Finite Group Databasebeta

← C59×#8610 #28420719

Subgroups — C59×#8610 #28420719

Order 15104.

524 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C59×#435C211yesmaximal, characteristic
2C59×#1808C211yesmaximal, characteristic, complemented
3C59×#1807C211yesmaximal, characteristic, complemented
4C59×#1799C212yesmaximal
5C59×#1289C212yesmaximal, complemented
6C22×M16×C59C411yescharacteristic, complemented
7C23×C8×C59C2211yescharacteristic
8C2×C4×D4×C59C2211yescharacteristic
9C59×#435—21no—
10C59×#435—21no—
11C59×#435—21no—
12C59×#435—21no—
13C2×#107×C59—21no—
14C2×#106×C59—21no—
15C2×C4⋊C8×C59C411yescharacteristic, complemented
16C2×#99×C59—22no—
17C2×C22⋊C8×C59C411yescharacteristic, complemented
18C2×C22⋊C8×C59C2211yescharacteristic
19C2×#97×C59C411yescharacteristic, complemented
20C59×#380C2212yes—
21C59×#380C2212yes—
22C59×#342—22no—
23C59×#340—21no—
24C59×#340—21no—
25C22×D4×C59D411yescharacteristic
26C23×C4×C59C2×C411yescharacteristic
27C23×C4×C59C2311yescharacteristic
28C2×M16×C59—21no—
29C2×M16×C59—21no—
30C2×M16×C59—42no—
31C22×C8×C59—42no—
32C22×C8×C59C2×C411yescharacteristic
33C22×C8×C59C2×C411yescharacteristic
34C22×C8×C59C2×C411yescharacteristic
35C22×C8×C59C2×C411yescharacteristic
36C22×C8×C59D411yescharacteristic
37C22×C8×C59D411yescharacteristic
38C22×C8×C59D411yescharacteristic
39C22×C8×C59D411yescharacteristic
40C4×D4×C59—21no—
41C4×D4×C59—21no—
42C4×D4×C59—21no—
43C4×D4×C59—21no—
44C2×C4⋊C4×C59—22no—
45C2×C4⋊C4×C59—22no—
46C2×C4⋊C4×C59Q811yescharacteristic
47C2×C22⋊C4×C59—22no—
48C2×C22⋊C4×C59—22no—
49C2×C22⋊C4×C59D411yescharacteristic
50C2×C22⋊C4×C59Q811yescharacteristic
51C2×C42×C59C2×C411yescharacteristic
52#107×C59—42no—
53#106×C59—42no—
54C4⋊C8×C59—21no—
55C4⋊C8×C59—21no—
56#99×C59—44no—
57C22⋊C8×C59—21no—
58C22⋊C8×C59—21no—
59C22⋊C8×C59—21no—
60C22⋊C8×C59—21no—
61#97×C59—21no—
62#97×C59—21no—
63#95×C59—22no—
64#95×C59—22no—
65C24×C59C4⋊C411yescharacteristic
66C24×C59C2×D411yescharacteristic
67C2×D4×C59—21no—
68C2×D4×C59—21no—
69C2×D4×C59—22no—
70C2×D4×C59—22no—
71C22×C4×C59—21no—
72C22×C4×C59—21no—
73C22×C4×C59—41no—
74C22×C4×C59—41no—
75C22×C4×C59—41no—
76C22×C4×C59—41no—
77C22×C4×C59—42no—
78C22×C4×C59—42no—
79C22×C4×C59C4⋊C411yescharacteristic
80C22×C4×C59C4⋊C411yescharacteristic
81C22×C4×C59C4⋊C411yescharacteristic
82C22×C4×C59C22×C411yescharacteristic
83C22×C4×C59C2×D411yescharacteristic
84C22×C4×C59C2×D411yescharacteristic
85C22×C4×C59C2×Q811yescharacteristic
86C22×C4×C59#4111yescharacteristic
87C22×C4×C59#4111yescharacteristic
88M16×C59—42no—
89M16×C59—42no—
90C2×C8×C59—22no—
91C2×C8×C59—22no—
92C2×C8×C59—22no—
93C2×C8×C59—21no—
94C2×C8×C59—21no—
95C2×C8×C59—41no—
96C2×C8×C59—41no—
97C2×C8×C59—41no—
98C2×C8×C59—41no—
99C2×C8×C59—41no—
100C2×C8×C59C22⋊C411yescharacteristic
101C2×C8×C59C22⋊C411yescharacteristic
102C2×C8×C59C22⋊C411yescharacteristic
103C2×C8×C59C22⋊C411yescharacteristic
104C4⋊C4×C59—21no—
105C4⋊C4×C59—21no—
106C4⋊C4×C59—42no—
107C4⋊C4×C59—42no—
108C4⋊C4×C59—42no—
109C4⋊C4×C59—42no—
110C22⋊C4×C59—21no—
111C22⋊C4×C59—21no—
112C22⋊C4×C59—21no—
113C22⋊C4×C59—21no—
114C22⋊C4×C59—42no—
115C22⋊C4×C59—42no—
116C22⋊C4×C59—42no—
117C22⋊C4×C59—42no—
118C42×C59—21no—
119C42×C59—21no—
120C23×C59—21no—
121C23×C59—22no—
122C23×C59—41no—
123C23×C59—41no—
124C23×C59—41no—
125C23×C59—41no—
126C23×C59C2×C4⋊C411yescharacteristic
127C23×C59#12111yescharacteristic
128C23×C59#12111yescharacteristic
129C23×C59AGL(1,ℤ/8)12yes—
130C23×C59#13712yes—
131D4×C59—42no—
132D4×C59—41no—
133D4×C59—41no—
134C2×C4×C59—21no—
135C2×C4×C59—21no—
136C2×C4×C59—21no—
137C2×C4×C59—21no—
138C2×C4×C59—21no—
139C2×C4×C59—21no—
140C2×C4×C59—21no—
141C2×C4×C59—21no—
142C2×C4×C59—21no—
143C2×C4×C59—22no—
144C2×C4×C59—41no—
145C2×C4×C59—41no—
146C2×C4×C59—41no—
147C2×C4×C59—42no—
148C2×C4×C59—41no—
149C2×C4×C59—41no—
150C2×C4×C59—41no—
151C2×C4×C59—41no—
152C2×C4×C59—82no—
153C2×C4×C59—82no—
154C2×C4×C59—82no—
155C2×C4×C59—82no—
156C2×C4×C59—82no—
157C2×C4×C59—82no—
158C2×C4×C59C2×C22⋊C411yescharacteristic
159C2×C4×C59#11711yescharacteristic
160C2×C4×C59C22⋊Q811yescharacteristic
161C2×C4×C59C22⋊Q811yescharacteristic
162C8×C59—21no—
163C8×C59—21no—
164C8×C59—21no—
165C8×C59—41no—
166C8×C59—41no—
167C8×C59#9912yescomplemented
168#8610C5911yesmaximal, characteristic, direct product factor, Sylow
169C22×C59—21no—
170C22×C59—21no—
171C22×C59—21no—
172C22×C59—21no—
173C22×C59—21no—
174C22×C59—21no—
175C22×C59—42no—
176C22×C59—42no—
177C22×C59—41no—
178C22×C59—41no—
179C22×C59—41no—
180C22×C59—82no—
181C22×C59#38011yescharacteristic
182C22×C59#42812yes—
183C22×C59#46812yes—
184C22×C59#46911yescharacteristic
185C22×C59#47011yescharacteristic
186C4×C59—21no—
187C4×C59—21no—
188C4×C59—21no—
189C4×C59—41no—
190C4×C59—41no—
191C4×C59—41no—
192C4×C59—162no—
193C4×C59—162no—
194C4×C59C2×#9911yescharacteristic
195C4×C59#41011yescharacteristic
196C2×#435C2×C5911yescharacteristic
197#1808C2×C5911yescharacteristic, complemented
198#1807C2×C5911yescharacteristic, complemented
199#1799C2×C5912yes—
200#1289C2×C5912yescomplemented
201C2×C59—21no—
202C2×C59—22no—
203C2×C59—22no—
204C2×C59—21no—
205C2×C59—81no—
206C2×C59#179911yescharacteristic
207C2×C59#180911yescharacteristic
208C2×C59#181211yescharacteristic
209C22×M16C4×C5911yescharacteristic, complemented
210C23×C8C22×C5911yescharacteristic
211C2×C4×D4C22×C5911yescharacteristic
212#435—21no—
213#435—21no—
214#435—21no—
215#435—21no—
216C2×#107—21no—
217C2×#106—21no—
218C2×C4⋊C8C4×C5911yescharacteristic, complemented
219C2×#99—22no—
220C2×C22⋊C8C4×C5911yescharacteristic, complemented
221C2×C22⋊C8C22×C5911yescharacteristic
222C2×#97C4×C5911yescharacteristic, complemented
223#380C22×C5912yes—
224#380C22×C5912yes—
225#342—22no—
226#340—21no—
227#340—21no—
228C59#861011yescharacteristic, direct product factor, Sylow
229C22×D4D4×C5911yescharacteristic
230C23×C4C2×C4×C5911yescharacteristic
231C23×C4C23×C5911yescharacteristic
232C2×M16—21no—
233C2×M16—21no—
234C2×M16—42no—
235C22×C8—42no—
236C22×C8C2×C4×C5911yescharacteristic
237C22×C8C2×C4×C5911yescharacteristic
238C22×C8C2×C4×C5911yescharacteristic
239C22×C8C2×C4×C5911yescharacteristic
240C22×C8D4×C5911yescharacteristic
241C22×C8D4×C5911yescharacteristic
242C22×C8D4×C5911yescharacteristic
243C22×C8D4×C5911yescharacteristic
244C4×D4—21no—
245C4×D4—21no—
246C4×D4—21no—
247C4×D4—21no—
248C2×C4⋊C4—22no—
249C2×C4⋊C4—22no—
250C2×C4⋊C4Q8×C5911yescharacteristic
251C2×C22⋊C4—22no—
252C2×C22⋊C4—22no—
253C2×C22⋊C4D4×C5911yescharacteristic
254C2×C22⋊C4Q8×C5911yescharacteristic
255C2×C42C2×C4×C5911yescharacteristic
256#107—42no—
257#106—42no—
258C4⋊C8—21no—
259C4⋊C8—21no—
260#99—44no—
261C22⋊C8—21no—
262C22⋊C8—21no—
263C22⋊C8—21no—
264C22⋊C8—21no—
265#97—21no—
266#97—21no—
267#95—22no—
268#95—22no—
269C24C4⋊C4×C5911yescharacteristic
270C24C2×D4×C5911yescharacteristic
271C2×D4—21no—
272C2×D4—21no—
273C2×D4—22no—
274C2×D4—22no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—41no—
278C22×C4—41no—
279C22×C4—41no—
280C22×C4—41no—
281C22×C4—42no—
282C22×C4—42no—
283C22×C4C4⋊C4×C5911yescharacteristic
284C22×C4C4⋊C4×C5911yescharacteristic
285C22×C4C4⋊C4×C5911yescharacteristic
286C22×C4C22×C4×C5911yescharacteristic
287C22×C4C2×D4×C5911yescharacteristic
288C22×C4C2×D4×C5911yescharacteristic
289C22×C4C2×Q8×C5911yescharacteristic
290C22×C4#41×C5911yescharacteristic
291C22×C4#41×C5911yescharacteristic
292M16—42no—
293M16—42no—
294C2×C8—22no—
295C2×C8—22no—
296C2×C8—22no—
297C2×C8—21no—
298C2×C8—21no—
299C2×C8—41no—
300C2×C8—41no—
301C2×C8—41no—
302C2×C8—41no—
303C2×C8—41no—
304C2×C8C22⋊C4×C5911yescharacteristic
305C2×C8C22⋊C4×C5911yescharacteristic
306C2×C8C22⋊C4×C5911yescharacteristic
307C2×C8C22⋊C4×C5911yescharacteristic
308C4⋊C4—21no—
309C4⋊C4—21no—
310C4⋊C4—42no—
311C4⋊C4—42no—
312C4⋊C4—42no—
313C4⋊C4—42no—
314C22⋊C4—21no—
315C22⋊C4—21no—
316C22⋊C4—21no—
317C22⋊C4—21no—
318C22⋊C4—42no—
319C22⋊C4—42no—
320C22⋊C4—42no—
321C22⋊C4—42no—
322C42—21no—
323C42—21no—
324C23—21no—
325C23—22no—
326C23—41no—
327C23—41no—
328C23—41no—
329C23—41no—
330C23C2×C4⋊C4×C5911yescharacteristic
331C23#121×C5911yescharacteristic
332C23#121×C5911yescharacteristic
333C23AGL(1,ℤ/8)×C5912yes—
334C23#137×C5912yes—
335D4—42no—
336D4—41no—
337D4—41no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—22no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—42no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—82no—
357C2×C4—82no—
358C2×C4—82no—
359C2×C4—82no—
360C2×C4—82no—
361C2×C4—82no—
362C2×C4C2×C22⋊C4×C5911yescharacteristic
363C2×C4#117×C5911yescharacteristic
364C2×C4C22⋊Q8×C5911yescharacteristic
365C2×C4C22⋊Q8×C5911yescharacteristic
366C8—21no—
367C8—21no—
368C8—21no—
369C8—41no—
370C8—41no—
371C8#99×C5912yescomplemented
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—21no—
378C22—42no—
379C22—42no—
380C22—41no—
381C22—41no—
382C22—41no—
383C22—82no—
384C22C59×#38011yescharacteristic
385C22C59×#42812yes—
386C22C59×#46812yes—
387C22C59×#46911yescharacteristic
388C22C59×#47011yescharacteristic
389C4—21no—
390C4—21no—
391C4—21no—
392C4—41no—
393C4—41no—
394C4—41no—
395C4—162no—
396C4—162no—
397C4C2×#99×C5911yescharacteristic
398C4C59×#41011yescharacteristic
399C2—21no—
400C2—22no—
401C2—22no—
402C2—21no—
403C2—81no—
404C2C59×#179911yescharacteristic
405C2C59×#180911yescharacteristic
406C2C59×#181211yescharacteristic
subgroupG/H
center, socleC22×C59#380
commutatorC22×C4C22×C4×C59
Frattini, cosocleC23×C4C23×C59
prime radicalC22×D4×C59D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C59 ◁ C23×C4×C59 ◁ G

Complements

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

NH ≅ G/Ntype
2. C59×#1808C2semidirect
3. C59×#1807C2semidirect
5. C59×#1289C2semidirect
6. C22×M16×C59C4semidirect
15. C2×C4⋊C8×C59C4semidirect
17. C2×C22⋊C8×C59C4semidirect
19. C2×#97×C59C4semidirect
167. C8×C59#99semidirect
168. #8610C59direct (N × H)
197. #1808C2×C59semidirect
198. #1807C2×C59semidirect
200. #1289C2×C59semidirect
209. C22×M16C4×C59semidirect
218. C2×C4⋊C8C4×C59semidirect
220. C2×C22⋊C8C4×C59semidirect
222. C2×#97C4×C59semidirect
228. C59#8610direct (N × H)
371. C8#99×C59semidirect

Maximal subgroups

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

subgroupindex
C2×C59×#4352
C59×#18082
C59×#18072
C59×#17992
C59×#12892
#861059