Finite Group Databasebeta

← C59×#18432 #28430541

Subgroups — C59×#18432 #28430541

Order 15104.

940 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C59×#3563C211yesmaximal, characteristic, complemented
2C59×#3217C211yesmaximal, characteristic
3C59×#3208C211yesmaximal, characteristic, complemented
4C59×#2641C211yesmaximal, characteristic, complemented
5C59×#1599C214yesmaximal, complemented
6C59×#1597C214yesmaximal, complemented
7C59×#1506C211yesmaximal, characteristic, complemented
8C59×#1500C211yesmaximal, characteristic, complemented
9C59×#1470C211yesmaximal, characteristic, complemented
10C59×#564—21no—
11C59×#563—21no—
12C59×#557—21no—
13C59×#554—21no—
14C59×#552—21no—
15C59×#552—21no—
16C59×#552—22no—
17C59×#544—21no—
18C59×#544C2212yes—
19C59×#541—21no—
20C59×#541—22no—
21C59×#539C2212yes—
22C59×#533C2211yescharacteristic
23C2×#127×C59C2211yescharacteristic
24C59×#529C2211yescharacteristic
25C2×#125×C59C2211yescharacteristic
26C59×#496—21no—
27C59×#492—21no—
28C59×#490—21no—
29C59×#486—21no—
30C59×#460—22no—
31C59×#460—21no—
32C59×#459—21no—
33C59×#450C2214yes—
34C59×#450C2212yes—
35C59×#447C2212yes—
36C59×#432C2211yescharacteristic
37C59×#431C2211yescharacteristic
38C59×#394—22no—
39C59×#394C2214yes—
40C59×#390—21no—
41C59×#390—21no—
42C59×#376C2211yescharacteristic
43C59×#328C2212yes—
44C59×#328C2214yes—
45C59×#327C2212yes—
46C59×#324C2214yes—
47C22×D4×C59—21no—
48C22×D4×C59—21no—
49C22×D4×C59C2312yes—
50C2×SD16×C59—24no—
51C2×SD16×C59—22no—
52C2×D8×C59—22no—
53C4⋊Q8×C59—21no—
54C4⋊Q8×C59—22no—
55C4⋊Q8×C59—22no—
56C4⋊Q8×C59D411yescharacteristic
57C4⋊Q8×C59D411yescharacteristic
58#127×C59—21no—
59#127×C59—21no—
60#127×C59—21no—
61#127×C59—21no—
62#126×C59—22no—
63#126×C59—22no—
64#126×C59—22no—
65#126×C59—22no—
66#126×C59—21no—
67#125×C59—22no—
68#125×C59—22no—
69#125×C59—22no—
70#125×C59—22no—
71#125×C59—21no—
72#125×C59—22no—
73#125×C59—22no—
74#125×C59—22no—
75#125×C59—22no—
76#125×C59—21no—
77#125×C59—21no—
78#125×C59—21no—
79#125×C59—21no—
80#125×C59—21no—
81#125×C59D411yescharacteristic
82#124×C59D411yescharacteristic
83#123×C59—22no—
84#123×C59—21no—
85#123×C59—22no—
86C22⋊Q8×C59—21no—
87C22⋊Q8×C59—21no—
88C22⋊Q8×C59—22no—
89C22⋊Q8×C59—22no—
90C22⋊Q8×C59—22no—
91C22⋊Q8×C59—21no—
92C22⋊Q8×C59—22no—
93C22⋊Q8×C59C2311yescharacteristic
94C22⋊Q8×C59C2312yes—
95#121×C59C2311yescharacteristic
96C4×Q8×C59—21no—
97C4×Q8×C59—22no—
98C4×Q8×C59—21no—
99C4×Q8×C59—21no—
100C4×Q8×C59D411yescharacteristic
101C4×Q8×C59D412yes—
102C4×D4×C59—21no—
103C4×D4×C59—22no—
104C4×D4×C59D411yescharacteristic
105#117×C59—22no—
106#117×C59—21no—
107#117×C59—21no—
108#117×C59—22no—
109#117×C59—21no—
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—22no—
122#102×C59—22no—
123#102×C59—24no—
124C22⋊C8×C59C2312yes—
125C22⋊C8×C59C2312yes—
126#97×C59—21no—
127C4×C8×C59—21no—
128#95×C59—21no—
129#95×C59C2312yes—
130C24×C59—22no—
131C2×Q8×C59—22no—
132C2×Q8×C59—21no—
133C2×Q8×C59C2×D412yes—
134C2×Q8×C59C2×D411yescharacteristic
135C2×D4×C59—21no—
136C2×D4×C59—22no—
137C2×D4×C59—22no—
138C2×D4×C59—44no—
139C2×D4×C59—41no—
140C2×D4×C59—41no—
141C2×D4×C59—41no—
142C2×D4×C59—41no—
143C2×D4×C59—82no—
144C2×D4×C59—82no—
145C2×D4×C59C2×D411yescharacteristic
146C22×C4×C59—22no—
147C22×C4×C59—21no—
148C22×C4×C59—22no—
149C22×C4×C59C2×D412yes—
150C22×C4×C59C2×D411yescharacteristic
151C22×C4×C59C2×D411yescharacteristic
152C22×C4×C59C2×D412yes—
153C22×C4×C59C2411yescharacteristic
154SD16×C59—82no—
155SD16×C59—84no—
156D8×C59—82no—
157C2×C8×C59—22no—
158C2×C8×C59—22no—
159C4⋊C4×C59—22no—
160C4⋊C4×C59—22no—
161C4⋊C4×C59—22no—
162C4⋊C4×C59—22no—
163C4⋊C4×C59—22no—
164C4⋊C4×C59—22no—
165C4⋊C4×C59—22no—
166C4⋊C4×C59—22no—
167C4⋊C4×C59—21no—
168C4⋊C4×C59—21no—
169C4⋊C4×C59—21no—
170C4⋊C4×C59—22no—
171C4⋊C4×C59—21no—
172C4⋊C4×C59—22no—
173C4⋊C4×C59—21no—
174C4⋊C4×C59—21no—
175C4⋊C4×C59—21no—
176C4⋊C4×C59—21no—
177C4⋊C4×C59—21no—
178C4⋊C4×C59—21no—
179C4⋊C4×C59—22no—
180C4⋊C4×C59—22no—
181C4⋊C4×C59—22no—
182C4⋊C4×C59—21no—
183C4⋊C4×C59—22no—
184C4⋊C4×C59C2×D411yescharacteristic
185C4⋊C4×C59C2×D411yescharacteristic
186C4⋊C4×C59C2×D412yes—
187C22⋊C4×C59—22no—
188C22⋊C4×C59—22no—
189C22⋊C4×C59—22no—
190C22⋊C4×C59—22no—
191C22⋊C4×C59—21no—
192C22⋊C4×C59—21no—
193C22⋊C4×C59—21no—
194C22⋊C4×C59—21no—
195C22⋊C4×C59—21no—
196C22⋊C4×C59—84no—
197C22⋊C4×C59—84no—
198C42×C59—22no—
199C42×C59—22no—
200C42×C59—22no—
201C42×C59—22no—
202C42×C59—21no—
203C42×C59—42no—
204C42×C59C2×D411yescharacteristic
205C42×C59C2×D411yescharacteristic
206C42×C59C2×D411yescharacteristic
207C42×C59C2×D411yescharacteristic
208C23×C59—21no—
209C23×C59—44no—
210C23×C59—44no—
211C23×C59—42no—
212C23×C59—44no—
213C23×C59C22×D411yescharacteristic
214Q8×C59—41no—
215Q8×C59—42no—
216Q8×C59—42no—
217Q8×C59—82no—
218D4×C59—41no—
219D4×C59—42no—
220D4×C59—42no—
221D4×C59—44no—
222D4×C59—42no—
223D4×C59—82no—
224D4×C59—82no—
225D4×C59—82no—
226D4×C59—82no—
227C2×C4×C59—22no—
228C2×C4×C59—22no—
229C2×C4×C59—22no—
230C2×C4×C59—21no—
231C2×C4×C59—21no—
232C2×C4×C59—22no—
233C2×C4×C59—21no—
234C2×C4×C59—22no—
235C2×C4×C59—22no—
236C2×C4×C59—24no—
237C2×C4×C59—41no—
238C2×C4×C59—42no—
239C2×C4×C59—42no—
240C2×C4×C59—42no—
241C2×C4×C59—42no—
242C2×C4×C59—42no—
243C2×C4×C59—82no—
244C2×C4×C59#12011yescharacteristic
245C2×C4×C59#12011yescharacteristic
246C2×C4×C59#12011yescharacteristic
247C2×C4×C59#12011yescharacteristic
248C2×C4×C59C22×D411yescharacteristic
249C2×C4×C59C22×D411yescharacteristic
250C8×C59—42no—
251C8×C59—42no—
252#18432C5911yesmaximal, characteristic, direct product factor, Sylow
253C22×C59—21no—
254C22×C59—21no—
255C22×C59—41no—
256C22×C59—41no—
257C22×C59—41no—
258C22×C59—88no—
259C22×C59—82no—
260C22×C59—82no—
261C22×C59—82no—
262C22×C59C2×#12011yescharacteristic
263C22×C59#57712yes—
264C4×C59—21no—
265C4×C59—21no—
266C4×C59—21no—
267C4×C59—21no—
268C4×C59—21no—
269C4×C59—42no—
270C4×C59—41no—
271C4×C59—41no—
272C4×C59—42no—
273C4×C59—42no—
274C4×C59—42no—
275C4×C59—41no—
276C4×C59—82no—
277C4×C59#45412yes—
278#3563C2×C5911yescharacteristic, complemented
279#3217C2×C5911yescharacteristic
280#3208C2×C5911yescharacteristic, complemented
281#2641C2×C5911yescharacteristic, complemented
282#1599C2×C5914yescomplemented
283#1597C2×C5914yescomplemented
284#1506C2×C5911yescharacteristic, complemented
285#1500C2×C5911yescharacteristic, complemented
286#1470C2×C5911yescharacteristic, complemented
287C2×C59—22no—
288C2×C59—81no—
289C2×C59—162no—
290C2×C59#301011yescharacteristic
291C2×C59C2×#45411yescharacteristic
292C2×C59#302711yescharacteristic
293#564—21no—
294#563—21no—
295#557—21no—
296#554—21no—
297#552—21no—
298#552—21no—
299#552—22no—
300#544—21no—
301#544C22×C5912yes—
302#541—21no—
303#541—22no—
304#539C22×C5912yes—
305#533C22×C5911yescharacteristic
306C2×#127C22×C5911yescharacteristic
307#529C22×C5911yescharacteristic
308C2×#125C22×C5911yescharacteristic
309#496—21no—
310#492—21no—
311#490—21no—
312#486—21no—
313#460—22no—
314#460—21no—
315#459—21no—
316#450C22×C5914yes—
317#450C22×C5912yes—
318#447C22×C5912yes—
319#432C22×C5911yescharacteristic
320#431C22×C5911yescharacteristic
321#394—22no—
322#394C22×C5914yes—
323#390—21no—
324#390—21no—
325#376C22×C5911yescharacteristic
326#328C22×C5914yes—
327#328C22×C5912yes—
328#327C22×C5912yes—
329#324C22×C5914yes—
330C59#1843211yescharacteristic, direct product factor, Sylow
331C22×D4—21no—
332C22×D4—21no—
333C22×D4C23×C5912yes—
334C2×SD16—24no—
335C2×SD16—22no—
336C2×D8—22no—
337C4⋊Q8—21no—
338C4⋊Q8—22no—
339C4⋊Q8—22no—
340C4⋊Q8D4×C5911yescharacteristic
341C4⋊Q8D4×C5911yescharacteristic
342#127—21no—
343#127—21no—
344#127—21no—
345#127—21no—
346#126—22no—
347#126—22no—
348#126—22no—
349#126—22no—
350#126—21no—
351#125—22no—
352#125—22no—
353#125—22no—
354#125—22no—
355#125—21no—
356#125—22no—
357#125—22no—
358#125—22no—
359#125—22no—
360#125—21no—
361#125—21no—
362#125—21no—
363#125—21no—
364#125—21no—
365#125D4×C5911yescharacteristic
366#124D4×C5911yescharacteristic
367#123—22no—
368#123—21no—
369#123—22no—
370C22⋊Q8—21no—
371C22⋊Q8—21no—
372C22⋊Q8—22no—
373C22⋊Q8—22no—
374C22⋊Q8—22no—
375C22⋊Q8—21no—
376C22⋊Q8—22no—
377C22⋊Q8C23×C5911yescharacteristic
378C22⋊Q8C23×C5912yes—
379#121C23×C5911yescharacteristic
380C4×Q8—21no—
381C4×Q8—22no—
382C4×Q8—21no—
383C4×Q8—21no—
384C4×Q8D4×C5911yescharacteristic
385C4×Q8D4×C5912yes—
386C4×D4—21no—
387C4×D4—22no—
388C4×D4D4×C5911yescharacteristic
389#117—22no—
390#117—21no—
391#117—21no—
392#117—22no—
393#117—21no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4D4×C5911yescharacteristic
396C2×C4⋊C4D4×C5912yes—
397C2×C4⋊C4D4×C5911yescharacteristic
398C2×C4⋊C4C23×C5912yes—
399C2×C22⋊C4—24no—
400C2×C22⋊C4—24no—
401C2×C42—21no—
402C2×C42C23×C5911yescharacteristic
403C4⋊C8—21no—
404C4⋊C8—21no—
405#102—22no—
406#102—22no—
407#102—24no—
408C22⋊C8C23×C5912yes—
409C22⋊C8C23×C5912yes—
410#97—21no—
411C4×C8—21no—
412#95—21no—
413#95C23×C5912yes—
414C24—22no—
415C2×Q8—22no—
416C2×Q8—21no—
417C2×Q8C2×D4×C5912yes—
418C2×Q8C2×D4×C5911yescharacteristic
419C2×D4—21no—
420C2×D4—22no—
421C2×D4—22no—
422C2×D4—44no—
423C2×D4—41no—
424C2×D4—41no—
425C2×D4—41no—
426C2×D4—41no—
427C2×D4—82no—
428C2×D4—82no—
429C2×D4C2×D4×C5911yescharacteristic
430C22×C4—22no—
431C22×C4—21no—
432C22×C4—22no—
433C22×C4C2×D4×C5912yes—
434C22×C4C2×D4×C5911yescharacteristic
435C22×C4C2×D4×C5911yescharacteristic
436C22×C4C2×D4×C5912yes—
437C22×C4C24×C5911yescharacteristic
438SD16—82no—
439SD16—84no—
440D8—82no—
441C2×C8—22no—
442C2×C8—22no—
443C4⋊C4—22no—
444C4⋊C4—22no—
445C4⋊C4—22no—
446C4⋊C4—22no—
447C4⋊C4—22no—
448C4⋊C4—22no—
449C4⋊C4—22no—
450C4⋊C4—22no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—22no—
455C4⋊C4—21no—
456C4⋊C4—22no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—22no—
464C4⋊C4—22no—
465C4⋊C4—22no—
466C4⋊C4—21no—
467C4⋊C4—22no—
468C4⋊C4C2×D4×C5911yescharacteristic
469C4⋊C4C2×D4×C5911yescharacteristic
470C4⋊C4C2×D4×C5912yes—
471C22⋊C4—22no—
472C22⋊C4—22no—
473C22⋊C4—22no—
474C22⋊C4—22no—
475C22⋊C4—21no—
476C22⋊C4—21no—
477C22⋊C4—21no—
478C22⋊C4—21no—
479C22⋊C4—21no—
480C22⋊C4—84no—
481C22⋊C4—84no—
482C42—22no—
483C42—22no—
484C42—22no—
485C42—22no—
486C42—21no—
487C42—42no—
488C42C2×D4×C5911yescharacteristic
489C42C2×D4×C5911yescharacteristic
490C42C2×D4×C5911yescharacteristic
491C42C2×D4×C5911yescharacteristic
492C23—21no—
493C23—44no—
494C23—44no—
495C23—42no—
496C23—44no—
497C23C22×D4×C5911yescharacteristic
498Q8—41no—
499Q8—42no—
500Q8—42no—
501Q8—82no—
502D4—41no—
503D4—42no—
504D4—42no—
505D4—44no—
506D4—42no—
507D4—82no—
508D4—82no—
509D4—82no—
510D4—82no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—22no—
517C2×C4—21no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—24no—
521C2×C4—41no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—82no—
528C2×C4#120×C5911yescharacteristic
529C2×C4#120×C5911yescharacteristic
530C2×C4#120×C5911yescharacteristic
531C2×C4#120×C5911yescharacteristic
532C2×C4C22×D4×C5911yescharacteristic
533C2×C4C22×D4×C5911yescharacteristic
534C8—42no—
535C8—42no—
536C22—21no—
537C22—21no—
538C22—41no—
539C22—41no—
540C22—41no—
541C22—88no—
542C22—82no—
543C22—82no—
544C22—82no—
545C22C2×#120×C5911yescharacteristic
546C22C59×#57712yes—
547C4—21no—
548C4—21no—
549C4—21no—
550C4—21no—
551C4—21no—
552C4—42no—
553C4—41no—
554C4—41no—
555C4—42no—
556C4—42no—
557C4—42no—
558C4—41no—
559C4—82no—
560C4C59×#45412yes—
561C2—22no—
562C2—81no—
563C2—162no—
564C2C59×#301011yescharacteristic
565C2C2×C59×#45411yescharacteristic
566C2C59×#302711yescharacteristic
subgroupG/H
center, socleC22×C59C2×#120
commutator, Frattini, cosocleC22×C4C24×C59
prime radicalC59×#3217C2
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×#3563C2semidirect
3. C59×#3208C2semidirect
4. C59×#2641C2semidirect
5. C59×#1599C2semidirect
6. C59×#1597C2semidirect
7. C59×#1506C2semidirect
8. C59×#1500C2semidirect
9. C59×#1470C2semidirect
252. #18432C59direct (N × H)
278. #3563C2×C59semidirect
280. #3208C2×C59semidirect
281. #2641C2×C59semidirect
282. #1599C2×C59semidirect
283. #1597C2×C59semidirect
284. #1506C2×C59semidirect
285. #1500C2×C59semidirect
286. #1470C2×C59semidirect
330. C59#18432direct (N × H)

Maximal subgroups

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

subgroupindex
C59×#35632
C59×#32172
C59×#32082
C59×#26412
C59×#15992
C59×#15972
C59×#15062
C59×#15002
C59×#14702
#1843259