Finite Group Databasebeta

← C59×#18430 #28430539

Subgroups — C59×#18430 #28430539

Order 15104.

996 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C59×#3559C211yesmaximal, characteristic, complemented
2C59×#3217C211yesmaximal, characteristic, complemented
3C59×#3205C211yesmaximal, characteristic, complemented
4C59×#2641C211yesmaximal, characteristic, complemented
5C59×#1598C214yesmaximal, complemented
6C59×#1597C214yesmaximal, complemented
7C59×#1505C211yesmaximal, characteristic, complemented
8C59×#1500C211yesmaximal, characteristic, complemented
9C59×#1470C211yesmaximal, characteristic, complemented
10C59×#563—21no—
11C59×#562—21no—
12C59×#554—21no—
13C59×#553—21no—
14C59×#553—21no—
15C59×#547—22no—
16C59×#547—21no—
17C59×#544—21no—
18C59×#540—21no—
19C59×#539—22no—
20C59×#539C2212yes—
21C59×#537C2212yes—
22C59×#532C2211yescharacteristic
23C2×#127×C59C2211yescharacteristic
24C59×#529C2211yescharacteristic
25C2×#125×C59C2211yescharacteristic
26C59×#496—21no—
27C59×#493—21no—
28C59×#490—21no—
29C59×#486—21no—
30C59×#460—21no—
31C59×#459—22no—
32C59×#459—21no—
33C59×#450C2212yes—
34C59×#447C2214yes—
35C59×#447C2212yes—
36C59×#432C2211yescharacteristic
37C59×#431C2211yescharacteristic
38C59×#394—22no—
39C59×#394C2214yes—
40C59×#390—21no—
41C59×#390—21no—
42C59×#376C2211yescharacteristic
43C59×#328C2212yes—
44C59×#327C2212yes—
45C59×#327C2214yes—
46C59×#324C2214yes—
47C2×#41×C59—21no—
48C2×#41×C59—22no—
49C22×D4×C59—21no—
50C22×D4×C59—21no—
51C22×D4×C59C2312yes—
52C2×SD16×C59—22no—
53C2×D8×C59—24no—
54C2×D8×C59—22no—
55C4⋊Q8×C59—21no—
56C4⋊Q8×C59—22no—
57C4⋊Q8×C59D411yescharacteristic
58#127×C59—21no—
59#127×C59—21no—
60#127×C59—21no—
61#127×C59—21no—
62#127×C59D411yescharacteristic
63#126×C59—22no—
64#126×C59—22no—
65#126×C59—21no—
66#125×C59—21no—
67#125×C59—22no—
68#125×C59—21no—
69#125×C59—21no—
70#125×C59—21no—
71#125×C59—21no—
72#125×C59D411yescharacteristic
73#124×C59—21no—
74#124×C59D411yescharacteristic
75#123×C59—22no—
76#123×C59—22no—
77#123×C59—22no—
78#123×C59—22no—
79#123×C59—22no—
80#123×C59—21no—
81#123×C59—22no—
82C22⋊Q8×C59—22no—
83C22⋊Q8×C59—22no—
84C22⋊Q8×C59—22no—
85C22⋊Q8×C59—22no—
86C22⋊Q8×C59—22no—
87C22⋊Q8×C59—22no—
88C22⋊Q8×C59C2311yescharacteristic
89#121×C59—21no—
90#121×C59—22no—
91#121×C59—21no—
92#121×C59—22no—
93#121×C59—22no—
94#121×C59—21no—
95#121×C59—22no—
96#121×C59C2311yescharacteristic
97#121×C59C2312yes—
98C4×Q8×C59D411yescharacteristic
99C4×D4×C59—22no—
100C4×D4×C59—21no—
101C4×D4×C59—21no—
102C4×D4×C59—21no—
103C4×D4×C59—22no—
104C4×D4×C59—21no—
105C4×D4×C59D411yescharacteristic
106C4×D4×C59D412yes—
107#117×C59—21no—
108#117×C59—21no—
109C2×C4⋊C4×C59—22no—
110C2×C4⋊C4×C59—21no—
111C2×C4⋊C4×C59D411yescharacteristic
112C2×C4⋊C4×C59D411yescharacteristic
113C2×C4⋊C4×C59D412yes—
114C2×C4⋊C4×C59C2312yes—
115C2×C22⋊C4×C59—24no—
116C2×C22⋊C4×C59—24no—
117C2×C42×C59—21no—
118C2×C42×C59C2311yescharacteristic
119C4⋊C8×C59—21no—
120C4⋊C8×C59—21no—
121#102×C59—24no—
122#102×C59—22no—
123#102×C59—22no—
124C22⋊C8×C59C2312yes—
125C22⋊C8×C59C2312yes—
126#97×C59—21no—
127C4×C8×C59—21no—
128#95×C59—21no—
129#95×C59C2312yes—
130C24×C59—22no—
131#41×C59—82no—
132#41×C59—84no—
133C2×Q8×C59—22no—
134C2×Q8×C59—21no—
135C2×Q8×C59C2×D411yescharacteristic
136C2×D4×C59—21no—
137C2×D4×C59—22no—
138C2×D4×C59—22no—
139C2×D4×C59—22no—
140C2×D4×C59—21no—
141C2×D4×C59—21no—
142C2×D4×C59—22no—
143C2×D4×C59—22no—
144C2×D4×C59—44no—
145C2×D4×C59—41no—
146C2×D4×C59—41no—
147C2×D4×C59—41no—
148C2×D4×C59—41no—
149C2×D4×C59—82no—
150C2×D4×C59—82no—
151C2×D4×C59C2×D411yescharacteristic
152C2×D4×C59C2×D412yes—
153C22×C4×C59—22no—
154C22×C4×C59—22no—
155C22×C4×C59—22no—
156C22×C4×C59—21no—
157C22×C4×C59—22no—
158C22×C4×C59—22no—
159C22×C4×C59C2×D412yes—
160C22×C4×C59C2×D411yescharacteristic
161C22×C4×C59C2×D411yescharacteristic
162C22×C4×C59C2×D412yes—
163C22×C4×C59C2411yescharacteristic
164SD16×C59—82no—
165D8×C59—84no—
166D8×C59—82no—
167C2×C8×C59—22no—
168C2×C8×C59—22no—
169C4⋊C4×C59—22no—
170C4⋊C4×C59—22no—
171C4⋊C4×C59—22no—
172C4⋊C4×C59—22no—
173C4⋊C4×C59—21no—
174C4⋊C4×C59—21no—
175C4⋊C4×C59—22no—
176C4⋊C4×C59—21no—
177C4⋊C4×C59—21no—
178C4⋊C4×C59—22no—
179C4⋊C4×C59—21no—
180C4⋊C4×C59—21no—
181C4⋊C4×C59—21no—
182C4⋊C4×C59—21no—
183C4⋊C4×C59—22no—
184C4⋊C4×C59—22no—
185C4⋊C4×C59—21no—
186C4⋊C4×C59C2×D412yes—
187C4⋊C4×C59C2×D411yescharacteristic
188C4⋊C4×C59C2×D411yescharacteristic
189C22⋊C4×C59—22no—
190C22⋊C4×C59—22no—
191C22⋊C4×C59—22no—
192C22⋊C4×C59—22no—
193C22⋊C4×C59—22no—
194C22⋊C4×C59—21no—
195C22⋊C4×C59—21no—
196C22⋊C4×C59—21no—
197C22⋊C4×C59—21no—
198C22⋊C4×C59—22no—
199C22⋊C4×C59—21no—
200C22⋊C4×C59—22no—
201C22⋊C4×C59—84no—
202C22⋊C4×C59—84no—
203C42×C59—22no—
204C42×C59—21no—
205C42×C59—42no—
206C42×C59C2×D411yescharacteristic
207C42×C59C2×D411yescharacteristic
208C42×C59C2×D411yescharacteristic
209C42×C59C2×D411yescharacteristic
210C23×C59—21no—
211C23×C59—22no—
212C23×C59—44no—
213C23×C59—44no—
214C23×C59—42no—
215C23×C59—44no—
216C23×C59C22×D411yescharacteristic
217Q8×C59—41no—
218Q8×C59—81no—
219Q8×C59—82no—
220D4×C59—42no—
221D4×C59—41no—
222D4×C59—44no—
223D4×C59—42no—
224D4×C59—42no—
225D4×C59—44no—
226D4×C59—42no—
227D4×C59—42no—
228D4×C59—81no—
229D4×C59—82no—
230D4×C59—82no—
231D4×C59—82no—
232D4×C59—82no—
233D4×C59—82no—
234D4×C59—82no—
235C2×C4×C59—22no—
236C2×C4×C59—22no—
237C2×C4×C59—21no—
238C2×C4×C59—21no—
239C2×C4×C59—22no—
240C2×C4×C59—22no—
241C2×C4×C59—21no—
242C2×C4×C59—22no—
243C2×C4×C59—24no—
244C2×C4×C59—41no—
245C2×C4×C59—42no—
246C2×C4×C59—42no—
247C2×C4×C59—42no—
248C2×C4×C59—42no—
249C2×C4×C59—42no—
250C2×C4×C59—82no—
251C2×C4×C59—82no—
252C2×C4×C59—82no—
253C2×C4×C59—82no—
254C2×C4×C59#12011yescharacteristic
255C2×C4×C59#12011yescharacteristic
256C2×C4×C59#12011yescharacteristic
257C2×C4×C59#12011yescharacteristic
258C2×C4×C59C22×D411yescharacteristic
259C2×C4×C59C22×D411yescharacteristic
260C8×C59—42no—
261C8×C59—42no—
262#18430C5911yesmaximal, characteristic, direct product factor, Sylow
263C22×C59—21no—
264C22×C59—21no—
265C22×C59—42no—
266C22×C59—41no—
267C22×C59—41no—
268C22×C59—42no—
269C22×C59—42no—
270C22×C59—41no—
271C22×C59—88no—
272C22×C59—82no—
273C22×C59—82no—
274C22×C59—82no—
275C22×C59C2×#12011yescharacteristic
276C22×C59#57612yes—
277C4×C59—21no—
278C4×C59—21no—
279C4×C59—21no—
280C4×C59—21no—
281C4×C59—21no—
282C4×C59—42no—
283C4×C59—42no—
284C4×C59—41no—
285C4×C59—41no—
286C4×C59—42no—
287C4×C59—41no—
288C4×C59—82no—
289C4×C59#45412yes—
290#3559C2×C5911yescharacteristic, complemented
291#3217C2×C5911yescharacteristic, complemented
292#3205C2×C5911yescharacteristic, complemented
293#2641C2×C5911yescharacteristic, complemented
294#1598C2×C5914yescomplemented
295#1597C2×C5914yescomplemented
296#1505C2×C5911yescharacteristic, complemented
297#1500C2×C5911yescharacteristic, complemented
298#1470C2×C5911yescharacteristic, complemented
299C2×C59—22no—
300C2×C59—81no—
301C2×C59—82no—
302C2×C59—162no—
303C2×C59#300811yescharacteristic
304C2×C59C2×#45411yescharacteristic
305C2×C59#302711yescharacteristic
306#563—21no—
307#562—21no—
308#554—21no—
309#553—21no—
310#553—21no—
311#547—22no—
312#547—21no—
313#544—21no—
314#540—21no—
315#539—22no—
316#539C22×C5912yes—
317#537C22×C5912yes—
318#532C22×C5911yescharacteristic
319C2×#127C22×C5911yescharacteristic
320#529C22×C5911yescharacteristic
321C2×#125C22×C5911yescharacteristic
322#496—21no—
323#493—21no—
324#490—21no—
325#486—21no—
326#460—21no—
327#459—22no—
328#459—21no—
329#450C22×C5912yes—
330#447C22×C5914yes—
331#447C22×C5912yes—
332#432C22×C5911yescharacteristic
333#431C22×C5911yescharacteristic
334#394—22no—
335#394C22×C5914yes—
336#390—21no—
337#390—21no—
338#376C22×C5911yescharacteristic
339#328C22×C5912yes—
340#327C22×C5914yes—
341#327C22×C5912yes—
342#324C22×C5914yes—
343C59#1843011yescharacteristic, direct product factor, Sylow
344C2×#41—21no—
345C2×#41—22no—
346C22×D4—21no—
347C22×D4—21no—
348C22×D4C23×C5912yes—
349C2×SD16—22no—
350C2×D8—24no—
351C2×D8—22no—
352C4⋊Q8—21no—
353C4⋊Q8—22no—
354C4⋊Q8D4×C5911yescharacteristic
355#127—21no—
356#127—21no—
357#127—21no—
358#127—21no—
359#127D4×C5911yescharacteristic
360#126—22no—
361#126—22no—
362#126—21no—
363#125—21no—
364#125—22no—
365#125—21no—
366#125—21no—
367#125—21no—
368#125—21no—
369#125D4×C5911yescharacteristic
370#124—21no—
371#124D4×C5911yescharacteristic
372#123—22no—
373#123—22no—
374#123—22no—
375#123—22no—
376#123—22no—
377#123—21no—
378#123—22no—
379C22⋊Q8—22no—
380C22⋊Q8—22no—
381C22⋊Q8—22no—
382C22⋊Q8—22no—
383C22⋊Q8—22no—
384C22⋊Q8—22no—
385C22⋊Q8C23×C5911yescharacteristic
386#121—21no—
387#121—22no—
388#121—21no—
389#121—22no—
390#121—22no—
391#121—21no—
392#121—22no—
393#121C23×C5911yescharacteristic
394#121C23×C5912yes—
395C4×Q8D4×C5911yescharacteristic
396C4×D4—22no—
397C4×D4—21no—
398C4×D4—21no—
399C4×D4—21no—
400C4×D4—22no—
401C4×D4—21no—
402C4×D4D4×C5911yescharacteristic
403C4×D4D4×C5912yes—
404#117—21no—
405#117—21no—
406C2×C4⋊C4—22no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4D4×C5911yescharacteristic
409C2×C4⋊C4D4×C5912yes—
410C2×C4⋊C4D4×C5911yescharacteristic
411C2×C4⋊C4C23×C5912yes—
412C2×C22⋊C4—24no—
413C2×C22⋊C4—24no—
414C2×C42—21no—
415C2×C42C23×C5911yescharacteristic
416C4⋊C8—21no—
417C4⋊C8—21no—
418#102—24no—
419#102—22no—
420#102—22no—
421C22⋊C8C23×C5912yes—
422C22⋊C8C23×C5912yes—
423#97—21no—
424C4×C8—21no—
425#95—21no—
426#95C23×C5912yes—
427C24—22no—
428#41—82no—
429#41—84no—
430C2×Q8—22no—
431C2×Q8—21no—
432C2×Q8C2×D4×C5911yescharacteristic
433C2×D4—21no—
434C2×D4—22no—
435C2×D4—22no—
436C2×D4—22no—
437C2×D4—21no—
438C2×D4—21no—
439C2×D4—22no—
440C2×D4—22no—
441C2×D4—44no—
442C2×D4—41no—
443C2×D4—41no—
444C2×D4—41no—
445C2×D4—41no—
446C2×D4—82no—
447C2×D4—82no—
448C2×D4C2×D4×C5911yescharacteristic
449C2×D4C2×D4×C5912yes—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—21no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4C2×D4×C5912yes—
457C22×C4C2×D4×C5911yescharacteristic
458C22×C4C2×D4×C5911yescharacteristic
459C22×C4C2×D4×C5912yes—
460C22×C4C24×C5911yescharacteristic
461SD16—82no—
462D8—84no—
463D8—82no—
464C2×C8—22no—
465C2×C8—22no—
466C4⋊C4—22no—
467C4⋊C4—22no—
468C4⋊C4—22no—
469C4⋊C4—22no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—22no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—22no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—22no—
481C4⋊C4—22no—
482C4⋊C4—21no—
483C4⋊C4C2×D4×C5912yes—
484C4⋊C4C2×D4×C5911yescharacteristic
485C4⋊C4C2×D4×C5911yescharacteristic
486C22⋊C4—22no—
487C22⋊C4—22no—
488C22⋊C4—22no—
489C22⋊C4—22no—
490C22⋊C4—22no—
491C22⋊C4—21no—
492C22⋊C4—21no—
493C22⋊C4—21no—
494C22⋊C4—21no—
495C22⋊C4—22no—
496C22⋊C4—21no—
497C22⋊C4—22no—
498C22⋊C4—84no—
499C22⋊C4—84no—
500C42—22no—
501C42—21no—
502C42—42no—
503C42C2×D4×C5911yescharacteristic
504C42C2×D4×C5911yescharacteristic
505C42C2×D4×C5911yescharacteristic
506C42C2×D4×C5911yescharacteristic
507C23—21no—
508C23—22no—
509C23—44no—
510C23—44no—
511C23—42no—
512C23—44no—
513C23C22×D4×C5911yescharacteristic
514Q8—41no—
515Q8—81no—
516Q8—82no—
517D4—42no—
518D4—41no—
519D4—44no—
520D4—42no—
521D4—42no—
522D4—44no—
523D4—42no—
524D4—42no—
525D4—81no—
526D4—82no—
527D4—82no—
528D4—82no—
529D4—82no—
530D4—82no—
531D4—82no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—21no—
539C2×C4—22no—
540C2×C4—24no—
541C2×C4—41no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—82no—
548C2×C4—82no—
549C2×C4—82no—
550C2×C4—82no—
551C2×C4#120×C5911yescharacteristic
552C2×C4#120×C5911yescharacteristic
553C2×C4#120×C5911yescharacteristic
554C2×C4#120×C5911yescharacteristic
555C2×C4C22×D4×C5911yescharacteristic
556C2×C4C22×D4×C5911yescharacteristic
557C8—42no—
558C8—42no—
559C22—21no—
560C22—21no—
561C22—42no—
562C22—41no—
563C22—41no—
564C22—42no—
565C22—42no—
566C22—41no—
567C22—88no—
568C22—82no—
569C22—82no—
570C22—82no—
571C22C2×#120×C5911yescharacteristic
572C22C59×#57612yes—
573C4—21no—
574C4—21no—
575C4—21no—
576C4—21no—
577C4—21no—
578C4—42no—
579C4—42no—
580C4—41no—
581C4—41no—
582C4—42no—
583C4—41no—
584C4—82no—
585C4C59×#45412yes—
586C2—22no—
587C2—81no—
588C2—82no—
589C2—162no—
590C2C59×#300811yescharacteristic
591C2C2×C59×#45411yescharacteristic
592C2C59×#302711yescharacteristic
subgroupG/H
center, socleC22×C59C2×#120
commutator, Frattini, cosocleC22×C4C24×C59
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C59 ◁ C2×C42×C59 ◁ G

Complements

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

NH ≅ G/Ntype
1. C59×#3559C2semidirect
2. C59×#3217C2semidirect
3. C59×#3205C2semidirect
4. C59×#2641C2semidirect
5. C59×#1598C2semidirect
6. C59×#1597C2semidirect
7. C59×#1505C2semidirect
8. C59×#1500C2semidirect
9. C59×#1470C2semidirect
262. #18430C59direct (N × H)
290. #3559C2×C59semidirect
291. #3217C2×C59semidirect
292. #3205C2×C59semidirect
293. #2641C2×C59semidirect
294. #1598C2×C59semidirect
295. #1597C2×C59semidirect
296. #1505C2×C59semidirect
297. #1500C2×C59semidirect
298. #1470C2×C59semidirect
343. C59#18430direct (N × H)

Maximal subgroups

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

subgroupindex
C59×#35592
C59×#32172
C59×#32052
C59×#26412
C59×#15982
C59×#15972
C59×#15052
C59×#15002
C59×#14702
#1843059