Finite Group Databasebeta

← C59×#9050 #28421159

Subgroups — C59×#9050 #28421159

Order 15104.

476 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C59×#3101C211yesmaximal, characteristic
2C59×#2961C211yesmaximal, characteristic, complemented
3C59×#1955C211yesmaximal, characteristic
4C59×#1542C211yesmaximal, characteristic, complemented
5C59×#1486C211yesmaximal, characteristic
6C59×#1301C211yesmaximal, characteristic, complemented
7C59×#1281C211yesmaximal, characteristic, complemented
8C59×#533C2211yescharacteristic
9C2×C4×D4×C59C2211yescharacteristic
10C59×#483C412yes—
11C59×#476—21no—
12C59×#461—21no—
13C59×#450C412yes—
14C59×#446—22no—
15C59×#446—22no—
16C4×SD16×C59—22no—
17C59×#431C2211yescharacteristic
18C59×#431C2211yescharacteristic
19C59×#424—21no—
20C59×#423C2211yescharacteristic
21C2×C4⋊C8×C59C2211yescharacteristic
22C2×C22⋊C8×C59—21no—
23C2×C22⋊C8×C59—21no—
24C59×#405—21no—
25C2×#97×C59C2211yescharacteristic
26C59×#333—21no—
27C59×#332—21no—
28C59×D4⋊C8—22no—
29C22×D4×C59C2×C411yescharacteristic
30C23×C4×C59—21no—
31C2×SD16×C59—22no—
32C2×M16×C59—21no—
33C22×C8×C59—21no—
34C22×C8×C59D411yescharacteristic
35C22×C8×C59D411yescharacteristic
36C4⋊Q8×C59D411yescharacteristic
37C4⋊Q8×C59D411yescharacteristic
38#125×C59—21no—
39C22⋊Q8×C59—21no—
40C22⋊Q8×C59C2×C412yes—
41C4×Q8×C59—21no—
42C4×Q8×C59D412yes—
43C4×D4×C59—21no—
44C4×D4×C59—21no—
45C4×D4×C59—21no—
46C4×D4×C59—21no—
47#117×C59—21no—
48C2×C4⋊C4×C59C2×C411yescharacteristic
49C2×C22⋊C4×C59—21no—
50C2×C42×C59C2311yescharacteristic
51#106×C59—22no—
52C4⋊C8×C59—24no—
53C4⋊C8×C59—21no—
54C4⋊C8×C59—21no—
55C4⋊C8×C59—21no—
56C4⋊C8×C59—21no—
57C4⋊C8×C59—21no—
58C4⋊C8×C59D412yes—
59#103×C59—22no—
60#102×C59—22no—
61C22⋊C8×C59—21no—
62C22⋊C8×C59—42no—
63C22⋊C8×C59—42no—
64C22⋊C8×C59C2×C412yes—
65#97×C59—22no—
66#97×C59—21no—
67#97×C59—21no—
68C4×C8×C59—22no—
69C4×C8×C59—21no—
70C4×C8×C59—21no—
71C24×C59—21no—
72C2×Q8×C59—21no—
73C2×Q8×C59C22⋊C412yes—
74C2×D4×C59—21no—
75C2×D4×C59—21no—
76C2×D4×C59—42no—
77C22×C4×C59—21no—
78C22×C4×C59—41no—
79C22×C4×C59—41no—
80C22×C4×C59—41no—
81C22×C4×C59—41no—
82C22×C4×C59—41no—
83C22×C4×C59—41no—
84C22×C4×C59C22×C411yescharacteristic
85C22×C4×C59C2×D411yescharacteristic
86C22×C4×C59#4111yescharacteristic
87SD16×C59—44no—
88M16×C59—41no—
89M16×C59—41no—
90C2×C8×C59—21no—
91C2×C8×C59—21no—
92C2×C8×C59—22no—
93C2×C8×C59—22no—
94C2×C8×C59—21no—
95C2×C8×C59—21no—
96C2×C8×C59—21no—
97C2×C8×C59—41no—
98C2×C8×C59—41no—
99C2×C8×C59—41no—
100C2×C8×C59—41no—
101C2×C8×C59SD1612yescomplemented
102C4⋊C4×C59—22no—
103C4⋊C4×C59—21no—
104C4⋊C4×C59—21no—
105C4⋊C4×C59—21no—
106C4⋊C4×C59—22no—
107C4⋊C4×C59—21no—
108C4⋊C4×C59—21no—
109C4⋊C4×C59C22⋊C412yes—
110C22⋊C4×C59—22no—
111C22⋊C4×C59—41no—
112C22⋊C4×C59—41no—
113C42×C59—22no—
114C42×C59C2×D411yescharacteristic
115C42×C59C2×D411yescharacteristic
116C42×C59C2×D411yescharacteristic
117C42×C59#4111yescharacteristic
118C23×C59—22no—
119C23×C59—41no—
120C23×C59—41no—
121C23×C59—41no—
122C23×C59—41no—
123C23×C59—41no—
124C23×C59—41no—
125C23×C59C4×D411yescharacteristic
126Q8×C59—42no—
127Q8×C59—81no—
128D4×C59—22no—
129D4×C59—22no—
130D4×C59—41no—
131D4×C59—41no—
132C2×C4×C59—22no—
133C2×C4×C59—22no—
134C2×C4×C59—41no—
135C2×C4×C59—41no—
136C2×C4×C59—41no—
137C2×C4×C59—41no—
138C2×C4×C59—41no—
139C2×C4×C59—81no—
140C2×C4×C59—81no—
141C2×C4×C59—81no—
142C2×C4×C59—81no—
143C2×C4×C59C2×C22⋊C411yescharacteristic
144C2×C4×C59C4×D411yescharacteristic
145C2×C4×C59#12011yescharacteristic
146C2×C4×C59#12111yescharacteristic
147C2×C4×C59#12111yescharacteristic
148C2×C4×C59#12311yescharacteristic
149C2×C4×C59C2×SD1611yescharacteristic
150C2×C4×C59#13511yescharacteristic
151C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
152C2×C4×C59#13711yescharacteristic
153C8×C59—22no—
154C8×C59—42no—
155C8×C59—41no—
156C8×C59—42no—
157C8×C59—81no—
158C8×C59—81no—
159#9050C5911yesmaximal, characteristic, direct product factor, Sylow
160C22×C59—21no—
161C22×C59—21no—
162C22×C59—42no—
163C22×C59—42no—
164C22×C59—42no—
165C22×C59—81no—
166C22×C59—81no—
167C22×C59—81no—
168C22×C59—81no—
169C22×C59#38611yescharacteristic
170C22×C59C4×SD1611yescharacteristic
171C22×C59#44011yescharacteristic
172C4×C59—21no—
173C4×C59—21no—
174C4×C59—21no—
175C4×C59—21no—
176C4×C59—42no—
177C4×C59—42no—
178C4×C59—81no—
179C4×C59#44811yescharacteristic
180C4×C59#44911yescharacteristic
181C4×C59#46011yescharacteristic
182C4×C59#46411yescharacteristic
183#3101C2×C5911yescharacteristic
184#2961C2×C5911yescharacteristic, complemented
185#1955C2×C5911yescharacteristic
186#1542C2×C5911yescharacteristic, complemented
187#1486C2×C5911yescharacteristic
188#1301C2×C5911yescharacteristic, complemented
189#1281C2×C5911yescharacteristic, complemented
190C2×C59—21no—
191C2×C59—21no—
192C2×C59—82no—
193C2×C59#188011yescharacteristic
194C2×C59#188111yescharacteristic
195C2×C59#189111yescharacteristic
196#533C22×C5911yescharacteristic
197C2×C4×D4C22×C5911yescharacteristic
198#483C4×C5912yes—
199#476—21no—
200#461—21no—
201#450C4×C5912yes—
202#446—22no—
203#446—22no—
204C4×SD16—22no—
205#431C22×C5911yescharacteristic
206#431C22×C5911yescharacteristic
207#424—21no—
208#423C22×C5911yescharacteristic
209C2×C4⋊C8C22×C5911yescharacteristic
210C2×C22⋊C8—21no—
211C2×C22⋊C8—21no—
212#405—21no—
213C2×#97C22×C5911yescharacteristic
214#333—21no—
215#332—21no—
216D4⋊C8—22no—
217C59#905011yescharacteristic, direct product factor, Sylow
218C22×D4C2×C4×C5911yescharacteristic
219C23×C4—21no—
220C2×SD16—22no—
221C2×M16—21no—
222C22×C8—21no—
223C22×C8D4×C5911yescharacteristic
224C22×C8D4×C5911yescharacteristic
225C4⋊Q8D4×C5911yescharacteristic
226C4⋊Q8D4×C5911yescharacteristic
227#125—21no—
228C22⋊Q8—21no—
229C22⋊Q8C2×C4×C5912yes—
230C4×Q8—21no—
231C4×Q8D4×C5912yes—
232C4×D4—21no—
233C4×D4—21no—
234C4×D4—21no—
235C4×D4—21no—
236#117—21no—
237C2×C4⋊C4C2×C4×C5911yescharacteristic
238C2×C22⋊C4—21no—
239C2×C42C23×C5911yescharacteristic
240#106—22no—
241C4⋊C8—24no—
242C4⋊C8—21no—
243C4⋊C8—21no—
244C4⋊C8—21no—
245C4⋊C8—21no—
246C4⋊C8—21no—
247C4⋊C8D4×C5912yes—
248#103—22no—
249#102—22no—
250C22⋊C8—21no—
251C22⋊C8—42no—
252C22⋊C8—42no—
253C22⋊C8C2×C4×C5912yes—
254#97—22no—
255#97—21no—
256#97—21no—
257C4×C8—22no—
258C4×C8—21no—
259C4×C8—21no—
260C24—21no—
261C2×Q8—21no—
262C2×Q8C22⋊C4×C5912yes—
263C2×D4—21no—
264C2×D4—21no—
265C2×D4—42no—
266C22×C4—21no—
267C22×C4—41no—
268C22×C4—41no—
269C22×C4—41no—
270C22×C4—41no—
271C22×C4—41no—
272C22×C4—41no—
273C22×C4C22×C4×C5911yescharacteristic
274C22×C4C2×D4×C5911yescharacteristic
275C22×C4#41×C5911yescharacteristic
276SD16—44no—
277M16—41no—
278M16—41no—
279C2×C8—21no—
280C2×C8—21no—
281C2×C8—22no—
282C2×C8—22no—
283C2×C8—21no—
284C2×C8—21no—
285C2×C8—21no—
286C2×C8—41no—
287C2×C8—41no—
288C2×C8—41no—
289C2×C8—41no—
290C2×C8SD16×C5912yescomplemented
291C4⋊C4—22no—
292C4⋊C4—21no—
293C4⋊C4—21no—
294C4⋊C4—21no—
295C4⋊C4—22no—
296C4⋊C4—21no—
297C4⋊C4—21no—
298C4⋊C4C22⋊C4×C5912yes—
299C22⋊C4—22no—
300C22⋊C4—41no—
301C22⋊C4—41no—
302C42—22no—
303C42C2×D4×C5911yescharacteristic
304C42C2×D4×C5911yescharacteristic
305C42C2×D4×C5911yescharacteristic
306C42#41×C5911yescharacteristic
307C23—22no—
308C23—41no—
309C23—41no—
310C23—41no—
311C23—41no—
312C23—41no—
313C23—41no—
314C23C4×D4×C5911yescharacteristic
315Q8—42no—
316Q8—81no—
317D4—22no—
318D4—22no—
319D4—41no—
320D4—41no—
321C2×C4—22no—
322C2×C4—22no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—81no—
329C2×C4—81no—
330C2×C4—81no—
331C2×C4—81no—
332C2×C4C2×C22⋊C4×C5911yescharacteristic
333C2×C4C4×D4×C5911yescharacteristic
334C2×C4#120×C5911yescharacteristic
335C2×C4#121×C5911yescharacteristic
336C2×C4#121×C5911yescharacteristic
337C2×C4#123×C5911yescharacteristic
338C2×C4C2×SD16×C5911yescharacteristic
339C2×C4#135×C5911yescharacteristic
340C2×C4AGL(1,ℤ/8)×C5911yescharacteristic
341C2×C4#137×C5911yescharacteristic
342C8—22no—
343C8—42no—
344C8—41no—
345C8—42no—
346C8—81no—
347C8—81no—
348C22—21no—
349C22—21no—
350C22—42no—
351C22—42no—
352C22—42no—
353C22—81no—
354C22—81no—
355C22—81no—
356C22—81no—
357C22C59×#38611yescharacteristic
358C22C4×SD16×C5911yescharacteristic
359C22C59×#44011yescharacteristic
360C4—21no—
361C4—21no—
362C4—21no—
363C4—21no—
364C4—42no—
365C4—42no—
366C4—81no—
367C4C59×#44811yescharacteristic
368C4C59×#44911yescharacteristic
369C4C59×#46011yescharacteristic
370C4C59×#46411yescharacteristic
371C2—21no—
372C2—21no—
373C2—82no—
374C2C59×#188011yescharacteristic
375C2C59×#188111yescharacteristic
376C2C59×#189111yescharacteristic
subgroupG/H
centerC2×C4×C59#120
commutatorC22×C4C22×C4×C59
Frattini, cosocleC2×C42C23×C59
socleC22×C59#386
prime radicalC22×D4×C59C2×C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C59 ◁ C2×C42×C59 ◁ G

Complements

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

NH ≅ G/Ntype
2. C59×#2961C2semidirect
4. C59×#1542C2semidirect
6. C59×#1301C2semidirect
7. C59×#1281C2semidirect
101. C2×C8×C59SD16semidirect
159. #9050C59direct (N × H)
184. #2961C2×C59semidirect
186. #1542C2×C59semidirect
188. #1301C2×C59semidirect
189. #1281C2×C59semidirect
217. C59#9050direct (N × H)
290. C2×C8SD16×C59semidirect

Maximal subgroups

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

subgroupindex
C59×#31012
C59×#29612
C59×#19552
C59×#15422
C59×#14862
C59×#13012
C59×#12812
#905059