Finite Group Databasebeta

← C59×#19328 #28431437

Subgroups — C59×#19328 #28431437

Order 15104.

650 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C59×#3235C211yesmaximal, characteristic, complemented
2C59×#3214C211yesmaximal, characteristic
3C59×#3167C211yesmaximal, characteristic, complemented
4C59×#2931C211yesmaximal, characteristic, complemented
5C59×#1699C212yesmaximal, complemented
6C59×#1697C212yesmaximal, complemented
7C59×#1671C212yesmaximal, complemented
8C59×#1665C212yesmaximal, complemented
9C59×#1568C211yesmaximal, characteristic, complemented
10C59×#1559C211yesmaximal, characteristic, complemented
11C59×#1557C211yesmaximal, characteristic, complemented
12C2×#131×C59—21no—
13C59×#533C2211yescharacteristic
14C59×#532C2211yescharacteristic
15C59×#532C2211yescharacteristic
16C59×#501—21no—
17C59×#498C2211yescharacteristic
18C59×#496—21no—
19C59×#492C2211yescharacteristic
20C59×#490—21no—
21C59×#489—21no—
22C59×#487C2211yescharacteristic
23C59×#486C2211yescharacteristic
24C59×#482—22no—
25C59×#476C2212yes—
26C59×#474C2212yes—
27C59×#465—21no—
28C59×#465—21no—
29C59×#461C2212yes—
30C59×#459C2212yes—
31C59×#449—22no—
32C4×SD16×C59—21no—
33C4×SD16×C59—21no—
34C59×#436—21no—
35C59×#436C2212yes—
36C8×D4×C59—21no—
37C8×D4×C59C2212yes—
38C59×#432C2211yescharacteristic
39C59×#432C2211yescharacteristic
40C59×#423C2211yescharacteristic
41C59×#408—21no—
42C2×C4×C8×C59C2211yescharacteristic
43C59×#335C2212yes—
44C59×#334C2212yes—
45C59×#333C2212yes—
46C59×#332C2212yes—
47C59×#332C2212yes—
48C59×#331C2212yes—
49C2×#41×C59—21no—
50C2×#41×C59—21no—
51C2×SD16×C59—22no—
52C2×SD16×C59—21no—
53C2×SD16×C59—21no—
54C2×D8×C59—22no—
55#131×C59—44no—
56C2×M16×C59—21no—
57C2×M16×C59—22no—
58C22×C8×C59—22no—
59C22×C8×C59D411yescharacteristic
60C22×C8×C59D411yescharacteristic
61C4⋊Q8×C59D411yescharacteristic
62C4⋊Q8×C59C2311yescharacteristic
63C4⋊Q8×C59C2311yescharacteristic
64C4⋊Q8×C59C2311yescharacteristic
65#127×C59D411yescharacteristic
66#127×C59C2311yescharacteristic
67#125×C59—21no—
68#124×C59—21no—
69#124×C59—21no—
70C22⋊Q8×C59—21no—
71C22⋊Q8×C59—21no—
72#121×C59—21no—
73#121×C59—21no—
74#121×C59—21no—
75#121×C59D412yes—
76C4×Q8×C59—21no—
77C4×Q8×C59—21no—
78C4×D4×C59—21no—
79C4×D4×C59—21no—
80C4×D4×C59—21no—
81C4×D4×C59C2312yes—
82#117×C59—21no—
83C2×C42×C59C2311yescharacteristic
84#107×C59—22no—
85#106×C59—21no—
86#106×C59—21no—
87#106×C59—22no—
88C4⋊C8×C59—21no—
89C4⋊C8×C59C2312yes—
90C4⋊C8×C59C2312yes—
91C4⋊C8×C59C2312yes—
92#103×C59—21no—
93#103×C59—21no—
94#103×C59—22no—
95#102×C59—22no—
96#102×C59—22no—
97#102×C59—21no—
98#102×C59—21no—
99#102×C59—22no—
100C22⋊C8×C59—21no—
101C22⋊C8×C59—21no—
102C22⋊C8×C59—22no—
103C22⋊C8×C59—22no—
104#97×C59—21no—
105#97×C59—21no—
106C4×C8×C59D411yescharacteristic
107C4×C8×C59D411yescharacteristic
108C4×C8×C59C2311yescharacteristic
109C4×C8×C59C2311yescharacteristic
110#41×C59—42no—
111#41×C59—42no—
112#41×C59—82no—
113C2×Q8×C59—21no—
114C2×Q8×C59—21no—
115C2×Q8×C59—21no—
116C2×Q8×C59—21no—
117C2×D4×C59—22no—
118C2×D4×C59—21no—
119C2×D4×C59—21no—
120C2×D4×C59—21no—
121C2×D4×C59—21no—
122C2×D4×C59—21no—
123C2×D4×C59—41no—
124C2×D4×C59C2×D412yes—
125C22×C4×C59—22no—
126C22×C4×C59—41no—
127C22×C4×C59C2×D411yescharacteristic
128C22×C4×C59C2×D411yescharacteristic
129C22×C4×C59#4111yescharacteristic
130SD16×C59—42no—
131SD16×C59—42no—
132SD16×C59—82no—
133D8×C59—82no—
134M16×C59—44no—
135M16×C59—42no—
136C2×C8×C59—22no—
137C2×C8×C59—22no—
138C2×C8×C59—22no—
139C2×C8×C59—22no—
140C2×C8×C59—41no—
141C2×C8×C59—44no—
142C2×C8×C59C2×D411yescharacteristic
143C2×C8×C59C2×D411yescharacteristic
144C2×C8×C59C2×D411yescharacteristic
145C2×C8×C59C2×D411yescharacteristic
146C4⋊C4×C59—21no—
147C4⋊C4×C59—21no—
148C4⋊C4×C59—21no—
149C4⋊C4×C59—21no—
150C4⋊C4×C59—21no—
151C4⋊C4×C59—21no—
152C4⋊C4×C59—21no—
153C4⋊C4×C59—41no—
154C4⋊C4×C59—41no—
155C4⋊C4×C59C2×D412yes—
156C22⋊C4×C59—22no—
157C22⋊C4×C59—22no—
158C22⋊C4×C59—41no—
159C22⋊C4×C59—41no—
160C22⋊C4×C59—41no—
161C42×C59—41no—
162C42×C59C2×D411yescharacteristic
163C42×C59C2×D411yescharacteristic
164C42×C59#4111yescharacteristic
165C42×C59C2411yescharacteristic
166C23×C59—22no—
167C23×C59—41no—
168C23×C59#12111yescharacteristic
169Q8×C59—42no—
170Q8×C59—41no—
171Q8×C59—41no—
172Q8×C59—42no—
173Q8×C59—81no—
174D4×C59—22no—
175D4×C59—22no—
176D4×C59—42no—
177D4×C59—42no—
178D4×C59—44no—
179D4×C59—41no—
180D4×C59—41no—
181D4×C59—42no—
182D4×C59—81no—
183D4×C59—82no—
184C2×C4×C59—21no—
185C2×C4×C59—21no—
186C2×C4×C59—22no—
187C2×C4×C59—22no—
188C2×C4×C59—41no—
189C2×C4×C59—42no—
190C2×C4×C59—42no—
191C2×C4×C59—41no—
192C2×C4×C59—41no—
193C2×C4×C59—41no—
194C2×C4×C59—82no—
195C2×C4×C59#12111yescharacteristic
196C2×C4×C59#12111yescharacteristic
197C2×C4×C59#12111yescharacteristic
198C2×C4×C59C22×D411yescharacteristic
199C2×C4×C59C22×D411yescharacteristic
200C2×C4×C59C2×#4111yescharacteristic
201C8×C59—21no—
202C8×C59—21no—
203C8×C59—21no—
204C8×C59—42no—
205C8×C59—42no—
206C8×C59—42no—
207C8×C59AGL(1,ℤ/8)12yes—
208#19328C5911yesmaximal, characteristic, direct product factor, Sylow
209C22×C59—21no—
210C22×C59—21no—
211C22×C59—21no—
212C22×C59—42no—
213C22×C59—42no—
214C22×C59—42no—
215C22×C59—81no—
216C22×C59—81no—
217C22×C59—81no—
218C22×C59C2×#12111yescharacteristic
219C4×C59—21no—
220C4×C59—21no—
221C4×C59—21no—
222C4×C59—21no—
223C4×C59—42no—
224C4×C59—81no—
225C4×C59—81no—
226C4×C59—81no—
227C4×C59C2×AGL(1,ℤ/8)11yescharacteristic
228C4×C59#57511yescharacteristic
229C4×C59#57712yes—
230#3235C2×C5911yescharacteristic, complemented
231#3214C2×C5911yescharacteristic
232#3167C2×C5911yescharacteristic, complemented
233#2931C2×C5911yescharacteristic, complemented
234#1699C2×C5912yescomplemented
235#1697C2×C5912yescomplemented
236#1671C2×C5912yescomplemented
237#1665C2×C5912yescomplemented
238#1568C2×C5911yescharacteristic, complemented
239#1559C2×C5911yescharacteristic, complemented
240#1557C2×C5911yescharacteristic, complemented
241C2×C59—41no—
242C2×C59—82no—
243C2×C59—161no—
244C2×C59#303611yescharacteristic
245C2×C59#305711yescharacteristic
246C2×C59#306711yescharacteristic
247C2×#131—21no—
248#533C22×C5911yescharacteristic
249#532C22×C5911yescharacteristic
250#532C22×C5911yescharacteristic
251#501—21no—
252#498C22×C5911yescharacteristic
253#496—21no—
254#492C22×C5911yescharacteristic
255#490—21no—
256#489—21no—
257#487C22×C5911yescharacteristic
258#486C22×C5911yescharacteristic
259#482—22no—
260#476C22×C5912yes—
261#474C22×C5912yes—
262#465—21no—
263#465—21no—
264#461C22×C5912yes—
265#459C22×C5912yes—
266#449—22no—
267C4×SD16—21no—
268C4×SD16—21no—
269#436—21no—
270#436C22×C5912yes—
271C8×D4—21no—
272C8×D4C22×C5912yes—
273#432C22×C5911yescharacteristic
274#432C22×C5911yescharacteristic
275#423C22×C5911yescharacteristic
276#408—21no—
277C2×C4×C8C22×C5911yescharacteristic
278#335C22×C5912yes—
279#334C22×C5912yes—
280#333C22×C5912yes—
281#332C22×C5912yes—
282#332C22×C5912yes—
283#331C22×C5912yes—
284C59#1932811yescharacteristic, direct product factor, Sylow
285C2×#41—21no—
286C2×#41—21no—
287C2×SD16—22no—
288C2×SD16—21no—
289C2×SD16—21no—
290C2×D8—22no—
291#131—44no—
292C2×M16—21no—
293C2×M16—22no—
294C22×C8—22no—
295C22×C8D4×C5911yescharacteristic
296C22×C8D4×C5911yescharacteristic
297C4⋊Q8D4×C5911yescharacteristic
298C4⋊Q8C23×C5911yescharacteristic
299C4⋊Q8C23×C5911yescharacteristic
300C4⋊Q8C23×C5911yescharacteristic
301#127D4×C5911yescharacteristic
302#127C23×C5911yescharacteristic
303#125—21no—
304#124—21no—
305#124—21no—
306C22⋊Q8—21no—
307C22⋊Q8—21no—
308#121—21no—
309#121—21no—
310#121—21no—
311#121D4×C5912yes—
312C4×Q8—21no—
313C4×Q8—21no—
314C4×D4—21no—
315C4×D4—21no—
316C4×D4—21no—
317C4×D4C23×C5912yes—
318#117—21no—
319C2×C42C23×C5911yescharacteristic
320#107—22no—
321#106—21no—
322#106—21no—
323#106—22no—
324C4⋊C8—21no—
325C4⋊C8C23×C5912yes—
326C4⋊C8C23×C5912yes—
327C4⋊C8C23×C5912yes—
328#103—21no—
329#103—21no—
330#103—22no—
331#102—22no—
332#102—22no—
333#102—21no—
334#102—21no—
335#102—22no—
336C22⋊C8—21no—
337C22⋊C8—21no—
338C22⋊C8—22no—
339C22⋊C8—22no—
340#97—21no—
341#97—21no—
342C4×C8D4×C5911yescharacteristic
343C4×C8D4×C5911yescharacteristic
344C4×C8C23×C5911yescharacteristic
345C4×C8C23×C5911yescharacteristic
346#41—42no—
347#41—42no—
348#41—82no—
349C2×Q8—21no—
350C2×Q8—21no—
351C2×Q8—21no—
352C2×Q8—21no—
353C2×D4—22no—
354C2×D4—21no—
355C2×D4—21no—
356C2×D4—21no—
357C2×D4—21no—
358C2×D4—21no—
359C2×D4—41no—
360C2×D4C2×D4×C5912yes—
361C22×C4—22no—
362C22×C4—41no—
363C22×C4C2×D4×C5911yescharacteristic
364C22×C4C2×D4×C5911yescharacteristic
365C22×C4#41×C5911yescharacteristic
366SD16—42no—
367SD16—42no—
368SD16—82no—
369D8—82no—
370M16—44no—
371M16—42no—
372C2×C8—22no—
373C2×C8—22no—
374C2×C8—22no—
375C2×C8—22no—
376C2×C8—41no—
377C2×C8—44no—
378C2×C8C2×D4×C5911yescharacteristic
379C2×C8C2×D4×C5911yescharacteristic
380C2×C8C2×D4×C5911yescharacteristic
381C2×C8C2×D4×C5911yescharacteristic
382C4⋊C4—21no—
383C4⋊C4—21no—
384C4⋊C4—21no—
385C4⋊C4—21no—
386C4⋊C4—21no—
387C4⋊C4—21no—
388C4⋊C4—21no—
389C4⋊C4—41no—
390C4⋊C4—41no—
391C4⋊C4C2×D4×C5912yes—
392C22⋊C4—22no—
393C22⋊C4—22no—
394C22⋊C4—41no—
395C22⋊C4—41no—
396C22⋊C4—41no—
397C42—41no—
398C42C2×D4×C5911yescharacteristic
399C42C2×D4×C5911yescharacteristic
400C42#41×C5911yescharacteristic
401C42C24×C5911yescharacteristic
402C23—22no—
403C23—41no—
404C23#121×C5911yescharacteristic
405Q8—42no—
406Q8—41no—
407Q8—41no—
408Q8—42no—
409Q8—81no—
410D4—22no—
411D4—22no—
412D4—42no—
413D4—42no—
414D4—44no—
415D4—41no—
416D4—41no—
417D4—42no—
418D4—81no—
419D4—82no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—22no—
423C2×C4—22no—
424C2×C4—41no—
425C2×C4—42no—
426C2×C4—42no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—82no—
431C2×C4#121×C5911yescharacteristic
432C2×C4#121×C5911yescharacteristic
433C2×C4#121×C5911yescharacteristic
434C2×C4C22×D4×C5911yescharacteristic
435C2×C4C22×D4×C5911yescharacteristic
436C2×C4C2×#41×C5911yescharacteristic
437C8—21no—
438C8—21no—
439C8—21no—
440C8—42no—
441C8—42no—
442C8—42no—
443C8AGL(1,ℤ/8)×C5912yes—
444C22—21no—
445C22—21no—
446C22—21no—
447C22—42no—
448C22—42no—
449C22—42no—
450C22—81no—
451C22—81no—
452C22—81no—
453C22C2×#121×C5911yescharacteristic
454C4—21no—
455C4—21no—
456C4—21no—
457C4—21no—
458C4—42no—
459C4—81no—
460C4—81no—
461C4—81no—
462C4C2×AGL(1,ℤ/8)×C5911yescharacteristic
463C4C59×#57511yescharacteristic
464C4C59×#57712yes—
465C2—41no—
466C2—82no—
467C2—161no—
468C2C59×#303611yescharacteristic
469C2C59×#305711yescharacteristic
470C2C59×#306711yescharacteristic
subgroupG/H
center, socleC22×C59C2×#121
commutator, Frattini, cosocleC42C24×C59
prime radicalC59×#3214C2
LCSG ▷ C42 ▷ 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×#3235C2semidirect
3. C59×#3167C2semidirect
4. C59×#2931C2semidirect
5. C59×#1699C2semidirect
6. C59×#1697C2semidirect
7. C59×#1671C2semidirect
8. C59×#1665C2semidirect
9. C59×#1568C2semidirect
10. C59×#1559C2semidirect
11. C59×#1557C2semidirect
208. #19328C59direct (N × H)
230. #3235C2×C59semidirect
232. #3167C2×C59semidirect
233. #2931C2×C59semidirect
234. #1699C2×C59semidirect
235. #1697C2×C59semidirect
236. #1671C2×C59semidirect
237. #1665C2×C59semidirect
238. #1568C2×C59semidirect
239. #1559C2×C59semidirect
240. #1557C2×C59semidirect
284. C59#19328direct (N × H)

Maximal subgroups

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

subgroupindex
C59×#32352
C59×#32142
C59×#31672
C59×#29312
C59×#16992
C59×#16972
C59×#16712
C59×#16652
C59×#15682
C59×#15592
C59×#15572
#1932859