Finite Group Databasebeta

← C59×#23894 #28436003

Subgroups — C59×#23894 #28436003

Order 15104.

1642 conjugacy classes of subgroups.

The subgroup lattice has 1018 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C59×#3586C211yesmaximal, characteristic, complemented
2C59×#3585C211yesmaximal, characteristic, complemented
3C59×#3020C211yesmaximal, characteristic, complemented
4C59×#3019C211yesmaximal, characteristic, complemented
5C59×#3010C211yesmaximal, characteristic, complemented
6C59×#3009C211yesmaximal, characteristic, complemented
7C59×#2019C211yesmaximal, characteristic, complemented
8C59×#2017C211yesmaximal, characteristic, complemented
9C59×#2009C211yesmaximal, characteristic, complemented
10C59×#2008C211yesmaximal, characteristic, complemented
11C59×#1903C211yesmaximal, characteristic, complemented
12C59×#1902C211yesmaximal, characteristic, complemented
13C59×#1881C211yesmaximal, characteristic, complemented
14C59×#1881C211yesmaximal, characteristic, complemented
15C59×#1794C211yesmaximal, characteristic, complemented
16C59×#585C2211yescharacteristic
17C2×2−1+4×C59C2211yescharacteristic, complemented
18C2×H(5,𝔽2)×C59C2211yescharacteristic
19C59×#578—22no—
20C59×#578—22no—
21C59×#577—22no—
22C59×#577—22no—
23C59×#577—22no—
24C59×#577—22no—
25C59×#576—22no—
26C59×#576—22no—
27C59×#575—22no—
28C59×#575—22no—
29C59×#575C2211yescharacteristic
30C59×#575C2211yescharacteristic
31C59×#575C2211yescharacteristic
32C59×#575C2211yescharacteristic, complemented
33C59×#575C2211yescharacteristic, complemented
34C2×#137×C59—22no—
35C2×#137×C59C2211yescharacteristic
36C2×#137×C59C2211yescharacteristic, complemented
37C2×AGL(1,ℤ/8)×C59—22no—
38C2×AGL(1,ℤ/8)×C59C2211yescharacteristic
39C2×AGL(1,ℤ/8)×C59C2211yescharacteristic
40C22×SD16×C59C2211yescharacteristic, complemented
41C59×#568C2211yescharacteristic
42C59×#568C2211yescharacteristic, complemented
43C59×#536C2211yescharacteristic, complemented
44C59×#535C2211yescharacteristic, complemented
45C59×#456—22no—
46C59×#455—22no—
47C59×#454—22no—
48C59×#453—22no—
49C59×#452—22no—
50C59×#450—22no—
51C59×#449—22no—
52C59×#448—22no—
53C59×#421C2211yescharacteristic
54C59×#421C2211yescharacteristic, complemented
55C59×#421C2211yescharacteristic, complemented
56C59×#421C2211yescharacteristic, complemented
57C59×#419C2211yescharacteristic, complemented
58C59×#418C2211yescharacteristic, complemented
59C59×#416C2211yescharacteristic
60C59×#416C2211yescharacteristic, complemented
61C2×#101×C59C2211yescharacteristic, complemented
62C2×#100×C59C2211yescharacteristic, complemented
63C59×#410C2211yescharacteristic, complemented
64C59×#408C2211yescharacteristic, complemented
65C59×#408C2211yescharacteristic, complemented
66C59×#408C2211yescharacteristic, complemented
67C59×#344C2211yescharacteristic, complemented
68C59×#344C2211yescharacteristic, complemented
69C59×#341C2211yescharacteristic, complemented
70C59×#338C2211yescharacteristic, complemented
712−1+4×C59—22no—
722−1+4×C59—21no—
732−1+4×C59—22no—
742−1+4×C59—21no—
752−1+4×C59—22no—
762−1+4×C59—41no—
772−1+4×C59D412yescomplemented
78H(5,𝔽2)×C59—22no—
79H(5,𝔽2)×C59—21no—
80H(5,𝔽2)×C59—22no—
81H(5,𝔽2)×C59—21no—
82H(5,𝔽2)×C59—22no—
83H(5,𝔽2)×C59—41no—
84H(5,𝔽2)×C59—41no—
85H(5,𝔽2)×C59D412yescomplemented
86C2×#41×C59—22no—
87C2×#41×C59—22no—
88C2×#41×C59—21no—
89C2×#41×C59—21no—
90C2×#41×C59—21no—
91C2×#41×C59—21no—
92C2×#41×C59—41no—
93C2×#41×C59—41no—
94C2×#41×C59C2311yescharacteristic
95C2×#41×C59C2311yescharacteristic
96C2×#41×C59C2311yescharacteristic
97C2×#41×C59C2311yescharacteristic
98C2×#41×C59C2311yescharacteristic
99C22×Q8×C59—21no—
100C22×Q8×C59—21no—
101C22×Q8×C59C2311yescharacteristic
102C22×D4×C59—21no—
103C22×D4×C59—21no—
104C22×D4×C59—41no—
105C22×D4×C59C2311yescharacteristic
106#137×C59—24no—
107#137×C59—24no—
108#137×C59—24no—
109#137×C59—24no—
110#137×C59—22no—
111#137×C59—22no—
112#137×C59—21no—
113#137×C59—22no—
114#137×C59—21no—
115#137×C59—21no—
116#137×C59—21no—
117#137×C59—21no—
118#137×C59—21no—
119#137×C59—21no—
120#137×C59—21no—
121#137×C59—22no—
122#137×C59D412yes—
123#137×C59D412yescomplemented
124AGL(1,ℤ/8)×C59—24no—
125AGL(1,ℤ/8)×C59—24no—
126AGL(1,ℤ/8)×C59—24no—
127AGL(1,ℤ/8)×C59—24no—
128AGL(1,ℤ/8)×C59—22no—
129AGL(1,ℤ/8)×C59—22no—
130AGL(1,ℤ/8)×C59—21no—
131AGL(1,ℤ/8)×C59—22no—
132AGL(1,ℤ/8)×C59—21no—
133AGL(1,ℤ/8)×C59—21no—
134AGL(1,ℤ/8)×C59—21no—
135AGL(1,ℤ/8)×C59—21no—
136AGL(1,ℤ/8)×C59—21no—
137AGL(1,ℤ/8)×C59—21no—
138AGL(1,ℤ/8)×C59—21no—
139AGL(1,ℤ/8)×C59—22no—
140AGL(1,ℤ/8)×C59D412yes—
141AGL(1,ℤ/8)×C59D412yescomplemented
142#135×C59—24no—
143#135×C59—24no—
144#135×C59—24no—
145#135×C59—24no—
146#135×C59—22no—
147#135×C59—22no—
148#135×C59—22no—
149#135×C59—22no—
150#135×C59—41no—
151C2×Q16×C59—24no—
152C2×Q16×C59—21no—
153C2×Q16×C59D412yescomplemented
154C2×SD16×C59—24no—
155C2×SD16×C59—24no—
156C2×SD16×C59—21no—
157C2×SD16×C59—21no—
158C2×SD16×C59—22no—
159C2×SD16×C59—22no—
160C2×SD16×C59—41no—
161C2×SD16×C59D412yes—
162C2×SD16×C59D412yescomplemented
163C2×D8×C59—24no—
164C2×D8×C59—21no—
165C2×D8×C59D412yes—
166#131×C59—22no—
167#131×C59—22no—
168#131×C59—22no—
169#131×C59—22no—
170C2×M16×C59—22no—
171C2×M16×C59—22no—
172C2×M16×C59C2311yescharacteristic
173C2×M16×C59C2311yescharacteristic
174C2×M16×C59C2311yescharacteristic
175C2×M16×C59C2311yescharacteristic
176C2×M16×C59C2311yescharacteristic
177C22×C8×C59C2311yescharacteristic
178C4⋊Q8×C59—21no—
179#127×C59—21no—
180#124×C59—21no—
181#124×C59—21no—
182#123×C59—41no—
183C22⋊Q8×C59—22no—
184#121×C59—22no—
185#120×C59—41no—
186#117×C59C2311yescharacteristic
187#117×C59C2311yescharacteristic
188#104×C59—22no—
189#104×C59—22no—
190#104×C59—22no—
191#104×C59—22no—
192#103×C59—21no—
193#103×C59—21no—
194#103×C59—22no—
195#102×C59—21no—
196#102×C59—21no—
197#102×C59—22no—
198#101×C59—22no—
199#100×C59—22no—
200#99×C59—41no—
201C22⋊C8×C59—22no—
202C22⋊C8×C59—22no—
203C22⋊C8×C59—41no—
204C24×C59—21no—
205C24×C59—41no—
206#41×C59—21no—
207#41×C59—21no—
208#41×C59—21no—
209#41×C59—21no—
210#41×C59—24no—
211#41×C59—24no—
212#41×C59—22no—
213#41×C59—22no—
214#41×C59—22no—
215#41×C59—22no—
216#41×C59—21no—
217#41×C59—21no—
218#41×C59—21no—
219#41×C59—21no—
220#41×C59—21no—
221#41×C59—21no—
222#41×C59—21no—
223#41×C59—21no—
224#41×C59—21no—
225#41×C59—21no—
226#41×C59—21no—
227#41×C59—21no—
228#41×C59—42no—
229#41×C59—42no—
230#41×C59—42no—
231#41×C59—42no—
232#41×C59—42no—
233#41×C59—44no—
234#41×C59—42no—
235#41×C59—42no—
236#41×C59—42no—
237#41×C59—41no—
238#41×C59—41no—
239#41×C59—44no—
240#41×C59—42no—
241#41×C59—42no—
242#41×C59C2×D412yes—
243#41×C59C2×D412yes—
244#41×C59C2×D412yes—
245#41×C59C2×D412yes—
246C2×Q8×C59—21no—
247C2×Q8×C59—24no—
248C2×Q8×C59—22no—
249C2×Q8×C59—22no—
250C2×Q8×C59—21no—
251C2×Q8×C59—21no—
252C2×Q8×C59—21no—
253C2×Q8×C59—21no—
254C2×Q8×C59—41no—
255C2×Q8×C59—42no—
256C2×Q8×C59—42no—
257C2×Q8×C59—41no—
258C2×Q8×C59—42no—
259C2×Q8×C59C2×D412yes—
260C2×Q8×C59C2×D411yescharacteristic
261C2×Q8×C59C2×D411yescharacteristic
262C2×Q8×C59C2×D411yescharacteristic
263C2×Q8×C59C2×D411yescharacteristic
264C2×Q8×C59C2×D411yescharacteristic
265C2×D4×C59—21no—
266C2×D4×C59—21no—
267C2×D4×C59—24no—
268C2×D4×C59—22no—
269C2×D4×C59—22no—
270C2×D4×C59—21no—
271C2×D4×C59—21no—
272C2×D4×C59—21no—
273C2×D4×C59—21no—
274C2×D4×C59—21no—
275C2×D4×C59—21no—
276C2×D4×C59—21no—
277C2×D4×C59—21no—
278C2×D4×C59—42no—
279C2×D4×C59—41no—
280C2×D4×C59—41no—
281C2×D4×C59—42no—
282C2×D4×C59—42no—
283C2×D4×C59—41no—
284C2×D4×C59—44no—
285C2×D4×C59—42no—
286C2×D4×C59—42no—
287C2×D4×C59—44no—
288C2×D4×C59—41no—
289C2×D4×C59—42no—
290C2×D4×C59—42no—
291C2×D4×C59C2×D412yes—
292C2×D4×C59C2×D411yescharacteristic
293C2×D4×C59C2×D411yescharacteristic
294C2×D4×C59C2×D411yescharacteristic
295C2×D4×C59C2×D411yescharacteristic
296C2×D4×C59C2×D411yescharacteristic
297C22×C4×C59—21no—
298C22×C4×C59—21no—
299C22×C4×C59—21no—
300C22×C4×C59—21no—
301C22×C4×C59—21no—
302C22×C4×C59—21no—
303C22×C4×C59—41no—
304C22×C4×C59—42no—
305C22×C4×C59—41no—
306C22×C4×C59—41no—
307C22×C4×C59C2411yescharacteristic
308Q16×C59—24no—
309Q16×C59—22no—
310Q16×C59—22no—
311Q16×C59—22no—
312Q16×C59—24no—
313Q16×C59—22no—
314Q16×C59—41no—
315SD16×C59—24no—
316SD16×C59—22no—
317SD16×C59—24no—
318SD16×C59—22no—
319SD16×C59—22no—
320SD16×C59—22no—
321SD16×C59—22no—
322SD16×C59—24no—
323SD16×C59—22no—
324SD16×C59—22no—
325SD16×C59—24no—
326SD16×C59—22no—
327SD16×C59—44no—
328SD16×C59—41no—
329SD16×C59—41no—
330D8×C59—24no—
331D8×C59—22no—
332D8×C59—22no—
333D8×C59—22no—
334D8×C59—24no—
335D8×C59—22no—
336D8×C59—41no—
337M16×C59—24no—
338M16×C59—24no—
339M16×C59—21no—
340M16×C59—21no—
341M16×C59—21no—
342M16×C59—21no—
343M16×C59—21no—
344M16×C59—21no—
345M16×C59—21no—
346M16×C59—21no—
347M16×C59C2×D412yes—
348M16×C59C2×D412yes—
349C2×C8×C59—24no—
350C2×C8×C59—24no—
351C2×C8×C59—21no—
352C2×C8×C59—21no—
353C2×C8×C59—21no—
354C2×C8×C59—21no—
355C2×C8×C59—21no—
356C2×C8×C59—21no—
357C2×C8×C59C2×D412yes—
358C2×C8×C59C2×D412yes—
359C4⋊C4×C59—21no—
360C4⋊C4×C59—21no—
361C4⋊C4×C59—42no—
362C22⋊C4×C59—21no—
363C22⋊C4×C59—21no—
364C22⋊C4×C59—42no—
365C22⋊C4×C59—42no—
366C42×C59—21no—
367C42×C59—21no—
368C23×C59—21no—
369C23×C59—21no—
370C23×C59—21no—
371C23×C59—21no—
372C23×C59—21no—
373C23×C59—22no—
374C23×C59—42no—
375C23×C59—44no—
376C23×C59—41no—
377C23×C59—41no—
378C23×C59—161no—
379C23×C59—162no—
380C23×C59H(5,𝔽2)11yescharacteristic
381Q8×C59—21no—
382Q8×C59—21no—
383Q8×C59—21no—
384Q8×C59—21no—
385Q8×C59—22no—
386Q8×C59—21no—
387Q8×C59—21no—
388Q8×C59—22no—
389Q8×C59—21no—
390Q8×C59—21no—
391Q8×C59—42no—
392Q8×C59—44no—
393Q8×C59—41no—
394Q8×C59—41no—
395Q8×C59#12012yes—
396Q8×C59#12012yes—
397D4×C59—22no—
398D4×C59—22no—
399D4×C59—22no—
400D4×C59—22no—
401D4×C59—21no—
402D4×C59—21no—
403D4×C59—22no—
404D4×C59—21no—
405D4×C59—21no—
406D4×C59—21no—
407D4×C59—21no—
408D4×C59—21no—
409D4×C59—21no—
410D4×C59—22no—
411D4×C59—42no—
412D4×C59—42no—
413D4×C59—44no—
414D4×C59—42no—
415D4×C59—44no—
416D4×C59—44no—
417D4×C59—41no—
418D4×C59—41no—
419D4×C59—41no—
420D4×C59—41no—
421D4×C59—41no—
422D4×C59—41no—
423D4×C59—41no—
424D4×C59—41no—
425D4×C59—162no—
426D4×C59#12012yes—
427D4×C59#12012yes—
428C2×C4×C59—21no—
429C2×C4×C59—21no—
430C2×C4×C59—22no—
431C2×C4×C59—22no—
432C2×C4×C59—22no—
433C2×C4×C59—22no—
434C2×C4×C59—21no—
435C2×C4×C59—21no—
436C2×C4×C59—22no—
437C2×C4×C59—21no—
438C2×C4×C59—42no—
439C2×C4×C59—42no—
440C2×C4×C59—42no—
441C2×C4×C59—44no—
442C2×C4×C59—44no—
443C2×C4×C59—44no—
444C2×C4×C59—41no—
445C2×C4×C59—41no—
446C2×C4×C59—41no—
447C2×C4×C59—41no—
448C2×C4×C59—41no—
449C2×C4×C59—41no—
450C2×C4×C59—41no—
451C2×C4×C59—41no—
452C2×C4×C59—41no—
453C2×C4×C59—41no—
454C2×C4×C59C22×D411yescharacteristic
455C2×C4×C59C22×D411yescharacteristic
456C2×C4×C59C22×D411yescharacteristic
457C2×C4×C59C22×D411yescharacteristic
458C2×C4×C59C22×D411yescharacteristic
459C2×C4×C59H(5,𝔽2)11yescharacteristic
460C8×C59—22no—
461C8×C59—22no—
462C8×C59—22no—
463C8×C59—22no—
464C8×C59—41no—
465C8×C59—41no—
466#23894C5911yesmaximal, characteristic, direct product factor, Sylow
467C22×C59—22no—
468C22×C59—22no—
469C22×C59—41no—
470C22×C59—42no—
471C22×C59—42no—
472C22×C59—41no—
473C22×C59—41no—
474C22×C59—41no—
475C22×C59—42no—
476C22×C59—81no—
477C22×C59—81no—
478C22×C59—82no—
479C22×C59—81no—
480C22×C59—82no—
481C22×C59—161no—
482C22×C59—162no—
483C22×C59—164no—
484C22×C59#53411yescharacteristic
485C22×C59D4211yescharacteristic
486C22×C59D4211yescharacteristic
487C4×C59—22no—
488C4×C59—22no—
489C4×C59—41no—
490C4×C59—41no—
491C4×C59—41no—
492C4×C59—42no—
493C4×C59—81no—
494C4×C59—81no—
495C4×C59C2×#12011yescharacteristic
496C4×C59C2×#12011yescharacteristic
497C4×C59D4211yescharacteristic
498C4×C59D4211yescharacteristic
499#3586C2×C5911yescharacteristic, complemented
500#3585C2×C5911yescharacteristic, complemented
501#3020C2×C5911yescharacteristic, complemented
502#3019C2×C5911yescharacteristic, complemented
503#3010C2×C5911yescharacteristic, complemented
504#3009C2×C5911yescharacteristic, complemented
505#2019C2×C5911yescharacteristic, complemented
506#2017C2×C5911yescharacteristic, complemented
507#2009C2×C5911yescharacteristic, complemented
508#2008C2×C5911yescharacteristic, complemented
509#1903C2×C5911yescharacteristic, complemented
510#1902C2×C5911yescharacteristic, complemented
511#1881C2×C5911yescharacteristic, complemented
512#1881C2×C5911yescharacteristic, complemented
513#1794C2×C5911yescharacteristic, complemented
514C2×C59—21no—
515C2×C59—21no—
516C2×C59—21no—
517C2×C59—42no—
518C2×C59—42no—
519C2×C59—81no—
520C2×C59—81no—
521C2×C59—82no—
522C2×C59—81no—
523C2×C59#240311yescharacteristic
524#585C22×C5911yescharacteristic
525C2×2−1+4C22×C5911yescharacteristic, complemented
526C2×H(5,𝔽2)C22×C5911yescharacteristic
527#578—22no—
528#578—22no—
529#577—22no—
530#577—22no—
531#577—22no—
532#577—22no—
533#576—22no—
534#576—22no—
535#575—22no—
536#575—22no—
537#575C22×C5911yescharacteristic
538#575C22×C5911yescharacteristic
539#575C22×C5911yescharacteristic
540#575C22×C5911yescharacteristic, complemented
541#575C22×C5911yescharacteristic, complemented
542C2×#137—22no—
543C2×#137C22×C5911yescharacteristic
544C2×#137C22×C5911yescharacteristic, complemented
545C2×AGL(1,ℤ/8)—22no—
546C2×AGL(1,ℤ/8)C22×C5911yescharacteristic
547C2×AGL(1,ℤ/8)C22×C5911yescharacteristic
548C22×SD16C22×C5911yescharacteristic, complemented
549#568C22×C5911yescharacteristic
550#568C22×C5911yescharacteristic, complemented
551#536C22×C5911yescharacteristic, complemented
552#535C22×C5911yescharacteristic, complemented
553#456—22no—
554#455—22no—
555#454—22no—
556#453—22no—
557#452—22no—
558#450—22no—
559#449—22no—
560#448—22no—
561#421C22×C5911yescharacteristic
562#421C22×C5911yescharacteristic, complemented
563#421C22×C5911yescharacteristic, complemented
564#421C22×C5911yescharacteristic, complemented
565#419C22×C5911yescharacteristic, complemented
566#418C22×C5911yescharacteristic, complemented
567#416C22×C5911yescharacteristic
568#416C22×C5911yescharacteristic, complemented
569C2×#101C22×C5911yescharacteristic, complemented
570C2×#100C22×C5911yescharacteristic, complemented
571#410C22×C5911yescharacteristic, complemented
572#408C22×C5911yescharacteristic, complemented
573#408C22×C5911yescharacteristic, complemented
574#408C22×C5911yescharacteristic, complemented
575#344C22×C5911yescharacteristic, complemented
576#344C22×C5911yescharacteristic, complemented
577#341C22×C5911yescharacteristic, complemented
578#338C22×C5911yescharacteristic, complemented
579C59#2389411yescharacteristic, direct product factor, Sylow
5802−1+4—22no—
5812−1+4—21no—
5822−1+4—22no—
5832−1+4—21no—
5842−1+4—22no—
5852−1+4—41no—
5862−1+4D4×C5912yescomplemented
587H(5,𝔽2)—22no—
588H(5,𝔽2)—21no—
589H(5,𝔽2)—22no—
590H(5,𝔽2)—21no—
591H(5,𝔽2)—22no—
592H(5,𝔽2)—41no—
593H(5,𝔽2)—41no—
594H(5,𝔽2)D4×C5912yescomplemented
595C2×#41—22no—
596C2×#41—22no—
597C2×#41—21no—
598C2×#41—21no—
599C2×#41—21no—
600C2×#41—21no—
601C2×#41—41no—
602C2×#41—41no—
603C2×#41C23×C5911yescharacteristic
604C2×#41C23×C5911yescharacteristic
605C2×#41C23×C5911yescharacteristic
606C2×#41C23×C5911yescharacteristic
607C2×#41C23×C5911yescharacteristic
608C22×Q8—21no—
609C22×Q8—21no—
610C22×Q8C23×C5911yescharacteristic
611C22×D4—21no—
612C22×D4—21no—
613C22×D4—41no—
614C22×D4C23×C5911yescharacteristic
615#137—24no—
616#137—24no—
617#137—24no—
618#137—24no—
619#137—22no—
620#137—22no—
621#137—21no—
622#137—22no—
623#137—21no—
624#137—21no—
625#137—21no—
626#137—21no—
627#137—21no—
628#137—21no—
629#137—21no—
630#137—22no—
631#137D4×C5912yes—
632#137D4×C5912yescomplemented
633AGL(1,ℤ/8)—24no—
634AGL(1,ℤ/8)—24no—
635AGL(1,ℤ/8)—24no—
636AGL(1,ℤ/8)—24no—
637AGL(1,ℤ/8)—22no—
638AGL(1,ℤ/8)—22no—
639AGL(1,ℤ/8)—21no—
640AGL(1,ℤ/8)—22no—
641AGL(1,ℤ/8)—21no—
642AGL(1,ℤ/8)—21no—
643AGL(1,ℤ/8)—21no—
644AGL(1,ℤ/8)—21no—
645AGL(1,ℤ/8)—21no—
646AGL(1,ℤ/8)—21no—
647AGL(1,ℤ/8)—21no—
648AGL(1,ℤ/8)—22no—
649AGL(1,ℤ/8)D4×C5912yes—
650AGL(1,ℤ/8)D4×C5912yescomplemented
651#135—24no—
652#135—24no—
653#135—24no—
654#135—24no—
655#135—22no—
656#135—22no—
657#135—22no—
658#135—22no—
659#135—41no—
660C2×Q16—24no—
661C2×Q16—21no—
662C2×Q16D4×C5912yescomplemented
663C2×SD16—24no—
664C2×SD16—24no—
665C2×SD16—21no—
666C2×SD16—21no—
667C2×SD16—22no—
668C2×SD16—22no—
669C2×SD16—41no—
670C2×SD16D4×C5912yes—
671C2×SD16D4×C5912yescomplemented
672C2×D8—24no—
673C2×D8—21no—
674C2×D8D4×C5912yes—
675#131—22no—
676#131—22no—
677#131—22no—
678#131—22no—
679C2×M16—22no—
680C2×M16—22no—
681C2×M16C23×C5911yescharacteristic
682C2×M16C23×C5911yescharacteristic
683C2×M16C23×C5911yescharacteristic
684C2×M16C23×C5911yescharacteristic
685C2×M16C23×C5911yescharacteristic
686C22×C8C23×C5911yescharacteristic
687C4⋊Q8—21no—
688#127—21no—
689#124—21no—
690#124—21no—
691#123—41no—
692C22⋊Q8—22no—
693#121—22no—
694#120—41no—
695#117C23×C5911yescharacteristic
696#117C23×C5911yescharacteristic
697#104—22no—
698#104—22no—
699#104—22no—
700#104—22no—
701#103—21no—
702#103—21no—
703#103—22no—
704#102—21no—
705#102—21no—
706#102—22no—
707#101—22no—
708#100—22no—
709#99—41no—
710C22⋊C8—22no—
711C22⋊C8—22no—
712C22⋊C8—41no—
713C24—21no—
714C24—41no—
715#41—21no—
716#41—21no—
717#41—21no—
718#41—21no—
719#41—24no—
720#41—24no—
721#41—22no—
722#41—22no—
723#41—22no—
724#41—22no—
725#41—21no—
726#41—21no—
727#41—21no—
728#41—21no—
729#41—21no—
730#41—21no—
731#41—21no—
732#41—21no—
733#41—21no—
734#41—21no—
735#41—21no—
736#41—21no—
737#41—42no—
738#41—42no—
739#41—42no—
740#41—42no—
741#41—42no—
742#41—44no—
743#41—42no—
744#41—42no—
745#41—42no—
746#41—41no—
747#41—41no—
748#41—44no—
749#41—42no—
750#41—42no—
751#41C2×D4×C5912yes—
752#41C2×D4×C5912yes—
753#41C2×D4×C5912yes—
754#41C2×D4×C5912yes—
755C2×Q8—21no—
756C2×Q8—24no—
757C2×Q8—22no—
758C2×Q8—22no—
759C2×Q8—21no—
760C2×Q8—21no—
761C2×Q8—21no—
762C2×Q8—21no—
763C2×Q8—41no—
764C2×Q8—42no—
765C2×Q8—42no—
766C2×Q8—41no—
767C2×Q8—42no—
768C2×Q8C2×D4×C5912yes—
769C2×Q8C2×D4×C5911yescharacteristic
770C2×Q8C2×D4×C5911yescharacteristic
771C2×Q8C2×D4×C5911yescharacteristic
772C2×Q8C2×D4×C5911yescharacteristic
773C2×Q8C2×D4×C5911yescharacteristic
774C2×D4—21no—
775C2×D4—21no—
776C2×D4—24no—
777C2×D4—22no—
778C2×D4—22no—
779C2×D4—21no—
780C2×D4—21no—
781C2×D4—21no—
782C2×D4—21no—
783C2×D4—21no—
784C2×D4—21no—
785C2×D4—21no—
786C2×D4—21no—
787C2×D4—42no—
788C2×D4—41no—
789C2×D4—41no—
790C2×D4—42no—
791C2×D4—42no—
792C2×D4—41no—
793C2×D4—44no—
794C2×D4—42no—
795C2×D4—42no—
796C2×D4—44no—
797C2×D4—41no—
798C2×D4—42no—
799C2×D4—42no—
800C2×D4C2×D4×C5912yes—
801C2×D4C2×D4×C5911yescharacteristic
802C2×D4C2×D4×C5911yescharacteristic
803C2×D4C2×D4×C5911yescharacteristic
804C2×D4C2×D4×C5911yescharacteristic
805C2×D4C2×D4×C5911yescharacteristic
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—41no—
813C22×C4—42no—
814C22×C4—41no—
815C22×C4—41no—
816C22×C4C24×C5911yescharacteristic
817Q16—24no—
818Q16—22no—
819Q16—22no—
820Q16—22no—
821Q16—24no—
822Q16—22no—
823Q16—41no—
824SD16—24no—
825SD16—22no—
826SD16—24no—
827SD16—22no—
828SD16—22no—
829SD16—22no—
830SD16—22no—
831SD16—24no—
832SD16—22no—
833SD16—22no—
834SD16—24no—
835SD16—22no—
836SD16—44no—
837SD16—41no—
838SD16—41no—
839D8—24no—
840D8—22no—
841D8—22no—
842D8—22no—
843D8—24no—
844D8—22no—
845D8—41no—
846M16—24no—
847M16—24no—
848M16—21no—
849M16—21no—
850M16—21no—
851M16—21no—
852M16—21no—
853M16—21no—
854M16—21no—
855M16—21no—
856M16C2×D4×C5912yes—
857M16C2×D4×C5912yes—
858C2×C8—24no—
859C2×C8—24no—
860C2×C8—21no—
861C2×C8—21no—
862C2×C8—21no—
863C2×C8—21no—
864C2×C8—21no—
865C2×C8—21no—
866C2×C8C2×D4×C5912yes—
867C2×C8C2×D4×C5912yes—
868C4⋊C4—21no—
869C4⋊C4—21no—
870C4⋊C4—42no—
871C22⋊C4—21no—
872C22⋊C4—21no—
873C22⋊C4—42no—
874C22⋊C4—42no—
875C42—21no—
876C42—21no—
877C23—21no—
878C23—21no—
879C23—21no—
880C23—21no—
881C23—21no—
882C23—22no—
883C23—42no—
884C23—44no—
885C23—41no—
886C23—41no—
887C23—161no—
888C23—162no—
889C23H(5,𝔽2)×C5911yescharacteristic
890Q8—21no—
891Q8—21no—
892Q8—21no—
893Q8—21no—
894Q8—22no—
895Q8—21no—
896Q8—21no—
897Q8—22no—
898Q8—21no—
899Q8—21no—
900Q8—42no—
901Q8—44no—
902Q8—41no—
903Q8—41no—
904Q8#120×C5912yes—
905Q8#120×C5912yes—
906D4—22no—
907D4—22no—
908D4—22no—
909D4—22no—
910D4—21no—
911D4—21no—
912D4—22no—
913D4—21no—
914D4—21no—
915D4—21no—
916D4—21no—
917D4—21no—
918D4—21no—
919D4—22no—
920D4—42no—
921D4—42no—
922D4—44no—
923D4—42no—
924D4—44no—
925D4—44no—
926D4—41no—
927D4—41no—
928D4—41no—
929D4—41no—
930D4—41no—
931D4—41no—
932D4—41no—
933D4—41no—
934D4—162no—
935D4#120×C5912yes—
936D4#120×C5912yes—
937C2×C4—21no—
938C2×C4—21no—
939C2×C4—22no—
940C2×C4—22no—
941C2×C4—22no—
942C2×C4—22no—
943C2×C4—21no—
944C2×C4—21no—
945C2×C4—22no—
946C2×C4—21no—
947C2×C4—42no—
948C2×C4—42no—
949C2×C4—42no—
950C2×C4—44no—
951C2×C4—44no—
952C2×C4—44no—
953C2×C4—41no—
954C2×C4—41no—
955C2×C4—41no—
956C2×C4—41no—
957C2×C4—41no—
958C2×C4—41no—
959C2×C4—41no—
960C2×C4—41no—
961C2×C4—41no—
962C2×C4—41no—
963C2×C4C22×D4×C5911yescharacteristic
964C2×C4C22×D4×C5911yescharacteristic
965C2×C4C22×D4×C5911yescharacteristic
966C2×C4C22×D4×C5911yescharacteristic
967C2×C4C22×D4×C5911yescharacteristic
968C2×C4H(5,𝔽2)×C5911yescharacteristic
969C8—22no—
970C8—22no—
971C8—22no—
972C8—22no—
973C8—41no—
974C8—41no—
975C22—22no—
976C22—22no—
977C22—41no—
978C22—42no—
979C22—42no—
980C22—41no—
981C22—41no—
982C22—41no—
983C22—42no—
984C22—81no—
985C22—81no—
986C22—82no—
987C22—81no—
988C22—82no—
989C22—161no—
990C22—162no—
991C22—164no—
992C22C59×#53411yescharacteristic
993C22D42×C5911yescharacteristic
994C22D42×C5911yescharacteristic
995C4—22no—
996C4—22no—
997C4—41no—
998C4—41no—
999C4—41no—
1000C4—42no—
1001C4—81no—
1002C4—81no—
1003C4C2×#120×C5911yescharacteristic
1004C4C2×#120×C5911yescharacteristic
1005C4D42×C5911yescharacteristic
1006C4D42×C5911yescharacteristic
1007C2—21no—
1008C2—21no—
1009C2—21no—
1010C2—42no—
1011C2—42no—
1012C2—81no—
1013C2—81no—
1014C2—82no—
1015C2—81no—
1016C2C59×#240311yescharacteristic
subgroupG/H
center, socleC2×C59#2403
commutator, Frattini, cosocleC22×C4C24×C59
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C59 ◁ C22×C4×C59 ◁ G

Complements

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

NH ≅ G/Ntype
1. C59×#3586C2semidirect
2. C59×#3585C2semidirect
3. C59×#3020C2semidirect
4. C59×#3019C2semidirect
5. C59×#3010C2semidirect
6. C59×#3009C2semidirect
7. C59×#2019C2semidirect
8. C59×#2017C2semidirect
9. C59×#2009C2semidirect
10. C59×#2008C2semidirect
11. C59×#1903C2semidirect
12. C59×#1902C2semidirect
13. C59×#1881C2semidirect
14. C59×#1881C2semidirect
15. C59×#1794C2semidirect
17. C2×2−1+4×C59C22semidirect
32. C59×#575C22semidirect
33. C59×#575C22semidirect
36. C2×#137×C59C22semidirect
40. C22×SD16×C59C22semidirect
42. C59×#568C22semidirect
43. C59×#536C22semidirect
44. C59×#535C22semidirect
54. C59×#421C22semidirect
55. C59×#421C22semidirect
56. C59×#421C22semidirect
57. C59×#419C22semidirect
58. C59×#418C22semidirect
60. C59×#416C22semidirect
61. C2×#101×C59C22semidirect
62. C2×#100×C59C22semidirect
63. C59×#410C22semidirect
64. C59×#408C22semidirect
65. C59×#408C22semidirect
66. C59×#408C22semidirect
67. C59×#344C22semidirect
68. C59×#344C22semidirect
69. C59×#341C22semidirect
70. C59×#338C22semidirect
77. 2−1+4×C59D4semidirect
85. H(5,𝔽2)×C59D4semidirect
123. #137×C59D4semidirect
141. AGL(1,ℤ/8)×C59D4semidirect
153. C2×Q16×C59D4semidirect
162. C2×SD16×C59D4semidirect
466. #23894C59direct (N × H)
499. #3586C2×C59semidirect
500. #3585C2×C59semidirect
501. #3020C2×C59semidirect
502. #3019C2×C59semidirect
503. #3010C2×C59semidirect
504. #3009C2×C59semidirect
505. #2019C2×C59semidirect
506. #2017C2×C59semidirect
507. #2009C2×C59semidirect
508. #2008C2×C59semidirect
509. #1903C2×C59semidirect
510. #1902C2×C59semidirect
511. #1881C2×C59semidirect
512. #1881C2×C59semidirect
513. #1794C2×C59semidirect
525. C2×2−1+4C22×C59semidirect
540. #575C22×C59semidirect
541. #575C22×C59semidirect
544. C2×#137C22×C59semidirect
548. C22×SD16C22×C59semidirect
550. #568C22×C59semidirect
551. #536C22×C59semidirect
552. #535C22×C59semidirect
562. #421C22×C59semidirect
563. #421C22×C59semidirect
564. #421C22×C59semidirect
565. #419C22×C59semidirect
566. #418C22×C59semidirect
568. #416C22×C59semidirect
569. C2×#101C22×C59semidirect
570. C2×#100C22×C59semidirect
571. #410C22×C59semidirect
572. #408C22×C59semidirect
573. #408C22×C59semidirect
574. #408C22×C59semidirect
575. #344C22×C59semidirect
576. #344C22×C59semidirect
577. #341C22×C59semidirect
578. #338C22×C59semidirect
579. C59#23894direct (N × H)
586. 2−1+4D4×C59semidirect
594. H(5,𝔽2)D4×C59semidirect
632. #137D4×C59semidirect
650. AGL(1,ℤ/8)D4×C59semidirect
662. C2×Q16D4×C59semidirect
671. C2×SD16D4×C59semidirect

Maximal subgroups

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

subgroupindex
C59×#35862
C59×#35852
C59×#30202
C59×#30192
C59×#30102
C59×#30092
C59×#20192
C59×#20172
C59×#20092
C59×#20082
C59×#19032
C59×#19022
C59×#18812
C59×#17942
#2389459