Finite Group Databasebeta

← C59×#18182 #28430291

Subgroups — C59×#18182 #28430291

Order 15104.

958 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C59×#3507C211yesmaximal, characteristic, complemented
2C59×#3110C211yesmaximal, characteristic, complemented
3C59×#3109C211yesmaximal, characteristic
4C59×#2398C211yesmaximal, characteristic, complemented
5C59×#1615C214yesmaximal, complemented
6C59×#1597C214yesmaximal, complemented
7C59×#1506C211yesmaximal, characteristic, complemented
8C59×#1505C211yesmaximal, characteristic, complemented
9C59×#1467C211yesmaximal, characteristic, complemented
10C59×#559—21no—
11C59×#557—21no—
12C59×#556—21no—
13C59×#556—22no—
14C59×#554—21no—
15C59×#552—22no—
16C59×#539C2214yes—
17C59×#536—21no—
18C59×#533C2211yescharacteristic
19C59×#532C2211yescharacteristic
20C59×#529—22no—
21C59×#520—21no—
22C2×C4×Q8×C59C2211yescharacteristic
23C2×C4×D4×C59C2211yescharacteristic
24C59×#484C2212yes—
25C59×#481C2212yes—
26C59×#476—21no—
27C59×#474—21no—
28C59×#461—21no—
29C59×#459—21no—
30C59×#450C2212yes—
31C59×#447C2212yes—
32C59×#442—22no—
33C59×#440—22no—
34C59×#432C2211yescharacteristic
35C59×#432C2211yescharacteristic
36C59×#400C2212yes—
37C59×#397—21no—
38C59×#394C2212yes—
39C59×#393—21no—
40C4×C22⋊C4×C59—22no—
41C59×#376C2211yescharacteristic
42C59×#328C2214yes—
43C59×#327C2214yes—
44C59×#324C2214yes—
45C2×#41×C59—21no—
46C22×Q8×C59D411yescharacteristic
47C22×D4×C59C2311yescharacteristic
48C23×C4×C59—21no—
49C2×SD16×C59—22no—
50C2×D8×C59—22no—
51C4⋊Q8×C59—22no—
52C4⋊Q8×C59D411yescharacteristic
53C4⋊Q8×C59D411yescharacteristic
54C4⋊Q8×C59D411yescharacteristic
55#127×C59D411yescharacteristic
56#126×C59—24no—
57#126×C59—24no—
58#125×C59—22no—
59#125×C59—24no—
60#125×C59—21no—
61#124×C59—22no—
62#124×C59—22no—
63#124×C59—21no—
64#123×C59—24no—
65#123×C59—24no—
66C22⋊Q8×C59—22no—
67C22⋊Q8×C59—22no—
68C22⋊Q8×C59—24no—
69C22⋊Q8×C59—21no—
70C22⋊Q8×C59C2312yes—
71#121×C59—21no—
72#121×C59C2312yes—
73C4×Q8×C59—22no—
74C4×Q8×C59—22no—
75C4×Q8×C59—21no—
76C4×Q8×C59—21no—
77C4×Q8×C59—21no—
78C4×Q8×C59—21no—
79C4×Q8×C59—21no—
80C4×Q8×C59D412yes—
81C4×D4×C59—22no—
82C4×D4×C59—22no—
83C4×D4×C59—24no—
84C4×D4×C59—21no—
85C4×D4×C59—21no—
86C4×D4×C59—21no—
87C4×D4×C59—21no—
88C4×D4×C59—21no—
89C4×D4×C59D412yes—
90#117×C59—22no—
91#117×C59—24no—
92#117×C59—21no—
93C2×C4⋊C4×C59—22no—
94C2×C4⋊C4×C59D411yescharacteristic
95C2×C4⋊C4×C59C2311yescharacteristic
96C2×C4⋊C4×C59C2312yes—
97C2×C22⋊C4×C59—22no—
98C2×C22⋊C4×C59—22no—
99C2×C22⋊C4×C59—21no—
100C2×C42×C59—21no—
101C2×C42×C59D412yes—
102C2×C42×C59C2311yescharacteristic
103#107×C59—22no—
104#106×C59—22no—
105C4⋊C8×C59—21no—
106C4⋊C8×C59—21no—
107#103×C59—22no—
108#102×C59—22no—
109#102×C59—22no—
110#102×C59—22no—
111C22⋊C8×C59C2312yes—
112C22⋊C8×C59C2312yes—
113#97×C59—21no—
114#97×C59—21no—
115#95×C59—21no—
116#95×C59—22no—
117#95×C59—22no—
118#95×C59C2312yes—
119C24×C59—21no—
120#41×C59—44no—
121C2×Q8×C59—21no—
122C2×Q8×C59—21no—
123C2×Q8×C59—21no—
124C2×Q8×C59—21no—
125C2×Q8×C59—42no—
126C2×Q8×C59C2×D412yes—
127C2×D4×C59—22no—
128C2×D4×C59—21no—
129C2×D4×C59—21no—
130C2×D4×C59—21no—
131C2×D4×C59—21no—
132C2×D4×C59—42no—
133C2×D4×C59C2×D412yes—
134C22×C4×C59—24no—
135C22×C4×C59—22no—
136C22×C4×C59—21no—
137C22×C4×C59—22no—
138C22×C4×C59—44no—
139C22×C4×C59—41no—
140C22×C4×C59—41no—
141C22×C4×C59C2×D412yes—
142C22×C4×C59C2×D411yescharacteristic
143C22×C4×C59C2×D411yescharacteristic
144C22×C4×C59C2×D412yes—
145C22×C4×C59C2411yescharacteristic
146SD16×C59—44no—
147D8×C59—44no—
148C2×C8×C59—22no—
149C2×C8×C59—22no—
150C4⋊C4×C59—24no—
151C4⋊C4×C59—24no—
152C4⋊C4×C59—24no—
153C4⋊C4×C59—21no—
154C4⋊C4×C59—21no—
155C4⋊C4×C59—21no—
156C4⋊C4×C59—21no—
157C4⋊C4×C59—22no—
158C4⋊C4×C59—21no—
159C4⋊C4×C59—21no—
160C4⋊C4×C59—22no—
161C4⋊C4×C59—22no—
162C4⋊C4×C59—22no—
163C4⋊C4×C59—21no—
164C4⋊C4×C59—21no—
165C4⋊C4×C59C2×D412yes—
166C4⋊C4×C59C2×D412yes—
167C22⋊C4×C59—24no—
168C22⋊C4×C59—24no—
169C22⋊C4×C59—24no—
170C22⋊C4×C59—22no—
171C22⋊C4×C59—22no—
172C22⋊C4×C59—22no—
173C22⋊C4×C59—44no—
174C22⋊C4×C59—44no—
175C22⋊C4×C59—41no—
176C22⋊C4×C59—41no—
177C42×C59—24no—
178C42×C59—22no—
179C42×C59—22no—
180C42×C59—22no—
181C42×C59—42no—
182C42×C59C2×D411yescharacteristic
183C42×C59C2×D411yescharacteristic
184C42×C59C2×D411yescharacteristic
185C42×C59C2×D411yescharacteristic
186C23×C59—22no—
187C23×C59—22no—
188C23×C59—42no—
189C23×C59—41no—
190C23×C59—41no—
191C23×C59—42no—
192C23×C59C22×D411yescharacteristic
193Q8×C59—42no—
194Q8×C59—42no—
195Q8×C59—42no—
196Q8×C59—42no—
197Q8×C59—42no—
198D4×C59—22no—
199D4×C59—22no—
200D4×C59—42no—
201D4×C59—41no—
202D4×C59—41no—
203D4×C59—42no—
204D4×C59—44no—
205D4×C59—42no—
206C2×C4×C59—22no—
207C2×C4×C59—22no—
208C2×C4×C59—22no—
209C2×C4×C59—22no—
210C2×C4×C59—22no—
211C2×C4×C59—22no—
212C2×C4×C59—22no—
213C2×C4×C59—22no—
214C2×C4×C59—22no—
215C2×C4×C59—41no—
216C2×C4×C59—44no—
217C2×C4×C59—42no—
218C2×C4×C59—42no—
219C2×C4×C59—42no—
220C2×C4×C59—42no—
221C2×C4×C59—41no—
222C2×C4×C59—42no—
223C2×C4×C59—82no—
224C2×C4×C59—84no—
225C2×C4×C59—82no—
226C2×C4×C59#12011yescharacteristic
227C2×C4×C59#12011yescharacteristic
228C2×C4×C59#12011yescharacteristic
229C2×C4×C59#12011yescharacteristic
230C2×C4×C59C22×D411yescharacteristic
231C2×C4×C59C22×D411yescharacteristic
232C8×C59—42no—
233C8×C59—42no—
234#18182C5911yesmaximal, characteristic, direct product factor, Sylow
235C22×C59—21no—
236C22×C59—21no—
237C22×C59—44no—
238C22×C59—42no—
239C22×C59—42no—
240C22×C59—42no—
241C22×C59—42no—
242C22×C59—82no—
243C22×C59—81no—
244C22×C59—81no—
245C22×C59C2×#12011yescharacteristic
246C22×C59#57512yes—
247C4×C59—21no—
248C4×C59—21no—
249C4×C59—21no—
250C4×C59—21no—
251C4×C59—21no—
252C4×C59—42no—
253C4×C59—42no—
254C4×C59—42no—
255C4×C59—42no—
256C4×C59—42no—
257C4×C59—82no—
258C4×C59—81no—
259C4×C59#45412yes—
260#3507C2×C5911yescharacteristic, complemented
261#3110C2×C5911yescharacteristic, complemented
262#3109C2×C5911yescharacteristic
263#2398C2×C5911yescharacteristic, complemented
264#1615C2×C5914yescomplemented
265#1597C2×C5914yescomplemented
266#1506C2×C5911yescharacteristic, complemented
267#1505C2×C5911yescharacteristic, complemented
268#1467C2×C5911yescharacteristic, complemented
269C2×C59—22no—
270C2×C59—82no—
271C2×C59—82no—
272C2×C59#300511yescharacteristic
273C2×C59C2×#45411yescharacteristic
274C2×C59#302511yescharacteristic
275#559—21no—
276#557—21no—
277#556—21no—
278#556—22no—
279#554—21no—
280#552—22no—
281#539C22×C5914yes—
282#536—21no—
283#533C22×C5911yescharacteristic
284#532C22×C5911yescharacteristic
285#529—22no—
286#520—21no—
287C2×C4×Q8C22×C5911yescharacteristic
288C2×C4×D4C22×C5911yescharacteristic
289#484C22×C5912yes—
290#481C22×C5912yes—
291#476—21no—
292#474—21no—
293#461—21no—
294#459—21no—
295#450C22×C5912yes—
296#447C22×C5912yes—
297#442—22no—
298#440—22no—
299#432C22×C5911yescharacteristic
300#432C22×C5911yescharacteristic
301#400C22×C5912yes—
302#397—21no—
303#394C22×C5912yes—
304#393—21no—
305C4×C22⋊C4—22no—
306#376C22×C5911yescharacteristic
307#328C22×C5914yes—
308#327C22×C5914yes—
309#324C22×C5914yes—
310C59#1818211yescharacteristic, direct product factor, Sylow
311C2×#41—21no—
312C22×Q8D4×C5911yescharacteristic
313C22×D4C23×C5911yescharacteristic
314C23×C4—21no—
315C2×SD16—22no—
316C2×D8—22no—
317C4⋊Q8—22no—
318C4⋊Q8D4×C5911yescharacteristic
319C4⋊Q8D4×C5911yescharacteristic
320C4⋊Q8D4×C5911yescharacteristic
321#127D4×C5911yescharacteristic
322#126—24no—
323#126—24no—
324#125—22no—
325#125—24no—
326#125—21no—
327#124—22no—
328#124—22no—
329#124—21no—
330#123—24no—
331#123—24no—
332C22⋊Q8—22no—
333C22⋊Q8—22no—
334C22⋊Q8—24no—
335C22⋊Q8—21no—
336C22⋊Q8C23×C5912yes—
337#121—21no—
338#121C23×C5912yes—
339C4×Q8—22no—
340C4×Q8—22no—
341C4×Q8—21no—
342C4×Q8—21no—
343C4×Q8—21no—
344C4×Q8—21no—
345C4×Q8—21no—
346C4×Q8D4×C5912yes—
347C4×D4—22no—
348C4×D4—22no—
349C4×D4—24no—
350C4×D4—21no—
351C4×D4—21no—
352C4×D4—21no—
353C4×D4—21no—
354C4×D4—21no—
355C4×D4D4×C5912yes—
356#117—22no—
357#117—24no—
358#117—21no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4D4×C5911yescharacteristic
361C2×C4⋊C4C23×C5911yescharacteristic
362C2×C4⋊C4C23×C5912yes—
363C2×C22⋊C4—21no—
364C2×C22⋊C4—22no—
365C2×C22⋊C4—22no—
366C2×C42—21no—
367C2×C42D4×C5912yes—
368C2×C42C23×C5911yescharacteristic
369#107—22no—
370#106—22no—
371C4⋊C8—21no—
372C4⋊C8—21no—
373#103—22no—
374#102—22no—
375#102—22no—
376#102—22no—
377C22⋊C8C23×C5912yes—
378C22⋊C8C23×C5912yes—
379#97—21no—
380#97—21no—
381#95—21no—
382#95—22no—
383#95—22no—
384#95C23×C5912yes—
385C24—21no—
386#41—44no—
387C2×Q8—21no—
388C2×Q8—21no—
389C2×Q8—21no—
390C2×Q8—21no—
391C2×Q8—42no—
392C2×Q8C2×D4×C5912yes—
393C2×D4—22no—
394C2×D4—21no—
395C2×D4—21no—
396C2×D4—21no—
397C2×D4—21no—
398C2×D4—42no—
399C2×D4C2×D4×C5912yes—
400C22×C4—24no—
401C22×C4—22no—
402C22×C4—21no—
403C22×C4—22no—
404C22×C4—44no—
405C22×C4—41no—
406C22×C4—41no—
407C22×C4C2×D4×C5912yes—
408C22×C4C2×D4×C5911yescharacteristic
409C22×C4C2×D4×C5911yescharacteristic
410C22×C4C2×D4×C5912yes—
411C22×C4C24×C5911yescharacteristic
412SD16—44no—
413D8—44no—
414C2×C8—22no—
415C2×C8—22no—
416C4⋊C4—24no—
417C4⋊C4—24no—
418C4⋊C4—24no—
419C4⋊C4—21no—
420C4⋊C4—21no—
421C4⋊C4—21no—
422C4⋊C4—21no—
423C4⋊C4—22no—
424C4⋊C4—21no—
425C4⋊C4—21no—
426C4⋊C4—22no—
427C4⋊C4—22no—
428C4⋊C4—22no—
429C4⋊C4—21no—
430C4⋊C4—21no—
431C4⋊C4C2×D4×C5912yes—
432C4⋊C4C2×D4×C5912yes—
433C22⋊C4—24no—
434C22⋊C4—24no—
435C22⋊C4—24no—
436C22⋊C4—22no—
437C22⋊C4—22no—
438C22⋊C4—22no—
439C22⋊C4—44no—
440C22⋊C4—44no—
441C22⋊C4—41no—
442C22⋊C4—41no—
443C42—24no—
444C42—22no—
445C42—22no—
446C42—22no—
447C42—42no—
448C42C2×D4×C5911yescharacteristic
449C42C2×D4×C5911yescharacteristic
450C42C2×D4×C5911yescharacteristic
451C42C2×D4×C5911yescharacteristic
452C23—22no—
453C23—22no—
454C23—42no—
455C23—41no—
456C23—41no—
457C23—42no—
458C23C22×D4×C5911yescharacteristic
459Q8—42no—
460Q8—42no—
461Q8—42no—
462Q8—42no—
463Q8—42no—
464D4—22no—
465D4—22no—
466D4—42no—
467D4—41no—
468D4—41no—
469D4—42no—
470D4—44no—
471D4—42no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—41no—
482C2×C4—44no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—41no—
488C2×C4—42no—
489C2×C4—82no—
490C2×C4—84no—
491C2×C4—82no—
492C2×C4#120×C5911yescharacteristic
493C2×C4#120×C5911yescharacteristic
494C2×C4#120×C5911yescharacteristic
495C2×C4#120×C5911yescharacteristic
496C2×C4C22×D4×C5911yescharacteristic
497C2×C4C22×D4×C5911yescharacteristic
498C8—42no—
499C8—42no—
500C22—21no—
501C22—21no—
502C22—44no—
503C22—42no—
504C22—42no—
505C22—42no—
506C22—42no—
507C22—82no—
508C22—81no—
509C22—81no—
510C22C2×#120×C5911yescharacteristic
511C22C59×#57512yes—
512C4—21no—
513C4—21no—
514C4—21no—
515C4—21no—
516C4—21no—
517C4—42no—
518C4—42no—
519C4—42no—
520C4—42no—
521C4—42no—
522C4—82no—
523C4—81no—
524C4C59×#45412yes—
525C2—22no—
526C2—82no—
527C2—82no—
528C2C59×#300511yescharacteristic
529C2C2×C59×#45411yescharacteristic
530C2C59×#302511yescharacteristic
subgroupG/H
center, socleC22×C59C2×#120
commutator, Frattini, cosocleC22×C4C24×C59
prime radicalC59×#3109C2
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×#3507C2semidirect
2. C59×#3110C2semidirect
4. C59×#2398C2semidirect
5. C59×#1615C2semidirect
6. C59×#1597C2semidirect
7. C59×#1506C2semidirect
8. C59×#1505C2semidirect
9. C59×#1467C2semidirect
234. #18182C59direct (N × H)
260. #3507C2×C59semidirect
261. #3110C2×C59semidirect
263. #2398C2×C59semidirect
264. #1615C2×C59semidirect
265. #1597C2×C59semidirect
266. #1506C2×C59semidirect
267. #1505C2×C59semidirect
268. #1467C2×C59semidirect
310. C59#18182direct (N × H)

Maximal subgroups

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

subgroupindex
C59×#35072
C59×#31102
C59×#31092
C59×#23982
C59×#16152
C59×#15972
C59×#15062
C59×#15052
C59×#14672
#1818259