Finite Group Databasebeta

← C59×#17524 #28429633

Subgroups — C59×#17524 #28429633

Order 15104.

936 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C59×#3482C211yesmaximal, characteristic
2C59×#2990C211yesmaximal, characteristic, complemented
3C59×#2922C211yesmaximal, characteristic, complemented
4C59×#1497C211yesmaximal, characteristic, complemented
5C59×#1495C211yesmaximal, characteristic, complemented
6C59×#1494C211yesmaximal, characteristic, complemented
7C59×#1491C211yesmaximal, characteristic, complemented
8C59×#1488C211yesmaximal, characteristic, complemented
9C59×#1487C211yesmaximal, characteristic, complemented
10C59×#1483C211yesmaximal, characteristic, complemented
11C59×#1482C211yesmaximal, characteristic, complemented
12C59×#1481C211yesmaximal, characteristic, complemented
13C59×#1479C211yesmaximal, characteristic, complemented
14C59×#1477C211yesmaximal, characteristic, complemented
15C2×C59×Q8⋊C8C211yesmaximal, characteristic, complemented
16C59×#557C411yescharacteristic
17C59×#556—21no—
18C59×#556C411yescharacteristic
19C59×#552—21no—
20C59×#552—21no—
21C59×#552C411yescharacteristic
22C59×#552C411yescharacteristic
23D4×Q8×C59C411yescharacteristic
24C59×#548C411yescharacteristic
25C59×#548C411yescharacteristic
26C59×#547—21no—
27C59×#547C411yescharacteristic
28C59×#533—21no—
29C59×#533C2211yescharacteristic
30C59×#529—21no—
31C59×#529—21no—
32C59×#529C2211yescharacteristic
33C59×#529C2211yescharacteristic
34C4×#41×C59—21no—
35C4×#41×C59C2211yescharacteristic
36C4×#41×C59C2211yescharacteristic
37C2×C4×Q8×C59C2211yescharacteristic
38C2×C4×Q8×C59C2211yescharacteristic
39C59×#446—21no—
40C59×#435—21no—
41C59×#435—21no—
42C8×D4×C59—21no—
43C59×#433—21no—
44C59×#433—21no—
45C59×#432C2211yescharacteristic
46C59×#432C2211yescharacteristic
47C59×#431C2211yescharacteristic
48C59×#431C2211yescharacteristic
49C59×#431C2211yescharacteristic
50C59×#431C2211yescharacteristic
51C59×#431C2211yescharacteristic
52C59×#424—21no—
53C59×#423C2211yescharacteristic
54C2×C4⋊C8×C59C2211yescharacteristic
55C2×C4⋊C8×C59C2211yescharacteristic
56C59×#408—21no—
57C4×M16×C59C2211yescharacteristic
58C2×C4×C8×C59C2211yescharacteristic
59C59×Q8⋊C8C2211yescharacteristic
60C59×Q8⋊C8C2211yescharacteristic
61C59×Q8⋊C8C2211yescharacteristic
62C59×Q8⋊C8C2211yescharacteristic
63C59×Q8⋊C8C2211yescharacteristic
64C59×Q8⋊C8C2211yescharacteristic
65C59×Q8⋊C8C2211yescharacteristic
66C59×Q8⋊C8C2211yescharacteristic
67C59×Q8⋊C8C2211yescharacteristic
68C59×Q8⋊C8C2211yescharacteristic
69C59×Q8⋊C8C2211yescharacteristic
70C59×Q8⋊C8C2211yescharacteristic
71C59×D4⋊C8C2211yescharacteristic
72C59×D4⋊C8C2211yescharacteristic
73C59×D4⋊C8C2211yescharacteristic
74C59×D4⋊C8C2211yescharacteristic
75C2×#41×C59—21no—
76C2×#41×C59C2×C411yescharacteristic
77C2×#41×C59D411yescharacteristic
78C22×Q8×C59C2×C411yescharacteristic
79C22×Q8×C59C2×C411yescharacteristic
80C2×M16×C59—21no—
81C2×M16×C59—21no—
82C22×C8×C59—21no—
83C22×C8×C59—21no—
84C22×C8×C59—21no—
85C4⋊Q8×C59—21no—
86C4⋊Q8×C59—21no—
87C4⋊Q8×C59C2×C411yescharacteristic
88C4⋊Q8×C59C2×C411yescharacteristic
89#126×C59—21no—
90#126×C59—21no—
91#126×C59—21no—
92#126×C59—21no—
93#126×C59—21no—
94#126×C59—21no—
95#125×C59—21no—
96#125×C59—21no—
97#125×C59—21no—
98#125×C59—21no—
99#125×C59—21no—
100#125×C59C2×C411yescharacteristic
101#125×C59C2×C411yescharacteristic
102#124×C59—21no—
103#124×C59—21no—
104#124×C59C2×C411yescharacteristic
105#124×C59C2×C411yescharacteristic
106#123×C59—21no—
107#123×C59—21no—
108#123×C59—21no—
109#123×C59—21no—
110#123×C59—21no—
111#123×C59—21no—
112C22⋊Q8×C59—21no—
113C22⋊Q8×C59—21no—
114C22⋊Q8×C59—21no—
115C22⋊Q8×C59—21no—
116C22⋊Q8×C59—21no—
117C22⋊Q8×C59—21no—
118C22⋊Q8×C59—21no—
119C22⋊Q8×C59C2×C411yescharacteristic
120C22⋊Q8×C59C2×C411yescharacteristic
121C22⋊Q8×C59C2×C411yescharacteristic
122C22⋊Q8×C59C2×C411yescharacteristic
123#121×C59—21no—
124#121×C59—21no—
125#121×C59C2×C411yescharacteristic
126#121×C59C2×C411yescharacteristic
127C4×Q8×C59—21no—
128C4×Q8×C59—21no—
129C4×Q8×C59—21no—
130C4×Q8×C59—21no—
131C4×Q8×C59—21no—
132C4×Q8×C59—21no—
133C4×Q8×C59C2×C411yescharacteristic
134C4×Q8×C59C2×C411yescharacteristic
135C4×Q8×C59C2×C411yescharacteristic
136C4×Q8×C59C2×C411yescharacteristic
137C4×Q8×C59C2×C411yescharacteristic
138C4×Q8×C59C2×C411yescharacteristic
139C4×Q8×C59D411yescharacteristic
140C4×Q8×C59C2311yescharacteristic
141C4×Q8×C59C2311yescharacteristic
142C4×Q8×C59C2311yescharacteristic
143C4×D4×C59—21no—
144C4×D4×C59—21no—
145C4×D4×C59—21no—
146C4×D4×C59—21no—
147C4×D4×C59—21no—
148C4×D4×C59—21no—
149C4×D4×C59—21no—
150C4×D4×C59C2×C411yescharacteristic
151C4×D4×C59C2×C411yescharacteristic
152C4×D4×C59C2×C411yescharacteristic
153C4×D4×C59C2×C411yescharacteristic
154C4×D4×C59D411yescharacteristic
155C4×D4×C59D411yescharacteristic
156C4×D4×C59D411yescharacteristic
157C4×D4×C59C2311yescharacteristic
158#117×C59—21no—
159#117×C59—21no—
160#117×C59—21no—
161#117×C59—21no—
162#117×C59—21no—
163#117×C59—21no—
164#117×C59—21no—
165#117×C59C2×C411yescharacteristic
166#117×C59D411yescharacteristic
167#117×C59D411yescharacteristic
168#117×C59D411yescharacteristic
169C2×C4⋊C4×C59—21no—
170C2×C4⋊C4×C59—21no—
171C2×C4⋊C4×C59C2×C411yescharacteristic
172C2×C4⋊C4×C59C2×C411yescharacteristic
173C2×C42×C59—21no—
174C2×C42×C59—21no—
175C2×C42×C59—21no—
176C2×C42×C59C2311yescharacteristic
177C2×C42×C59C2311yescharacteristic
178C2×C42×C59C2311yescharacteristic
179C4⋊C8×C59—21no—
180C4⋊C8×C59—21no—
181C4⋊C8×C59—21no—
182C4⋊C8×C59—21no—
183C4⋊C8×C59—21no—
184C4⋊C8×C59—21no—
185C4⋊C8×C59—21no—
186C4⋊C8×C59C2311yescharacteristic
187C4⋊C8×C59C2311yescharacteristic
188C4⋊C8×C59C2311yescharacteristic
189C4⋊C8×C59C2311yescharacteristic
190C22⋊C8×C59—21no—
191C22⋊C8×C59—21no—
192C22⋊C8×C59—21no—
193C22⋊C8×C59—21no—
194C22⋊C8×C59—21no—
195C22⋊C8×C59—21no—
196C22⋊C8×C59—21no—
197#97×C59—21no—
198#97×C59—21no—
199#97×C59—21no—
200C4×C8×C59—21no—
201C4×C8×C59—21no—
202C4×C8×C59C2311yescharacteristic
203C4×C8×C59C2311yescharacteristic
204C4×C8×C59C2311yescharacteristic
205C4×C8×C59C2311yescharacteristic
206#41×C59—22no—
207#41×C59—42no—
208#41×C59—41no—
209#41×C59—44no—
210C2×Q8×C59—21no—
211C2×Q8×C59—21no—
212C2×Q8×C59—21no—
213C2×Q8×C59—22no—
214C2×Q8×C59—22no—
215C2×Q8×C59—41no—
216C2×Q8×C59—41no—
217C2×Q8×C59C22⋊C411yescharacteristic
218C2×Q8×C59C22×C411yescharacteristic
219C2×Q8×C59C22×C411yescharacteristic
220C2×Q8×C59C22×C411yescharacteristic
221C2×D4×C59—21no—
222C2×D4×C59—21no—
223C2×D4×C59—21no—
224C2×D4×C59C22⋊C411yescharacteristic
225C2×D4×C59C22⋊C411yescharacteristic
226C2×D4×C59C22⋊C411yescharacteristic
227C2×D4×C59C22×C411yescharacteristic
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×C59C22×C411yescharacteristic
236C22×C4×C59C22×C411yescharacteristic
237C22×C4×C59C22×C411yescharacteristic
238C22×C4×C59C2×D411yescharacteristic
239C22×C4×C59C2×D411yescharacteristic
240C22×C4×C59C2×D411yescharacteristic
241C22×C4×C59C2×D411yescharacteristic
242C22×C4×C59C2×D411yescharacteristic
243C22×C4×C59C2×D411yescharacteristic
244M16×C59—42no—
245M16×C59—81no—
246C2×C8×C59—21no—
247C2×C8×C59—21no—
248C2×C8×C59—21no—
249C2×C8×C59—21no—
250C2×C8×C59—21no—
251C2×C8×C59—21no—
252C2×C8×C59—21no—
253C2×C8×C59—21no—
254C2×C8×C59—42no—
255C2×C8×C59—81no—
256C2×C8×C59—81no—
257C4⋊C4×C59—21no—
258C4⋊C4×C59—21no—
259C4⋊C4×C59—21no—
260C4⋊C4×C59—21no—
261C4⋊C4×C59—21no—
262C4⋊C4×C59—21no—
263C4⋊C4×C59—21no—
264C4⋊C4×C59—21no—
265C4⋊C4×C59—21no—
266C4⋊C4×C59—21no—
267C4⋊C4×C59—21no—
268C4⋊C4×C59—21no—
269C4⋊C4×C59—21no—
270C4⋊C4×C59—21no—
271C4⋊C4×C59—21no—
272C4⋊C4×C59—21no—
273C4⋊C4×C59—21no—
274C4⋊C4×C59—21no—
275C4⋊C4×C59—21no—
276C4⋊C4×C59—21no—
277C4⋊C4×C59—21no—
278C4⋊C4×C59C22⋊C411yescharacteristic
279C4⋊C4×C59C22⋊C411yescharacteristic
280C4⋊C4×C59C22⋊C411yescharacteristic
281C4⋊C4×C59C22⋊C411yescharacteristic
282C4⋊C4×C59C22⋊C411yescharacteristic
283C4⋊C4×C59C22⋊C411yescharacteristic
284C4⋊C4×C59C22×C411yescharacteristic
285C4⋊C4×C59C22×C411yescharacteristic
286C4⋊C4×C59C22×C411yescharacteristic
287C4⋊C4×C59C22×C411yescharacteristic
288C22⋊C4×C59—21no—
289C22⋊C4×C59—21no—
290C22⋊C4×C59—21no—
291C22⋊C4×C59—21no—
292C22⋊C4×C59—21no—
293C22⋊C4×C59—21no—
294C22⋊C4×C59—21no—
295C22⋊C4×C59—21no—
296C22⋊C4×C59—21no—
297C22⋊C4×C59—21no—
298C22⋊C4×C59—21no—
299C22⋊C4×C59—21no—
300C22⋊C4×C59—21no—
301C22⋊C4×C59C22⋊C411yescharacteristic
302C22⋊C4×C59C22⋊C411yescharacteristic
303C22⋊C4×C59C22⋊C411yescharacteristic
304C22⋊C4×C59C22⋊C411yescharacteristic
305C22⋊C4×C59C22⋊C411yescharacteristic
306C22⋊C4×C59C22⋊C411yescharacteristic
307C42×C59—21no—
308C42×C59—21no—
309C42×C59—21no—
310C42×C59—21no—
311C42×C59—21no—
312C42×C59—21no—
313C42×C59—21no—
314C42×C59—21no—
315C42×C59—21no—
316C42×C59C22×C411yescharacteristic
317C42×C59C22×C411yescharacteristic
318C42×C59C22×C411yescharacteristic
319C42×C59C2×D411yescharacteristic
320C42×C59C2×D411yescharacteristic
321C42×C59C2×D411yescharacteristic
322C42×C59C2×D411yescharacteristic
323C42×C59C2×D411yescharacteristic
324C42×C59C2×D411yescharacteristic
325C42×C59C2411yescharacteristic
326C23×C59—21no—
327C23×C59C2×C22⋊C411yescharacteristic
328C23×C59C2×C22⋊C411yescharacteristic
329C23×C59C2×C22⋊C411yescharacteristic
330Q8×C59—21no—
331Q8×C59—21no—
332Q8×C59—21no—
333Q8×C59—21no—
334Q8×C59—21no—
335Q8×C59—41no—
336Q8×C59—42no—
337Q8×C59—42no—
338Q8×C59—42no—
339Q8×C59#13112yes—
340D4×C59—22no—
341D4×C59—22no—
342D4×C59—21no—
343D4×C59—21no—
344D4×C59—41no—
345D4×C59—42no—
346D4×C59—42no—
347D4×C59—42no—
348C2×C4×C59—21no—
349C2×C4×C59—22no—
350C2×C4×C59—21no—
351C2×C4×C59—21no—
352C2×C4×C59—21no—
353C2×C4×C59—21no—
354C2×C4×C59—21no—
355C2×C4×C59—21no—
356C2×C4×C59—21no—
357C2×C4×C59—21no—
358C2×C4×C59—21no—
359C2×C4×C59—21no—
360C2×C4×C59—21no—
361C2×C4×C59—21no—
362C2×C4×C59—21no—
363C2×C4×C59—21no—
364C2×C4×C59—21no—
365C2×C4×C59—21no—
366C2×C4×C59—21no—
367C2×C4×C59—21no—
368C2×C4×C59—41no—
369C2×C4×C59—41no—
370C2×C4×C59—42no—
371C2×C4×C59—42no—
372C2×C4×C59—42no—
373C2×C4×C59—42no—
374C2×C4×C59—42no—
375C2×C4×C59—42no—
376C2×C4×C59—41no—
377C2×C4×C59—41no—
378C2×C4×C59C2×C22⋊C411yescharacteristic
379C2×C4×C59C2×C22⋊C411yescharacteristic
380C2×C4×C59C2×C22⋊C411yescharacteristic
381C2×C4×C59C2×C22⋊C411yescharacteristic
382C2×C4×C59C2×C22⋊C411yescharacteristic
383C2×C4×C59C2×C22⋊C411yescharacteristic
384C2×C4×C59C2×C22⋊C411yescharacteristic
385C2×C4×C59C2×C22⋊C411yescharacteristic
386C2×C4×C59C2×C22⋊C411yescharacteristic
387C2×C4×C59C23×C411yescharacteristic
388C2×C4×C59C22×D411yescharacteristic
389C2×C4×C59C22×D411yescharacteristic
390C8×C59—41no—
391C8×C59—41no—
392C8×C59—41no—
393C8×C59—41no—
394C8×C59—41no—
395C8×C59—41no—
396C8×C59—41no—
397C8×C59—41no—
398#17524C5911yesmaximal, characteristic, direct product factor, Sylow
399C22×C59—21no—
400C22×C59—21no—
401C22×C59—21no—
402C22×C59—21no—
403C22×C59—21no—
404C22×C59—21no—
405C22×C59—21no—
406C22×C59—21no—
407C22×C59—41no—
408C22×C59—41no—
409C22×C59—41no—
410C22×C59#42112yes—
411C22×C59C22×C22⋊C411yescharacteristic
412C4×C59—21no—
413C4×C59—21no—
414C4×C59—21no—
415C4×C59—22no—
416C4×C59—21no—
417C4×C59—21no—
418C4×C59—21no—
419C4×C59—21no—
420C4×C59—21no—
421C4×C59—21no—
422C4×C59—21no—
423C4×C59—41no—
424C4×C59—41no—
425C4×C59—41no—
426C4×C59—41no—
427C4×C59—41no—
428C4×C59—41no—
429C4×C59C2×#13111yescharacteristic
430C4×C59#56811yescharacteristic
431C4×C59#57711yescharacteristic
432C4×C59#57811yescharacteristic
433#3482C2×C5911yescharacteristic
434#2990C2×C5911yescharacteristic, complemented
435#2922C2×C5911yescharacteristic, complemented
436#1497C2×C5911yescharacteristic, complemented
437#1495C2×C5911yescharacteristic, complemented
438#1494C2×C5911yescharacteristic, complemented
439#1491C2×C5911yescharacteristic, complemented
440#1488C2×C5911yescharacteristic, complemented
441#1487C2×C5911yescharacteristic, complemented
442#1483C2×C5911yescharacteristic, complemented
443#1482C2×C5911yescharacteristic, complemented
444#1481C2×C5911yescharacteristic, complemented
445#1479C2×C5911yescharacteristic, complemented
446#1477C2×C5911yescharacteristic, complemented
447C2×Q8⋊C8C2×C5911yescharacteristic, complemented
448C2×C59—22no—
449C2×C59—41no—
450C2×C59—41no—
451C2×C59—81no—
452C2×C59#288011yescharacteristic
453C2×C59#289811yescharacteristic
454C2×C59C2×#42111yescharacteristic
455#557C4×C5911yescharacteristic
456#556—21no—
457#556C4×C5911yescharacteristic
458#552—21no—
459#552—21no—
460#552C4×C5911yescharacteristic
461#552C4×C5911yescharacteristic
462D4×Q8C4×C5911yescharacteristic
463#548C4×C5911yescharacteristic
464#548C4×C5911yescharacteristic
465#547—21no—
466#547C4×C5911yescharacteristic
467#533—21no—
468#533C22×C5911yescharacteristic
469#529—21no—
470#529—21no—
471#529C22×C5911yescharacteristic
472#529C22×C5911yescharacteristic
473C4×#41—21no—
474C4×#41C22×C5911yescharacteristic
475C4×#41C22×C5911yescharacteristic
476C2×C4×Q8C22×C5911yescharacteristic
477C2×C4×Q8C22×C5911yescharacteristic
478#446—21no—
479#435—21no—
480#435—21no—
481C8×D4—21no—
482#433—21no—
483#433—21no—
484#432C22×C5911yescharacteristic
485#432C22×C5911yescharacteristic
486#431C22×C5911yescharacteristic
487#431C22×C5911yescharacteristic
488#431C22×C5911yescharacteristic
489#431C22×C5911yescharacteristic
490#431C22×C5911yescharacteristic
491#424—21no—
492#423C22×C5911yescharacteristic
493C2×C4⋊C8C22×C5911yescharacteristic
494C2×C4⋊C8C22×C5911yescharacteristic
495#408—21no—
496C4×M16C22×C5911yescharacteristic
497C2×C4×C8C22×C5911yescharacteristic
498Q8⋊C8C22×C5911yescharacteristic
499Q8⋊C8C22×C5911yescharacteristic
500Q8⋊C8C22×C5911yescharacteristic
501Q8⋊C8C22×C5911yescharacteristic
502Q8⋊C8C22×C5911yescharacteristic
503Q8⋊C8C22×C5911yescharacteristic
504Q8⋊C8C22×C5911yescharacteristic
505Q8⋊C8C22×C5911yescharacteristic
506Q8⋊C8C22×C5911yescharacteristic
507Q8⋊C8C22×C5911yescharacteristic
508Q8⋊C8C22×C5911yescharacteristic
509Q8⋊C8C22×C5911yescharacteristic
510D4⋊C8C22×C5911yescharacteristic
511D4⋊C8C22×C5911yescharacteristic
512D4⋊C8C22×C5911yescharacteristic
513D4⋊C8C22×C5911yescharacteristic
514C59#1752411yescharacteristic, direct product factor, Sylow
515C2×#41—21no—
516C2×#41C2×C4×C5911yescharacteristic
517C2×#41D4×C5911yescharacteristic
518C22×Q8C2×C4×C5911yescharacteristic
519C22×Q8C2×C4×C5911yescharacteristic
520C2×M16—21no—
521C2×M16—21no—
522C22×C8—21no—
523C22×C8—21no—
524C22×C8—21no—
525C4⋊Q8—21no—
526C4⋊Q8—21no—
527C4⋊Q8C2×C4×C5911yescharacteristic
528C4⋊Q8C2×C4×C5911yescharacteristic
529#126—21no—
530#126—21no—
531#126—21no—
532#126—21no—
533#126—21no—
534#126—21no—
535#125—21no—
536#125—21no—
537#125—21no—
538#125—21no—
539#125—21no—
540#125C2×C4×C5911yescharacteristic
541#125C2×C4×C5911yescharacteristic
542#124—21no—
543#124—21no—
544#124C2×C4×C5911yescharacteristic
545#124C2×C4×C5911yescharacteristic
546#123—21no—
547#123—21no—
548#123—21no—
549#123—21no—
550#123—21no—
551#123—21no—
552C22⋊Q8—21no—
553C22⋊Q8—21no—
554C22⋊Q8—21no—
555C22⋊Q8—21no—
556C22⋊Q8—21no—
557C22⋊Q8—21no—
558C22⋊Q8—21no—
559C22⋊Q8C2×C4×C5911yescharacteristic
560C22⋊Q8C2×C4×C5911yescharacteristic
561C22⋊Q8C2×C4×C5911yescharacteristic
562C22⋊Q8C2×C4×C5911yescharacteristic
563#121—21no—
564#121—21no—
565#121C2×C4×C5911yescharacteristic
566#121C2×C4×C5911yescharacteristic
567C4×Q8—21no—
568C4×Q8—21no—
569C4×Q8—21no—
570C4×Q8—21no—
571C4×Q8—21no—
572C4×Q8—21no—
573C4×Q8C2×C4×C5911yescharacteristic
574C4×Q8C2×C4×C5911yescharacteristic
575C4×Q8C2×C4×C5911yescharacteristic
576C4×Q8C2×C4×C5911yescharacteristic
577C4×Q8C2×C4×C5911yescharacteristic
578C4×Q8C2×C4×C5911yescharacteristic
579C4×Q8D4×C5911yescharacteristic
580C4×Q8C23×C5911yescharacteristic
581C4×Q8C23×C5911yescharacteristic
582C4×Q8C23×C5911yescharacteristic
583C4×D4—21no—
584C4×D4—21no—
585C4×D4—21no—
586C4×D4—21no—
587C4×D4—21no—
588C4×D4—21no—
589C4×D4—21no—
590C4×D4C2×C4×C5911yescharacteristic
591C4×D4C2×C4×C5911yescharacteristic
592C4×D4C2×C4×C5911yescharacteristic
593C4×D4C2×C4×C5911yescharacteristic
594C4×D4D4×C5911yescharacteristic
595C4×D4D4×C5911yescharacteristic
596C4×D4D4×C5911yescharacteristic
597C4×D4C23×C5911yescharacteristic
598#117—21no—
599#117—21no—
600#117—21no—
601#117—21no—
602#117—21no—
603#117—21no—
604#117—21no—
605#117C2×C4×C5911yescharacteristic
606#117D4×C5911yescharacteristic
607#117D4×C5911yescharacteristic
608#117D4×C5911yescharacteristic
609C2×C4⋊C4—21no—
610C2×C4⋊C4—21no—
611C2×C4⋊C4C2×C4×C5911yescharacteristic
612C2×C4⋊C4C2×C4×C5911yescharacteristic
613C2×C42—21no—
614C2×C42—21no—
615C2×C42—21no—
616C2×C42C23×C5911yescharacteristic
617C2×C42C23×C5911yescharacteristic
618C2×C42C23×C5911yescharacteristic
619C4⋊C8—21no—
620C4⋊C8—21no—
621C4⋊C8—21no—
622C4⋊C8—21no—
623C4⋊C8—21no—
624C4⋊C8—21no—
625C4⋊C8—21no—
626C4⋊C8C23×C5911yescharacteristic
627C4⋊C8C23×C5911yescharacteristic
628C4⋊C8C23×C5911yescharacteristic
629C4⋊C8C23×C5911yescharacteristic
630C22⋊C8—21no—
631C22⋊C8—21no—
632C22⋊C8—21no—
633C22⋊C8—21no—
634C22⋊C8—21no—
635C22⋊C8—21no—
636C22⋊C8—21no—
637#97—21no—
638#97—21no—
639#97—21no—
640C4×C8—21no—
641C4×C8—21no—
642C4×C8C23×C5911yescharacteristic
643C4×C8C23×C5911yescharacteristic
644C4×C8C23×C5911yescharacteristic
645C4×C8C23×C5911yescharacteristic
646#41—22no—
647#41—42no—
648#41—41no—
649#41—44no—
650C2×Q8—21no—
651C2×Q8—21no—
652C2×Q8—21no—
653C2×Q8—22no—
654C2×Q8—22no—
655C2×Q8—41no—
656C2×Q8—41no—
657C2×Q8C22⋊C4×C5911yescharacteristic
658C2×Q8C22×C4×C5911yescharacteristic
659C2×Q8C22×C4×C5911yescharacteristic
660C2×Q8C22×C4×C5911yescharacteristic
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4C22⋊C4×C5911yescharacteristic
665C2×D4C22⋊C4×C5911yescharacteristic
666C2×D4C22⋊C4×C5911yescharacteristic
667C2×D4C22×C4×C5911yescharacteristic
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4C22×C4×C5911yescharacteristic
676C22×C4C22×C4×C5911yescharacteristic
677C22×C4C22×C4×C5911yescharacteristic
678C22×C4C2×D4×C5911yescharacteristic
679C22×C4C2×D4×C5911yescharacteristic
680C22×C4C2×D4×C5911yescharacteristic
681C22×C4C2×D4×C5911yescharacteristic
682C22×C4C2×D4×C5911yescharacteristic
683C22×C4C2×D4×C5911yescharacteristic
684M16—42no—
685M16—81no—
686C2×C8—21no—
687C2×C8—21no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—21no—
694C2×C8—42no—
695C2×C8—81no—
696C2×C8—81no—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—21no—
705C4⋊C4—21no—
706C4⋊C4—21no—
707C4⋊C4—21no—
708C4⋊C4—21no—
709C4⋊C4—21no—
710C4⋊C4—21no—
711C4⋊C4—21no—
712C4⋊C4—21no—
713C4⋊C4—21no—
714C4⋊C4—21no—
715C4⋊C4—21no—
716C4⋊C4—21no—
717C4⋊C4—21no—
718C4⋊C4C22⋊C4×C5911yescharacteristic
719C4⋊C4C22⋊C4×C5911yescharacteristic
720C4⋊C4C22⋊C4×C5911yescharacteristic
721C4⋊C4C22⋊C4×C5911yescharacteristic
722C4⋊C4C22⋊C4×C5911yescharacteristic
723C4⋊C4C22⋊C4×C5911yescharacteristic
724C4⋊C4C22×C4×C5911yescharacteristic
725C4⋊C4C22×C4×C5911yescharacteristic
726C4⋊C4C22×C4×C5911yescharacteristic
727C4⋊C4C22×C4×C5911yescharacteristic
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⋊C4C22⋊C4×C5911yescharacteristic
742C22⋊C4C22⋊C4×C5911yescharacteristic
743C22⋊C4C22⋊C4×C5911yescharacteristic
744C22⋊C4C22⋊C4×C5911yescharacteristic
745C22⋊C4C22⋊C4×C5911yescharacteristic
746C22⋊C4C22⋊C4×C5911yescharacteristic
747C42—21no—
748C42—21no—
749C42—21no—
750C42—21no—
751C42—21no—
752C42—21no—
753C42—21no—
754C42—21no—
755C42—21no—
756C42C22×C4×C5911yescharacteristic
757C42C22×C4×C5911yescharacteristic
758C42C22×C4×C5911yescharacteristic
759C42C2×D4×C5911yescharacteristic
760C42C2×D4×C5911yescharacteristic
761C42C2×D4×C5911yescharacteristic
762C42C2×D4×C5911yescharacteristic
763C42C2×D4×C5911yescharacteristic
764C42C2×D4×C5911yescharacteristic
765C42C24×C5911yescharacteristic
766C23—21no—
767C23C2×C22⋊C4×C5911yescharacteristic
768C23C2×C22⋊C4×C5911yescharacteristic
769C23C2×C22⋊C4×C5911yescharacteristic
770Q8—21no—
771Q8—21no—
772Q8—21no—
773Q8—21no—
774Q8—21no—
775Q8—41no—
776Q8—42no—
777Q8—42no—
778Q8—42no—
779Q8#131×C5912yes—
780D4—22no—
781D4—22no—
782D4—21no—
783D4—21no—
784D4—41no—
785D4—42no—
786D4—42no—
787D4—42no—
788C2×C4—22no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—21no—
799C2×C4—21no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4C2×C22⋊C4×C5911yescharacteristic
819C2×C4C2×C22⋊C4×C5911yescharacteristic
820C2×C4C2×C22⋊C4×C5911yescharacteristic
821C2×C4C2×C22⋊C4×C5911yescharacteristic
822C2×C4C2×C22⋊C4×C5911yescharacteristic
823C2×C4C2×C22⋊C4×C5911yescharacteristic
824C2×C4C2×C22⋊C4×C5911yescharacteristic
825C2×C4C2×C22⋊C4×C5911yescharacteristic
826C2×C4C2×C22⋊C4×C5911yescharacteristic
827C2×C4C23×C4×C5911yescharacteristic
828C2×C4C22×D4×C5911yescharacteristic
829C2×C4C22×D4×C5911yescharacteristic
830C8—41no—
831C8—41no—
832C8—41no—
833C8—41no—
834C8—41no—
835C8—41no—
836C8—41no—
837C8—41no—
838C22—21no—
839C22—21no—
840C22—21no—
841C22—21no—
842C22—21no—
843C22—21no—
844C22—21no—
845C22—21no—
846C22—41no—
847C22—41no—
848C22—41no—
849C22C59×#42112yes—
850C22C22×C22⋊C4×C5911yescharacteristic
851C4—21no—
852C4—21no—
853C4—21no—
854C4—22no—
855C4—21no—
856C4—21no—
857C4—21no—
858C4—21no—
859C4—21no—
860C4—21no—
861C4—21no—
862C4—41no—
863C4—41no—
864C4—41no—
865C4—41no—
866C4—41no—
867C4—41no—
868C4C2×#131×C5911yescharacteristic
869C4C59×#56811yescharacteristic
870C4C59×#57711yescharacteristic
871C4C59×#57811yescharacteristic
872C2—22no—
873C2—41no—
874C2—41no—
875C2—81no—
876C2C59×#288011yescharacteristic
877C2C59×#289811yescharacteristic
878C2C2×C59×#42111yescharacteristic
subgroupG/H
centerC2×C4×C59C22×D4
commutatorC2×C4C23×C4×C59
Frattini, cosocleC42C24×C59
socleC22×C59C22×C22⋊C4
prime radicalC59×#3482C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C59 ◁ C4×#41×C59 ◁ G

Complements

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

NH ≅ G/Ntype
2. C59×#2990C2semidirect
3. C59×#2922C2semidirect
4. C59×#1497C2semidirect
5. C59×#1495C2semidirect
6. C59×#1494C2semidirect
7. C59×#1491C2semidirect
8. C59×#1488C2semidirect
9. C59×#1487C2semidirect
10. C59×#1483C2semidirect
11. C59×#1482C2semidirect
12. C59×#1481C2semidirect
13. C59×#1479C2semidirect
14. C59×#1477C2semidirect
15. C2×C59×Q8⋊C8C2semidirect
398. #17524C59direct (N × H)
434. #2990C2×C59semidirect
435. #2922C2×C59semidirect
436. #1497C2×C59semidirect
437. #1495C2×C59semidirect
438. #1494C2×C59semidirect
439. #1491C2×C59semidirect
440. #1488C2×C59semidirect
441. #1487C2×C59semidirect
442. #1483C2×C59semidirect
443. #1482C2×C59semidirect
444. #1481C2×C59semidirect
445. #1479C2×C59semidirect
446. #1477C2×C59semidirect
447. C2×Q8⋊C8C2×C59semidirect
514. C59#17524direct (N × H)

Maximal subgroups

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

subgroupindex
C59×#34822
C59×#29902
C59×#29222
C59×#14972
C59×#14952
C59×#14942
C59×#14912
C59×#14882
C59×#14872
C59×#14832
C59×#14822
C59×#14812
C59×#14792
C59×#14772
C2×C59×Q8⋊C82
#1752459