614C8—41no—
615C8—41no—
616C8—41no—
617C8—41no—
618C8—41no—
619C8—41no—
620C8—41no—
621C22—22no—
622C22—22no—
623C22—22no—
624C22—41no—
625C22—41no—
626C22—41no—
627C22—41no—
628C22—41no—
629C22—41no—
630C22—41no—
631C22—41no—
632C22—41no—
633C22—41no—
634C22—41no—
635C22C2×#117×C5911yescharacteristic
636C22C59×#51811yescharacteristic
637C22C59×#52011yescharacteristic
638C22C2×#131×C5911yescharacteristic
639C22C2×#131×C5911yescharacteristic
640C22C59×#56811yescharacteristic
641C22C59×#56811yescharacteristic
642C4—22no—
643C4—22no—
644C4—22no—
645C4—41no—
646C4—41no—
647C4—41no—
648C4—41no—
649C4—41no—
650C4—41no—
651C4—41no—
652C4—41no—
653C4—41no—
654C4C59×#53811yescharacteristic
655C4C59×#53811yescharacteristic
656C4C59×#53911yescharacteristic
657C4C59×#53911yescharacteristic
658C2—42no—
659C2—81no—
660C2C59×#231811yescharacteristic
661C2C59×#292411yescharacteristic
662C2C59×#292511yescharacteristic
663C2C59×#297911yescharacteristic
664C2C59×#298011yescharacteristic
665C2C59×#299211yescharacteristic
666C2C59×#299311yescharacteristic
subgroupG/H
centerC22×C4×C59C24
commutatorC23C23×C4×C59
Frattini, cosocleC22×C4C24×C59
socleC23×C59C23×C4
prime radicalC22×D4×C59C2×C4
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C59 ◁ G

Complements

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

NH ≅ G/Ntype
2. C59×#1924C2semidirect
3. C59×#1923C2semidirect
4. C59×#1917C2semidirect
5. C59×#1916C2semidirect
8. C59×#1851C2semidirect
9. C59×#1850C2semidirect
10. C59×#1839C2semidirect
11. C59×#1831C2semidirect
12. C59×#1818C2semidirect
13. C59×#1798C2semidirect
14. C59×#1750C2semidirect
15. C59×#1729C2semidirect
287. #22005C59direct (N × H)
326. #1924C2×C59semidirect
327. #1923C2×C59semidirect
328. #1917C2×C59semidirect
329. #1916C2×C59semidirect
332. #1851C2×C59semidirect
333. #1850C2×C59semidirect
334. #1839C2×C59semidirect
335. #1831C2×C59semidirect
336. #1818C2×C59semidirect
337. #1798C2×C59semidirect
338. #1750C2×C59semidirect
339. #1729C2×C59semidirect
392. C59#22005direct (N × H)

Maximal subgroups

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

subgroupindex
C59×#22932
C59×#19242
C59×#19232
C59×#19172
C59×#19162
C59×#18702
C59×#18692
C59×#18512
C59×#18502
C59×#18392
C59×#18312
C59×#18182
C59×#17982
C59×#17502
C59×#17292
#2200559