Finite Group Databasebeta

← C59×#8249 #28420358

Subgroups — C59×#8249 #28420358

Order 15104.

436 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C59×#2966C211yesmaximal, characteristic
2C59×#1726C211yesmaximal, characteristic, complemented
3C59×#1524C211yesmaximal, characteristic
4C59×#1500C211yesmaximal, characteristic
5C59×#1451C211yesmaximal, characteristic, complemented
6C59×#1302C211yesmaximal, characteristic, complemented
7C59×#1300C211yesmaximal, characteristic, complemented
8C59×#529C2211yescharacteristic
9C59×#446C411yescharacteristic, complemented
10C8×Q8×C59C411yescharacteristic, complemented
11C59×#436C411yescharacteristic, complemented
12C59×#435—21no—
13C8×D4×C59—21no—
14C8×D4×C59C411yescharacteristic, complemented
15C59×#433—21no—
16C59×#432C2211yescharacteristic
17C59×#431C2211yescharacteristic
18C59×#405—21no—
19C4×M16×C59C2211yescharacteristic
20C2×#97×C59—21no—
21C2×#97×C59C2211yescharacteristic
22C2×C4×C8×C59—21no—
23C2×C4×C8×C59C2211yescharacteristic
24C59×#376C2211yescharacteristic
25C59×#330C412yescomplemented
26C59×#329C412yescomplemented
27C59×#328C412yes—
28C59×#327C412yes—
29C59×#322—21no—
30C59×#322—21no—
31C2×M16×C59—21no—
32C2×M16×C59—21no—
33C22×C8×C59—21no—
34C22×C8×C59—21no—
35C22×C8×C59D411yescharacteristic
36C22×C8×C59D411yescharacteristic
37#126×C59—21no—
38#125×C59C2×C411yescharacteristic
39#124×C59C2×C411yescharacteristic
40#123×C59—21no—
41C22⋊Q8×C59C2×C411yescharacteristic
42#121×C59C2×C411yescharacteristic
43C4×Q8×C59C2×C411yescharacteristic
44C4×D4×C59—21no—
45C4×D4×C59C2×C411yescharacteristic
46#117×C59—21no—
47C2×C42×C59—21no—
48C2×C42×C59C2311yescharacteristic
49C4⋊C8×C59—21no—
50C4⋊C8×C59—21no—
51C4⋊C8×C59—21no—
52C4⋊C8×C59C2×C411yescharacteristic
53C4⋊C8×C59C2×C411yescharacteristic
54C22⋊C8×C59—21no—
55C22⋊C8×C59—21no—
56C22⋊C8×C59—21no—
57C22⋊C8×C59C2×C412yes—
58#97×C59—24no—
59#97×C59—21no—
60#97×C59—21no—
61#97×C59—21no—
62#97×C59C2×C412yes—
63#97×C59C2×C412yes—
64C4×C8×C59—24no—
65C4×C8×C59—21no—
66C4×C8×C59—21no—
67C4×C8×C59—21no—
68C4×C8×C59C2×C411yescharacteristic
69C4×C8×C59C2×C411yescharacteristic
70C4×C8×C59D411yescharacteristic
71C4×C8×C59D411yescharacteristic
72#95×C59—21no—
73#95×C59C2×C412yes—
74C2×Q8×C59C4211yescharacteristic
75C2×D4×C59—21no—
76C2×D4×C59C4211yescharacteristic
77C22×C4×C59—22no—
78C22×C4×C59—21no—
79C22×C4×C59C22×C411yescharacteristic
80C22×C4×C59C2×D411yescharacteristic
81C22×C4×C59#4111yescharacteristic
82M16×C59—42no—
83M16×C59—42no—
84C2×C8×C59—22no—
85C2×C8×C59—22no—
86C2×C8×C59—22no—
87C2×C8×C59—22no—
88C2×C8×C59—22no—
89C2×C8×C59—21no—
90C2×C8×C59—21no—
91C2×C8×C59—22no—
92C2×C8×C59—22no—
93C2×C8×C59—42no—
94C2×C8×C59C22⋊C411yescharacteristic
95C2×C8×C59C22⋊C411yescharacteristic
96C2×C8×C59C22⋊C411yescharacteristic
97C2×C8×C59C22⋊C411yescharacteristic
98C4⋊C4×C59—21no—
99C4⋊C4×C59—21no—
100C4⋊C4×C59—21no—
101C4⋊C4×C59—21no—
102C4⋊C4×C59C4211yescharacteristic
103C4⋊C4×C59C4211yescharacteristic
104C22⋊C4×C59—21no—
105C22⋊C4×C59—21no—
106C22⋊C4×C59—21no—
107C22⋊C4×C59—21no—
108C22⋊C4×C59—21no—
109C42×C59—22no—
110C42×C59—22no—
111C42×C59—21no—
112C42×C59C22×C411yescharacteristic
113C42×C59C22×C411yescharacteristic
114C42×C59C2×D411yescharacteristic
115C42×C59#4111yescharacteristic
116C23×C59—21no—
117C23×C59C4×D411yescharacteristic
118Q8×C59—41no—
119D4×C59—41no—
120D4×C59—42no—
121C2×C4×C59—22no—
122C2×C4×C59—21no—
123C2×C4×C59—21no—
124C2×C4×C59—24no—
125C2×C4×C59—21no—
126C2×C4×C59—21no—
127C2×C4×C59—21no—
128C2×C4×C59—41no—
129C2×C4×C59—42no—
130C2×C4×C59—42no—
131C2×C4×C59—41no—
132C2×C4×C59—41no—
133C2×C4×C59C2×C4211yescharacteristic
134C2×C4×C59C2×C22⋊C411yescharacteristic
135C2×C4×C59#11711yescharacteristic
136C2×C4×C59C4×D411yescharacteristic
137C2×C4×C59C4×D411yescharacteristic
138C2×C4×C59C4×D411yescharacteristic
139C8×C59—24no—
140C8×C59—21no—
141C8×C59—21no—
142C8×C59—42no—
143C8×C59—42no—
144C8×C59—41no—
145C8×C59—41no—
146C8×C59#10412yes—
147C8×C59#10412yes—
148#8249C5911yesmaximal, characteristic, direct product factor, Sylow
149C22×C59—21no—
150C22×C59—21no—
151C22×C59—41no—
152C22×C59—41no—
153C22×C59—41no—
154C22×C59C4×C22⋊C411yescharacteristic
155C22×C59#44412yes—
156C4×C59—21no—
157C4×C59—21no—
158C4×C59—21no—
159C4×C59—21no—
160C4×C59—21no—
161C4×C59—44no—
162C4×C59—41no—
163C4×C59—41no—
164C4×C59—41no—
165C4×C59C2×#10411yescharacteristic
166C4×C59C2×#10411yescharacteristic
167#2966C2×C5911yescharacteristic
168#1726C2×C5911yescharacteristic, complemented
169#1524C2×C5911yescharacteristic
170#1500C2×C5911yescharacteristic
171#1451C2×C5911yescharacteristic, complemented
172#1302C2×C5911yescharacteristic, complemented
173#1300C2×C5911yescharacteristic, complemented
174C2×C59—22no—
175C2×C59—81no—
176C2×C59#175711yescharacteristic
177C2×C59C4×#10411yescharacteristic
178C2×C59#176511yescharacteristic
179#529C22×C5911yescharacteristic
180#446C4×C5911yescharacteristic, complemented
181C8×Q8C4×C5911yescharacteristic, complemented
182#436C4×C5911yescharacteristic, complemented
183#435—21no—
184C8×D4—21no—
185C8×D4C4×C5911yescharacteristic, complemented
186#433—21no—
187#432C22×C5911yescharacteristic
188#431C22×C5911yescharacteristic
189#405—21no—
190C4×M16C22×C5911yescharacteristic
191C2×#97—21no—
192C2×#97C22×C5911yescharacteristic
193C2×C4×C8—21no—
194C2×C4×C8C22×C5911yescharacteristic
195#376C22×C5911yescharacteristic
196#330C4×C5912yescomplemented
197#329C4×C5912yescomplemented
198#328C4×C5912yes—
199#327C4×C5912yes—
200#322—21no—
201#322—21no—
202C59#824911yescharacteristic, direct product factor, Sylow
203C2×M16—21no—
204C2×M16—21no—
205C22×C8—21no—
206C22×C8—21no—
207C22×C8D4×C5911yescharacteristic
208C22×C8D4×C5911yescharacteristic
209#126—21no—
210#125C2×C4×C5911yescharacteristic
211#124C2×C4×C5911yescharacteristic
212#123—21no—
213C22⋊Q8C2×C4×C5911yescharacteristic
214#121C2×C4×C5911yescharacteristic
215C4×Q8C2×C4×C5911yescharacteristic
216C4×D4—21no—
217C4×D4C2×C4×C5911yescharacteristic
218#117—21no—
219C2×C42—21no—
220C2×C42C23×C5911yescharacteristic
221C4⋊C8—21no—
222C4⋊C8—21no—
223C4⋊C8—21no—
224C4⋊C8C2×C4×C5911yescharacteristic
225C4⋊C8C2×C4×C5911yescharacteristic
226C22⋊C8—21no—
227C22⋊C8—21no—
228C22⋊C8—21no—
229C22⋊C8C2×C4×C5912yes—
230#97—24no—
231#97—21no—
232#97—21no—
233#97—21no—
234#97C2×C4×C5912yes—
235#97C2×C4×C5912yes—
236C4×C8—24no—
237C4×C8—21no—
238C4×C8—21no—
239C4×C8—21no—
240C4×C8C2×C4×C5911yescharacteristic
241C4×C8C2×C4×C5911yescharacteristic
242C4×C8D4×C5911yescharacteristic
243C4×C8D4×C5911yescharacteristic
244#95—21no—
245#95C2×C4×C5912yes—
246C2×Q8C42×C5911yescharacteristic
247C2×D4—21no—
248C2×D4C42×C5911yescharacteristic
249C22×C4—22no—
250C22×C4—21no—
251C22×C4C22×C4×C5911yescharacteristic
252C22×C4C2×D4×C5911yescharacteristic
253C22×C4#41×C5911yescharacteristic
254M16—42no—
255M16—42no—
256C2×C8—22no—
257C2×C8—22no—
258C2×C8—22no—
259C2×C8—22no—
260C2×C8—22no—
261C2×C8—21no—
262C2×C8—21no—
263C2×C8—22no—
264C2×C8—22no—
265C2×C8—42no—
266C2×C8C22⋊C4×C5911yescharacteristic
267C2×C8C22⋊C4×C5911yescharacteristic
268C2×C8C22⋊C4×C5911yescharacteristic
269C2×C8C22⋊C4×C5911yescharacteristic
270C4⋊C4—21no—
271C4⋊C4—21no—
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4C42×C5911yescharacteristic
275C4⋊C4C42×C5911yescharacteristic
276C22⋊C4—21no—
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—21no—
280C22⋊C4—21no—
281C42—22no—
282C42—22no—
283C42—21no—
284C42C22×C4×C5911yescharacteristic
285C42C22×C4×C5911yescharacteristic
286C42C2×D4×C5911yescharacteristic
287C42#41×C5911yescharacteristic
288C23—21no—
289C23C4×D4×C5911yescharacteristic
290Q8—41no—
291D4—41no—
292D4—42no—
293C2×C4—22no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—24no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—41no—
301C2×C4—42no—
302C2×C4—42no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4C2×C42×C5911yescharacteristic
306C2×C4C2×C22⋊C4×C5911yescharacteristic
307C2×C4#117×C5911yescharacteristic
308C2×C4C4×D4×C5911yescharacteristic
309C2×C4C4×D4×C5911yescharacteristic
310C2×C4C4×D4×C5911yescharacteristic
311C8—24no—
312C8—21no—
313C8—21no—
314C8—42no—
315C8—42no—
316C8—41no—
317C8—41no—
318C8#104×C5912yes—
319C8#104×C5912yes—
320C22—21no—
321C22—21no—
322C22—41no—
323C22—41no—
324C22—41no—
325C22C4×C22⋊C4×C5911yescharacteristic
326C22C59×#44412yes—
327C4—21no—
328C4—21no—
329C4—21no—
330C4—21no—
331C4—21no—
332C4—44no—
333C4—41no—
334C4—41no—
335C4—41no—
336C4C2×#104×C5911yescharacteristic
337C4C2×#104×C5911yescharacteristic
338C2—22no—
339C2—81no—
340C2C59×#175711yescharacteristic
341C2C4×#104×C5911yescharacteristic
342C2C59×#176511yescharacteristic
subgroupG/H
centerC2×C4×C59C2×C22⋊C4
commutatorC2×C4C2×C42×C59
Frattini, cosocleC2×C42C23×C59
socleC22×C59C4×C22⋊C4
prime radical#121×C59C2×C4
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C59 ◁ C2×C4×C8×C59 ◁ G

Complements

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

NH ≅ G/Ntype
2. C59×#1726C2semidirect
5. C59×#1451C2semidirect
6. C59×#1302C2semidirect
7. C59×#1300C2semidirect
9. C59×#446C4semidirect
10. C8×Q8×C59C4semidirect
11. C59×#436C4semidirect
14. C8×D4×C59C4semidirect
25. C59×#330C4semidirect
26. C59×#329C4semidirect
148. #8249C59direct (N × H)
168. #1726C2×C59semidirect
171. #1451C2×C59semidirect
172. #1302C2×C59semidirect
173. #1300C2×C59semidirect
180. #446C4×C59semidirect
181. C8×Q8C4×C59semidirect
182. #436C4×C59semidirect
185. C8×D4C4×C59semidirect
196. #330C4×C59semidirect
197. #329C4×C59semidirect
202. C59#8249direct (N × H)

Maximal subgroups

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

subgroupindex
C59×#29662
C59×#17262
C59×#15242
C59×#15002
C59×#14512
C59×#13022
C59×#13002
#824959