Finite Group Databasebeta

← C59×#25106 #28437215

Subgroups — C59×#25106 #28437215

Order 15104.

1230 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C59×#469C211yesmaximal, characteristic, complemented
2C2×C59×#463C211yesmaximal, characteristic, complemented
3C2×C59×#449C211yesmaximal, characteristic, complemented
4C2×C59×#417C211yesmaximal, characteristic, complemented
5C59×#2431C211yesmaximal, characteristic, complemented
6C59×#2361C211yesmaximal, characteristic, complemented
7C59×#2065C211yesmaximal, characteristic, complemented
8C59×#2055C211yesmaximal, characteristic, complemented
9C59×#2042C211yesmaximal, characteristic, complemented
10C59×#2011C211yesmaximal, characteristic, complemented
11C59×#1982C211yesmaximal, characteristic, complemented
12C59×#1927C211yesmaximal, characteristic, complemented
13C59×#1879C211yesmaximal, characteristic, complemented
14C59×#1874C211yesmaximal, characteristic, complemented
15C59×#1851C211yesmaximal, characteristic, complemented
16C22×#41×C59C2211yescharacteristic
17C22×SD16×C59C2211yescharacteristic
18C22×D8×C59C2211yescharacteristic
19C22×D8×C59C2211yescharacteristic
20C22×M16×C59C2211yescharacteristic
21C2×#127×C59C2211yescharacteristic
22C2×#124×C59C2211yescharacteristic
23C2×#121×C59C2211yescharacteristic
24C2×#121×C59C2211yescharacteristic
25C2×C4×D4×C59—21no—
26C2×C4×D4×C59C2211yescharacteristic
27C22×C4⋊C4×C59C2211yescharacteristic
28C59×#469—24no—
29C59×#463—24no—
30C59×#449—24no—
31C2×#106×C59C2211yescharacteristic
32C2×C4⋊C8×C59C2211yescharacteristic
33C2×C4⋊C8×C59C2211yescharacteristic
34C59×#417—24no—
35C2×#103×C59C2211yescharacteristic
36C2×#103×C59C2211yescharacteristic
37C2×#103×C59C2211yescharacteristic
38C2×#102×C59C2211yescharacteristic
39C2×#102×C59C2211yescharacteristic
40C2×#102×C59C2211yescharacteristic
41C2×#102×C59C2211yescharacteristic
42C2×#102×C59C2211yescharacteristic
43C2×#102×C59C2211yescharacteristic
44C2×#102×C59C2211yescharacteristic
45C2×C22⋊C8×C59C2211yescharacteristic
46C59×#392—21no—
47C59×#392—21no—
48C59×#391C2211yescharacteristic
49C59×#390C2211yescharacteristic
50C59×#390C2211yescharacteristic
51C59×#389C2211yescharacteristic
52C59×#388—21no—
53C59×#386—21no—
54C59×#386—21no—
55C59×#386—21no—
56C59×#385—21no—
57C4×C4⋊C4×C59C2211yescharacteristic
58C4×C22⋊C4×C59C2211yescharacteristic
59C59×#340C2211yescharacteristic
60C59×#340C2211yescharacteristic
61C59×#336C2211yescharacteristic
62C59×#336C2211yescharacteristic
63C2×#41×C59—22no—
64C2×#41×C59—22no—
65C2×#41×C59—22no—
66C2×#41×C59—22no—
67C2×#41×C59—41no—
68C2×#41×C59—41no—
69C22×Q8×C59C2311yescharacteristic
70C22×D4×C59—21no—
71C22×D4×C59—21no—
72C22×D4×C59—21no—
73C22×D4×C59—21no—
74C22×D4×C59—21no—
75C22×D4×C59C2311yescharacteristic
76C22×D4×C59C2311yescharacteristic
77C22×D4×C59C2311yescharacteristic
78C23×C4×C59—21no—
79C23×C4×C59—21no—
80C23×C4×C59—21no—
81C23×C4×C59C2311yescharacteristic
82C2×SD16×C59—22no—
83C2×SD16×C59—22no—
84C2×SD16×C59—41no—
85C2×D8×C59—22no—
86C2×D8×C59—22no—
87C2×D8×C59—22no—
88C2×D8×C59—22no—
89C2×D8×C59—41no—
90C2×D8×C59—41no—
91C2×M16×C59—22no—
92C2×M16×C59—22no—
93C2×M16×C59—41no—
94C22×C8×C59C2311yescharacteristic
95C22×C8×C59C2311yescharacteristic
96C22×C8×C59C2311yescharacteristic
97C22×C8×C59C2311yescharacteristic
98#127×C59—22no—
99#127×C59—41no—
100#124×C59—22no—
101#124×C59—41no—
102#121×C59—22no—
103#121×C59—22no—
104#121×C59—22no—
105#121×C59D414yescomplemented
106C4×D4×C59—22no—
107C4×D4×C59—41no—
108C4×D4×C59—44no—
109C2×C4⋊C4×C59—22no—
110C2×C4⋊C4×C59—21no—
111C2×C4⋊C4×C59—21no—
112C2×C4⋊C4×C59—41no—
113C2×C4⋊C4×C59C2311yescharacteristic
114C2×C4⋊C4×C59C2311yescharacteristic
115C2×C4⋊C4×C59C2311yescharacteristic
116C2×C4⋊C4×C59C2311yescharacteristic
117C2×C22⋊C4×C59—21no—
118C2×C22⋊C4×C59—21no—
119C2×C22⋊C4×C59—21no—
120C2×C22⋊C4×C59—21no—
121C2×C22⋊C4×C59—21no—
122C2×C22⋊C4×C59—21no—
123C2×C22⋊C4×C59—21no—
124C2×C22⋊C4×C59—21no—
125C2×C22⋊C4×C59—21no—
126C2×C22⋊C4×C59D411yescharacteristic
127C2×C22⋊C4×C59D411yescharacteristic
128C2×C42×C59—21no—
129C2×C42×C59C2311yescharacteristic
130C2×C42×C59C2311yescharacteristic
131#106×C59—22no—
132C4⋊C8×C59—22no—
133C4⋊C8×C59—41no—
134#103×C59—22no—
135#103×C59—22no—
136#103×C59D414yescomplemented
137#102×C59—22no—
138#102×C59—22no—
139#102×C59—22no—
140#102×C59—22no—
141#102×C59—22no—
142#102×C59—22no—
143#102×C59—41no—
144C22⋊C8×C59—22no—
145#95×C59—21no—
146#95×C59—21no—
147#95×C59—21no—
148#95×C59—21no—
149#95×C59D411yescharacteristic
150#95×C59D411yescharacteristic
151C24×C59—21no—
152C24×C59—21no—
153C24×C59—21no—
154C24×C59C2×D411yescharacteristic
155#41×C59—28no—
156#41×C59—44no—
157#41×C59—44no—
158#41×C59—44no—
159C2×Q8×C59—21no—
160C2×Q8×C59—21no—
161C2×Q8×C59—21no—
162C2×Q8×C59—21no—
163C2×Q8×C59—21no—
164C2×Q8×C59C2×D412yes—
165C2×D4×C59—24no—
166C2×D4×C59—21no—
167C2×D4×C59—21no—
168C2×D4×C59—21no—
169C2×D4×C59—21no—
170C2×D4×C59—21no—
171C2×D4×C59—21no—
172C2×D4×C59—21no—
173C2×D4×C59—21no—
174C2×D4×C59—21no—
175C2×D4×C59—21no—
176C2×D4×C59—21no—
177C2×D4×C59—21no—
178C2×D4×C59—21no—
179C2×D4×C59—21no—
180C2×D4×C59—21no—
181C2×D4×C59—21no—
182C2×D4×C59—42no—
183C2×D4×C59—42no—
184C2×D4×C59—42no—
185C2×D4×C59—42no—
186C2×D4×C59—42no—
187C2×D4×C59—42no—
188C2×D4×C59—42no—
189C2×D4×C59—42no—
190C2×D4×C59—42no—
191C2×D4×C59—42no—
192C2×D4×C59—81no—
193C2×D4×C59—81no—
194C2×D4×C59—81no—
195C2×D4×C59—81no—
196C2×D4×C59C2×D412yes—
197C2×D4×C59#4112yes—
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—42no—
208C22×C4×C59—42no—
209C22×C4×C59—42no—
210C22×C4×C59—42no—
211C22×C4×C59—42no—
212C22×C4×C59—42no—
213C22×C4×C59—42no—
214C22×C4×C59—81no—
215C22×C4×C59—81no—
216C22×C4×C59C2×D411yescharacteristic
217C22×C4×C59C2×D411yescharacteristic
218C22×C4×C59C2×D411yescharacteristic
219C22×C4×C59C2×D411yescharacteristic
220C22×C4×C59C2×D412yes—
221C22×C4×C59C2×D411yescharacteristic
222C22×C4×C59#4112yes—
223C22×C4×C59C2411yescharacteristic
224SD16×C59—44no—
225D8×C59—44no—
226D8×C59—44no—
227M16×C59—44no—
228C2×C8×C59—21no—
229C2×C8×C59—21no—
230C2×C8×C59—21no—
231C2×C8×C59—21no—
232C2×C8×C59—21no—
233C2×C8×C59—21no—
234C2×C8×C59—21no—
235C2×C8×C59—21no—
236C2×C8×C59—21no—
237C2×C8×C59—21no—
238C2×C8×C59—21no—
239C2×C8×C59C2×D412yes—
240C4⋊C4×C59—21no—
241C4⋊C4×C59—21no—
242C4⋊C4×C59—21no—
243C4⋊C4×C59—21no—
244C4⋊C4×C59—21no—
245C4⋊C4×C59—21no—
246C4⋊C4×C59—42no—
247C4⋊C4×C59—42no—
248C4⋊C4×C59C2×D412yes—
249C4⋊C4×C59C2×D412yes—
250C22⋊C4×C59—24no—
251C22⋊C4×C59—22no—
252C22⋊C4×C59—41no—
253C22⋊C4×C59—42no—
254C22⋊C4×C59—42no—
255C22⋊C4×C59—42no—
256C22⋊C4×C59—42no—
257C22⋊C4×C59—42no—
258C22⋊C4×C59—81no—
259C22⋊C4×C59—81no—
260C22⋊C4×C59—81no—
261C42×C59—21no—
262C42×C59—21no—
263C42×C59—21no—
264C42×C59—21no—
265C42×C59—42no—
266C23×C59—21no—
267C23×C59—21no—
268C23×C59—21no—
269C23×C59—21no—
270C23×C59—21no—
271C23×C59—21no—
272C23×C59—22no—
273C23×C59—22no—
274C23×C59—41no—
275C23×C59—41no—
276C23×C59—41no—
277C23×C59—41no—
278C23×C59—41no—
279C23×C59—41no—
280C23×C59—41no—
281C23×C59—41no—
282C23×C59—41no—
283C23×C59—41no—
284C23×C59—41no—
285C23×C59—41no—
286C23×C59—41no—
287C23×C59—41no—
288C23×C59—41no—
289C23×C59—41no—
290C23×C59—41no—
291C23×C59—41no—
292C23×C59—41no—
293C23×C59#12112yes—
294C23×C59C22×D411yescharacteristic
295Q8×C59—22no—
296Q8×C59—22no—
297Q8×C59—41no—
298Q8×C59—41no—
299D4×C59—22no—
300D4×C59—22no—
301D4×C59—22no—
302D4×C59—22no—
303D4×C59—48no—
304D4×C59—48no—
305D4×C59—41no—
306D4×C59—41no—
307D4×C59—41no—
308D4×C59—41no—
309D4×C59—41no—
310D4×C59—41no—
311D4×C59—41no—
312D4×C59—41no—
313D4×C59—84no—
314D4×C59—84no—
315D4×C59—84no—
316C2×C4×C59—21no—
317C2×C4×C59—21no—
318C2×C4×C59—21no—
319C2×C4×C59—21no—
320C2×C4×C59—22no—
321C2×C4×C59—22no—
322C2×C4×C59—22no—
323C2×C4×C59—22no—
324C2×C4×C59—22no—
325C2×C4×C59—21no—
326C2×C4×C59—21no—
327C2×C4×C59—22no—
328C2×C4×C59—22no—
329C2×C4×C59—21no—
330C2×C4×C59—21no—
331C2×C4×C59—21no—
332C2×C4×C59—21no—
333C2×C4×C59—21no—
334C2×C4×C59—21no—
335C2×C4×C59—21no—
336C2×C4×C59—48no—
337C2×C4×C59—41no—
338C2×C4×C59—41no—
339C2×C4×C59—41no—
340C2×C4×C59—41no—
341C2×C4×C59—41no—
342C2×C4×C59—41no—
343C2×C4×C59—41no—
344C2×C4×C59—41no—
345C2×C4×C59—41no—
346C2×C4×C59—41no—
347C2×C4×C59—41no—
348C2×C4×C59—41no—
349C2×C4×C59—84no—
350C2×C4×C59—84no—
351C2×C4×C59#12112yes—
352C2×C4×C59AGL(1,ℤ/8)12yes—
353C2×C4×C59C22×D411yescharacteristic
354C2×C4×C59C22×D411yescharacteristic
355C2×C4×C59C2×#4111yescharacteristic
356C2×C4×C59C2×#4111yescharacteristic
357C2×C4×C59H(5,𝔽2)11yescharacteristic
358C2×C4×C59H(5,𝔽2)11yescharacteristic
359C8×C59—22no—
360C8×C59—41no—
361C8×C59—41no—
362C8×C59—41no—
363#25106C5911yesmaximal, characteristic, direct product factor, Sylow
364C22×C59—22no—
365C22×C59—22no—
366C22×C59—22no—
367C22×C59—41no—
368C22×C59—41no—
369C22×C59—41no—
370C22×C59—41no—
371C22×C59—42no—
372C22×C59—42no—
373C22×C59—42no—
374C22×C59—42no—
375C22×C59—42no—
376C22×C59—42no—
377C22×C59—81no—
378C22×C59—81no—
379C22×C59—81no—
380C22×C59—81no—
381C22×C59—81no—
382C22×C59—81no—
383C22×C59—81no—
384C22×C59—81no—
385C22×C59—81no—
386C22×C59—81no—
387C22×C59—81no—
388C22×C59—81no—
389C22×C59—81no—
390C22×C59—81no—
391C22×C59—81no—
392C22×C59C2×#12111yescharacteristic
393C22×C59D4211yescharacteristic
394C22×C59#54611yescharacteristic
395C22×C59C2×AGL(1,ℤ/8)11yescharacteristic
396C22×C59#57511yescharacteristic
397C22×C59#57611yescharacteristic
398C22×C59#57711yescharacteristic
399C4×C59—22no—
400C4×C59—22no—
401C4×C59—42no—
402C4×C59—41no—
403C4×C59—41no—
404C4×C59—42no—
405C4×C59—42no—
406C4×C59—41no—
407C4×C59—81no—
408C4×C59—81no—
409C4×C59#52511yescharacteristic
410C4×C59#53811yescharacteristic
411C4×C59D4211yescharacteristic
412C4×C59#54611yescharacteristic
413C2×#469C2×C5911yescharacteristic, complemented
414C2×#463C2×C5911yescharacteristic, complemented
415C2×#449C2×C5911yescharacteristic, complemented
416C2×#417C2×C5911yescharacteristic, complemented
417#2431C2×C5911yescharacteristic, complemented
418#2361C2×C5911yescharacteristic, complemented
419#2065C2×C5911yescharacteristic, complemented
420#2055C2×C5911yescharacteristic, complemented
421#2042C2×C5911yescharacteristic, complemented
422#2011C2×C5911yescharacteristic, complemented
423#1982C2×C5911yescharacteristic, complemented
424#1927C2×C5911yescharacteristic, complemented
425#1879C2×C5911yescharacteristic, complemented
426#1874C2×C5911yescharacteristic, complemented
427#1851C2×C5911yescharacteristic, complemented
428C2×C59—42no—
429C2×C59—82no—
430C2×C59—82no—
431C2×C59—161no—
432C2×C59#242411yescharacteristic
433C2×C59#303611yescharacteristic
434C2×C59#304511yescharacteristic
435C2×C59#327111yescharacteristic
436C2×C59#327411yescharacteristic
437C2×C59#330611yescharacteristic
438C2×C59#332211yescharacteristic
439C22×#41C22×C5911yescharacteristic
440C22×SD16C22×C5911yescharacteristic
441C22×D8C22×C5911yescharacteristic
442C22×D8C22×C5911yescharacteristic
443C22×M16C22×C5911yescharacteristic
444C2×#127C22×C5911yescharacteristic
445C2×#124C22×C5911yescharacteristic
446C2×#121C22×C5911yescharacteristic
447C2×#121C22×C5911yescharacteristic
448C2×C4×D4—21no—
449C2×C4×D4C22×C5911yescharacteristic
450C22×C4⋊C4C22×C5911yescharacteristic
451#469—24no—
452#463—24no—
453#449—24no—
454C2×#106C22×C5911yescharacteristic
455C2×C4⋊C8C22×C5911yescharacteristic
456C2×C4⋊C8C22×C5911yescharacteristic
457#417—24no—
458C2×#103C22×C5911yescharacteristic
459C2×#103C22×C5911yescharacteristic
460C2×#103C22×C5911yescharacteristic
461C2×#102C22×C5911yescharacteristic
462C2×#102C22×C5911yescharacteristic
463C2×#102C22×C5911yescharacteristic
464C2×#102C22×C5911yescharacteristic
465C2×#102C22×C5911yescharacteristic
466C2×#102C22×C5911yescharacteristic
467C2×#102C22×C5911yescharacteristic
468C2×C22⋊C8C22×C5911yescharacteristic
469#392—21no—
470#392—21no—
471#391C22×C5911yescharacteristic
472#390C22×C5911yescharacteristic
473#390C22×C5911yescharacteristic
474#389C22×C5911yescharacteristic
475#388—21no—
476#386—21no—
477#386—21no—
478#386—21no—
479#385—21no—
480C4×C4⋊C4C22×C5911yescharacteristic
481C4×C22⋊C4C22×C5911yescharacteristic
482#340C22×C5911yescharacteristic
483#340C22×C5911yescharacteristic
484#336C22×C5911yescharacteristic
485#336C22×C5911yescharacteristic
486C59#2510611yescharacteristic, direct product factor, Sylow
487C2×#41—22no—
488C2×#41—22no—
489C2×#41—22no—
490C2×#41—22no—
491C2×#41—41no—
492C2×#41—41no—
493C22×Q8C23×C5911yescharacteristic
494C22×D4—21no—
495C22×D4—21no—
496C22×D4—21no—
497C22×D4—21no—
498C22×D4—21no—
499C22×D4C23×C5911yescharacteristic
500C22×D4C23×C5911yescharacteristic
501C22×D4C23×C5911yescharacteristic
502C23×C4—21no—
503C23×C4—21no—
504C23×C4—21no—
505C23×C4C23×C5911yescharacteristic
506C2×SD16—22no—
507C2×SD16—22no—
508C2×SD16—41no—
509C2×D8—22no—
510C2×D8—22no—
511C2×D8—22no—
512C2×D8—22no—
513C2×D8—41no—
514C2×D8—41no—
515C2×M16—22no—
516C2×M16—22no—
517C2×M16—41no—
518C22×C8C23×C5911yescharacteristic
519C22×C8C23×C5911yescharacteristic
520C22×C8C23×C5911yescharacteristic
521C22×C8C23×C5911yescharacteristic
522#127—22no—
523#127—41no—
524#124—22no—
525#124—41no—
526#121—22no—
527#121—22no—
528#121—22no—
529#121D4×C5914yescomplemented
530C4×D4—22no—
531C4×D4—41no—
532C4×D4—44no—
533C2×C4⋊C4—22no—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—41no—
537C2×C4⋊C4C23×C5911yescharacteristic
538C2×C4⋊C4C23×C5911yescharacteristic
539C2×C4⋊C4C23×C5911yescharacteristic
540C2×C4⋊C4C23×C5911yescharacteristic
541C2×C22⋊C4—21no—
542C2×C22⋊C4—21no—
543C2×C22⋊C4—21no—
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4D4×C5911yescharacteristic
551C2×C22⋊C4D4×C5911yescharacteristic
552C2×C42—21no—
553C2×C42C23×C5911yescharacteristic
554C2×C42C23×C5911yescharacteristic
555#106—22no—
556C4⋊C8—22no—
557C4⋊C8—41no—
558#103—22no—
559#103—22no—
560#103D4×C5914yescomplemented
561#102—22no—
562#102—22no—
563#102—22no—
564#102—22no—
565#102—22no—
566#102—22no—
567#102—41no—
568C22⋊C8—22no—
569#95—21no—
570#95—21no—
571#95—21no—
572#95—21no—
573#95D4×C5911yescharacteristic
574#95D4×C5911yescharacteristic
575C24—21no—
576C24—21no—
577C24—21no—
578C24C2×D4×C5911yescharacteristic
579#41—28no—
580#41—44no—
581#41—44no—
582#41—44no—
583C2×Q8—21no—
584C2×Q8—21no—
585C2×Q8—21no—
586C2×Q8—21no—
587C2×Q8—21no—
588C2×Q8C2×D4×C5912yes—
589C2×D4—24no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—42no—
607C2×D4—42no—
608C2×D4—42no—
609C2×D4—42no—
610C2×D4—42no—
611C2×D4—42no—
612C2×D4—42no—
613C2×D4—42no—
614C2×D4—42no—
615C2×D4—42no—
616C2×D4—81no—
617C2×D4—81no—
618C2×D4—81no—
619C2×D4—81no—
620C2×D4C2×D4×C5912yes—
621C2×D4#41×C5912yes—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—42no—
632C22×C4—42no—
633C22×C4—42no—
634C22×C4—42no—
635C22×C4—42no—
636C22×C4—42no—
637C22×C4—42no—
638C22×C4—81no—
639C22×C4—81no—
640C22×C4C2×D4×C5911yescharacteristic
641C22×C4C2×D4×C5911yescharacteristic
642C22×C4C2×D4×C5911yescharacteristic
643C22×C4C2×D4×C5911yescharacteristic
644C22×C4C2×D4×C5912yes—
645C22×C4C2×D4×C5911yescharacteristic
646C22×C4#41×C5912yes—
647C22×C4C24×C5911yescharacteristic
648SD16—44no—
649D8—44no—
650D8—44no—
651M16—44no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8—21no—
662C2×C8—21no—
663C2×C8C2×D4×C5912yes—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—42no—
671C4⋊C4—42no—
672C4⋊C4C2×D4×C5912yes—
673C4⋊C4C2×D4×C5912yes—
674C22⋊C4—24no—
675C22⋊C4—22no—
676C22⋊C4—41no—
677C22⋊C4—42no—
678C22⋊C4—42no—
679C22⋊C4—42no—
680C22⋊C4—42no—
681C22⋊C4—42no—
682C22⋊C4—81no—
683C22⋊C4—81no—
684C22⋊C4—81no—
685C42—21no—
686C42—21no—
687C42—21no—
688C42—21no—
689C42—42no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—22no—
697C23—22no—
698C23—41no—
699C23—41no—
700C23—41no—
701C23—41no—
702C23—41no—
703C23—41no—
704C23—41no—
705C23—41no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23#121×C5912yes—
718C23C22×D4×C5911yescharacteristic
719Q8—22no—
720Q8—22no—
721Q8—41no—
722Q8—41no—
723D4—22no—
724D4—22no—
725D4—22no—
726D4—22no—
727D4—48no—
728D4—48no—
729D4—41no—
730D4—41no—
731D4—41no—
732D4—41no—
733D4—41no—
734D4—41no—
735D4—41no—
736D4—41no—
737D4—84no—
738D4—84no—
739D4—84no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—48no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—84no—
774C2×C4—84no—
775C2×C4#121×C5912yes—
776C2×C4AGL(1,ℤ/8)×C5912yes—
777C2×C4C22×D4×C5911yescharacteristic
778C2×C4C22×D4×C5911yescharacteristic
779C2×C4C2×#41×C5911yescharacteristic
780C2×C4C2×#41×C5911yescharacteristic
781C2×C4H(5,𝔽2)×C5911yescharacteristic
782C2×C4H(5,𝔽2)×C5911yescharacteristic
783C8—22no—
784C8—41no—
785C8—41no—
786C8—41no—
787C22—22no—
788C22—22no—
789C22—22no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—42no—
795C22—42no—
796C22—42no—
797C22—42no—
798C22—42no—
799C22—42no—
800C22—81no—
801C22—81no—
802C22—81no—
803C22—81no—
804C22—81no—
805C22—81no—
806C22—81no—
807C22—81no—
808C22—81no—
809C22—81no—
810C22—81no—
811C22—81no—
812C22—81no—
813C22—81no—
814C22—81no—
815C22C2×#121×C5911yescharacteristic
816C22D42×C5911yescharacteristic
817C22C59×#54611yescharacteristic
818C22C2×AGL(1,ℤ/8)×C5911yescharacteristic
819C22C59×#57511yescharacteristic
820C22C59×#57611yescharacteristic
821C22C59×#57711yescharacteristic
822C4—22no—
823C4—22no—
824C4—41no—
825C4—41no—
826C4—42no—
827C4—42no—
828C4—41no—
829C4—42no—
830C4—81no—
831C4—81no—
832C4C59×#52511yescharacteristic
833C4C59×#53811yescharacteristic
834C4D42×C5911yescharacteristic
835C4C59×#54611yescharacteristic
836C2—42no—
837C2—82no—
838C2—82no—
839C2—161no—
840C2C59×#242411yescharacteristic
841C2C59×#303611yescharacteristic
842C2C59×#304511yescharacteristic
843C2C59×#327111yescharacteristic
844C2C59×#327411yescharacteristic
845C2C59×#330611yescharacteristic
846C2C59×#332211yescharacteristic
subgroupG/H
center, socleC23×C59C22×D4
commutator, Frattini, cosocleC22×C4C24×C59
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C59 ◁ C4×C22⋊C4×C59 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C59×#469C2semidirect
2. C2×C59×#463C2semidirect
3. C2×C59×#449C2semidirect
4. C2×C59×#417C2semidirect
5. C59×#2431C2semidirect
6. C59×#2361C2semidirect
7. C59×#2065C2semidirect
8. C59×#2055C2semidirect
9. C59×#2042C2semidirect
10. C59×#2011C2semidirect
11. C59×#1982C2semidirect
12. C59×#1927C2semidirect
13. C59×#1879C2semidirect
14. C59×#1874C2semidirect
15. C59×#1851C2semidirect
105. #121×C59D4semidirect
136. #103×C59D4semidirect
363. #25106C59direct (N × H)
413. C2×#469C2×C59semidirect
414. C2×#463C2×C59semidirect
415. C2×#449C2×C59semidirect
416. C2×#417C2×C59semidirect
417. #2431C2×C59semidirect
418. #2361C2×C59semidirect
419. #2065C2×C59semidirect
420. #2055C2×C59semidirect
421. #2042C2×C59semidirect
422. #2011C2×C59semidirect
423. #1982C2×C59semidirect
424. #1927C2×C59semidirect
425. #1879C2×C59semidirect
426. #1874C2×C59semidirect
427. #1851C2×C59semidirect
486. C59#25106direct (N × H)
529. #121D4×C59semidirect
560. #103D4×C59semidirect

Maximal subgroups

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

subgroupindex
C2×C59×#4692
C2×C59×#4632
C2×C59×#4492
C2×C59×#4172
C59×#24312
C59×#23612
C59×#20652
C59×#20552
C59×#20422
C59×#20112
C59×#19822
C59×#19272
C59×#18792
C59×#18742
C59×#18512
#2510659