Finite Group Databasebeta

← C59×#7674 #28419783

Subgroups — C59×#7674 #28419783

Order 15104.

550 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C59×#2854C211yesmaximal, characteristic
2C59×#1749C211yesmaximal, characteristic, complemented
3C4×C22⋊C8×C59C211yesmaximal, characteristic, complemented
4C59×#1271C212yesmaximal, complemented
5C59×#1270C212yesmaximal, complemented
6C2×#123×C59—21no—
7C2×#121×C59C411yescharacteristic
8C22×C42×C59C2211yescharacteristic
9C2×C22⋊C8×C59—21no—
10C2×C22⋊C8×C59—21no—
11C2×#97×C59—21no—
12C2×C4×C8×C59—21no—
13C59×#390C411yescharacteristic
14C59×#390C2211yescharacteristic
15C59×#389C411yescharacteristic
16C59×#389C2211yescharacteristic
17C59×#388—21no—
18C59×#388—21no—
19C59×#386—21no—
20C59×#380C411yescharacteristic
21C59×#336C2212yes—
22C59×#336C2212yes—
23C22×D4×C59—21no—
24C22×D4×C59C2×C411yescharacteristic
25C23×C4×C59C2×C411yescharacteristic
26C23×C4×C59D411yescharacteristic
27C23×C4×C59D411yescharacteristic
28C22×C8×C59—22no—
29C22×C8×C59—22no—
30#123×C59—44no—
31#121×C59—42no—
32C2×C4⋊C4×C59—21no—
33C2×C4⋊C4×C59—21no—
34C2×C4⋊C4×C59C2×C411yescharacteristic
35C2×C4⋊C4×C59C2×C411yescharacteristic
36C2×C4⋊C4×C59C2×C411yescharacteristic
37C2×C22⋊C4×C59—21no—
38C2×C22⋊C4×C59—21no—
39C2×C22⋊C4×C59—21no—
40C2×C22⋊C4×C59—21no—
41C2×C22⋊C4×C59—21no—
42C2×C22⋊C4×C59—21no—
43C2×C42×C59—42no—
44C2×C42×C59C2×C411yescharacteristic
45C2×C42×C59D411yescharacteristic
46C2×C42×C59D411yescharacteristic
47C2×C42×C59C2311yescharacteristic
48C22⋊C8×C59—24no—
49C22⋊C8×C59—24no—
50#97×C59—42no—
51C4×C8×C59—42no—
52#95×C59—21no—
53#95×C59—21no—
54#95×C59—21no—
55C24×C59—21no—
56C24×C59C22⋊C411yescharacteristic
57C2×D4×C59—22no—
58C2×D4×C59—41no—
59C2×D4×C59—41no—
60C2×D4×C59—42no—
61C2×D4×C59—42no—
62C2×D4×C59—42no—
63C22×C4×C59—22no—
64C22×C4×C59—22no—
65C22×C4×C59—22no—
66C22×C4×C59—22no—
67C22×C4×C59—22no—
68C22×C4×C59—22no—
69C22×C4×C59—21no—
70C22×C4×C59—21no—
71C22×C4×C59—21no—
72C22×C4×C59—41no—
73C22×C4×C59—41no—
74C22×C4×C59—41no—
75C22×C4×C59C22⋊C411yescharacteristic
76C22×C4×C59C22⋊C411yescharacteristic
77C22×C4×C59C22⋊C411yescharacteristic
78C22×C4×C59C22×C411yescharacteristic
79C22×C4×C59C2×D411yescharacteristic
80C22×C4×C59C2×D411yescharacteristic
81C2×C8×C59—24no—
82C2×C8×C59—24no—
83C2×C8×C59—42no—
84C2×C8×C59—42no—
85C2×C8×C59—42no—
86C2×C8×C59—42no—
87C4⋊C4×C59—22no—
88C4⋊C4×C59—42no—
89C4⋊C4×C59—41no—
90C4⋊C4×C59—41no—
91C4⋊C4×C59—42no—
92C22⋊C4×C59—42no—
93C22⋊C4×C59—42no—
94C22⋊C4×C59—42no—
95C22⋊C4×C59—42no—
96C22⋊C4×C59—42no—
97C22⋊C4×C59—42no—
98C42×C59—22no—
99C42×C59—22no—
100C42×C59—41no—
101C42×C59—41no—
102C23×C59—21no—
103C23×C59—21no—
104C23×C59—21no—
105C23×C59—21no—
106C23×C59—21no—
107C23×C59—21no—
108C23×C59—41no—
109C23×C59—41no—
110C23×C59—41no—
111C23×C59—41no—
112C23×C59—41no—
113C23×C59—41no—
114C23×C59—41no—
115C23×C59#10412yes—
116C23×C59C2×C22⋊C411yescharacteristic
117D4×C59—82no—
118D4×C59—84no—
119C2×C4×C59—21no—
120C2×C4×C59—21no—
121C2×C4×C59—21no—
122C2×C4×C59—21no—
123C2×C4×C59—21no—
124C2×C4×C59—21no—
125C2×C4×C59—21no—
126C2×C4×C59—21no—
127C2×C4×C59—21no—
128C2×C4×C59—21no—
129C2×C4×C59—21no—
130C2×C4×C59—21no—
131C2×C4×C59—21no—
132C2×C4×C59—44no—
133C2×C4×C59—44no—
134C2×C4×C59—44no—
135C2×C4×C59—41no—
136C2×C4×C59—41no—
137C2×C4×C59—41no—
138C2×C4×C59—41no—
139C2×C4×C59—41no—
140C2×C4×C59—41no—
141C2×C4×C59—41no—
142C2×C4×C59—41no—
143C2×C4×C59—41no—
144C2×C4×C59#9912yes—
145C2×C4×C59#10412yes—
146C2×C4×C59#13112yes—
147C2×C4×C59#13512yes—
148C2×C4×C59AGL(1,ℤ/8)12yes—
149C8×C59—44no—
150C8×C59—44no—
151#7674C5911yesmaximal, characteristic, direct product factor, Sylow
152C22×C59—22no—
153C22×C59—22no—
154C22×C59—22no—
155C22×C59—41no—
156C22×C59—41no—
157C22×C59—41no—
158C22×C59—41no—
159C22×C59—81no—
160C22×C59—81no—
161C22×C59—81no—
162C22×C59—81no—
163C22×C59—81no—
164C22×C59—81no—
165C22×C59—81no—
166C22×C59#40811yescharacteristic
167C22×C59C2×#9911yescharacteristic
168C22×C59#41311yescharacteristic
169C22×C59#41611yescharacteristic
170C22×C59#41811yescharacteristic
171C22×C59C2×#10411yescharacteristic
172C22×C59C2×#10411yescharacteristic
173C4×C59—22no—
174C4×C59—22no—
175C4×C59—22no—
176C4×C59—22no—
177C4×C59—22no—
178C4×C59—41no—
179C4×C59—81no—
180C4×C59—81no—
181C4×C59—81no—
182#2854C2×C5911yescharacteristic
183#1749C2×C5911yescharacteristic, complemented
184C4×C22⋊C8C2×C5911yescharacteristic, complemented
185#1271C2×C5912yescomplemented
186#1270C2×C5912yescomplemented
187C2×C59—42no—
188C2×C59—161no—
189C2×C59#146811yescharacteristic
190C2×C59#148411yescharacteristic
191C2×C59#149411yescharacteristic
192C2×C59#150111yescharacteristic
193C2×C59#150711yescharacteristic
194C2×C59#152411yescharacteristic
195C2×C59#155311yescharacteristic
196C2×#123—21no—
197C2×#121C4×C5911yescharacteristic
198C22×C42C22×C5911yescharacteristic
199C2×C22⋊C8—21no—
200C2×C22⋊C8—21no—
201C2×#97—21no—
202C2×C4×C8—21no—
203#390C4×C5911yescharacteristic
204#390C22×C5911yescharacteristic
205#389C4×C5911yescharacteristic
206#389C22×C5911yescharacteristic
207#388—21no—
208#388—21no—
209#386—21no—
210#380C4×C5911yescharacteristic
211#336C22×C5912yes—
212#336C22×C5912yes—
213C59#767411yescharacteristic, direct product factor, Sylow
214C22×D4—21no—
215C22×D4C2×C4×C5911yescharacteristic
216C23×C4C2×C4×C5911yescharacteristic
217C23×C4D4×C5911yescharacteristic
218C23×C4D4×C5911yescharacteristic
219C22×C8—22no—
220C22×C8—22no—
221#123—44no—
222#121—42no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4C2×C4×C5911yescharacteristic
226C2×C4⋊C4C2×C4×C5911yescharacteristic
227C2×C4⋊C4C2×C4×C5911yescharacteristic
228C2×C22⋊C4—21no—
229C2×C22⋊C4—21no—
230C2×C22⋊C4—21no—
231C2×C22⋊C4—21no—
232C2×C22⋊C4—21no—
233C2×C22⋊C4—21no—
234C2×C42—42no—
235C2×C42C2×C4×C5911yescharacteristic
236C2×C42D4×C5911yescharacteristic
237C2×C42D4×C5911yescharacteristic
238C2×C42C23×C5911yescharacteristic
239C22⋊C8—24no—
240C22⋊C8—24no—
241#97—42no—
242C4×C8—42no—
243#95—21no—
244#95—21no—
245#95—21no—
246C24—21no—
247C24C22⋊C4×C5911yescharacteristic
248C2×D4—22no—
249C2×D4—41no—
250C2×D4—41no—
251C2×D4—42no—
252C2×D4—42no—
253C2×D4—42no—
254C22×C4—22no—
255C22×C4—22no—
256C22×C4—22no—
257C22×C4—22no—
258C22×C4—22no—
259C22×C4—22no—
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—41no—
264C22×C4—41no—
265C22×C4—41no—
266C22×C4C22⋊C4×C5911yescharacteristic
267C22×C4C22⋊C4×C5911yescharacteristic
268C22×C4C22⋊C4×C5911yescharacteristic
269C22×C4C22×C4×C5911yescharacteristic
270C22×C4C2×D4×C5911yescharacteristic
271C22×C4C2×D4×C5911yescharacteristic
272C2×C8—24no—
273C2×C8—24no—
274C2×C8—42no—
275C2×C8—42no—
276C2×C8—42no—
277C2×C8—42no—
278C4⋊C4—22no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C4⋊C4—42no—
282C4⋊C4—42no—
283C22⋊C4—42no—
284C22⋊C4—42no—
285C22⋊C4—42no—
286C22⋊C4—42no—
287C22⋊C4—42no—
288C22⋊C4—42no—
289C42—22no—
290C42—22no—
291C42—41no—
292C42—41no—
293C23—21no—
294C23—21no—
295C23—21no—
296C23—21no—
297C23—21no—
298C23—21no—
299C23—41no—
300C23—41no—
301C23—41no—
302C23—41no—
303C23—41no—
304C23—41no—
305C23—41no—
306C23#104×C5912yes—
307C23C2×C22⋊C4×C5911yescharacteristic
308D4—82no—
309D4—84no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—44no—
324C2×C4—44no—
325C2×C4—44no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4#99×C5912yes—
336C2×C4#104×C5912yes—
337C2×C4#131×C5912yes—
338C2×C4#135×C5912yes—
339C2×C4AGL(1,ℤ/8)×C5912yes—
340C8—44no—
341C8—44no—
342C22—22no—
343C22—22no—
344C22—22no—
345C22—41no—
346C22—41no—
347C22—41no—
348C22—41no—
349C22—81no—
350C22—81no—
351C22—81no—
352C22—81no—
353C22—81no—
354C22—81no—
355C22—81no—
356C22C59×#40811yescharacteristic
357C22C2×#99×C5911yescharacteristic
358C22C59×#41311yescharacteristic
359C22C59×#41611yescharacteristic
360C22C59×#41811yescharacteristic
361C22C2×#104×C5911yescharacteristic
362C22C2×#104×C5911yescharacteristic
363C4—22no—
364C4—22no—
365C4—22no—
366C4—22no—
367C4—22no—
368C4—41no—
369C4—81no—
370C4—81no—
371C4—81no—
372C2—42no—
373C2—161no—
374C2C59×#146811yescharacteristic
375C2C59×#148411yescharacteristic
376C2C59×#149411yescharacteristic
377C2C59×#150111yescharacteristic
378C2C59×#150711yescharacteristic
379C2C59×#152411yescharacteristic
380C2C59×#155311yescharacteristic
subgroupG/H
center, socleC23×C59C2×C22⋊C4
commutatorC22×C4C22×C4×C59
Frattini, cosocleC2×C42C23×C59
prime radicalC2×#121×C59C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C59 ◁ C22×C42×C59 ◁ G

Complements

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

NH ≅ G/Ntype
2. C59×#1749C2semidirect
3. C4×C22⋊C8×C59C2semidirect
4. C59×#1271C2semidirect
5. C59×#1270C2semidirect
151. #7674C59direct (N × H)
183. #1749C2×C59semidirect
184. C4×C22⋊C8C2×C59semidirect
185. #1271C2×C59semidirect
186. #1270C2×C59semidirect
213. C59#7674direct (N × H)

Maximal subgroups

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

subgroupindex
C59×#28542
C59×#17492
C4×C22⋊C8×C592
C59×#12712
C59×#12702
#767459