Finite Group Databasebeta

← C59×#11845 #28423954

Subgroups — C59×#11845 #28423954

Order 15104.

506 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 506 conjugacy classes of subgroups — too many to draw. Only its 102 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C59×#2561C211yesmaximal, characteristic
2C59×#1819C211yesmaximal, characteristic
3C2×C59×#323C211yesmaximal, characteristic
4C59×#1351C212yesmaximal, complemented
5C59×#1344C212yesmaximal, complemented
6C2×C22⋊Q8×C59C411yescharacteristic, complemented
7C22×C22⋊C4×C59C2211yescharacteristic
8C2×C22⋊C8×C59—21no—
9C59×#397C411yescharacteristic, complemented
10C59×#397C2211yescharacteristic
11C59×#393C411yescharacteristic, complemented
12C59×#393C2211yescharacteristic
13C59×#388—21no—
14C59×#388—21no—
15C59×#381—21no—
16C59×#379—21no—
17C59×#379—21no—
18C4×C22⋊C4×C59C411yescharacteristic, complemented
19C59×#342—21no—
20C59×#342C2212yes—
21C59×#323—21no—
22C59×#323C2212yes—
23C25×C59D411yescharacteristic
24C22×Q8×C59C2×C411yescharacteristic
25C23×C4×C59C2×C411yescharacteristic
26C23×C4×C59D411yescharacteristic
27C22×C8×C59—41no—
28C22⋊Q8×C59—41no—
29C22⋊Q8×C59—41no—
30C2×C4⋊C4×C59—21no—
31C2×C4⋊C4×C59C2×C411yescharacteristic
32C2×C22⋊C4×C59—21no—
33C2×C22⋊C4×C59—21no—
34C2×C22⋊C4×C59—21no—
35C2×C22⋊C4×C59—21no—
36C2×C22⋊C4×C59—22no—
37C2×C22⋊C4×C59—21no—
38C2×C22⋊C4×C59—21no—
39C2×C22⋊C4×C59—41no—
40C2×C22⋊C4×C59—41no—
41C2×C22⋊C4×C59—41no—
42C2×C22⋊C4×C59—41no—
43C2×C22⋊C4×C59C2×C411yescharacteristic
44C2×C22⋊C4×C59D411yescharacteristic
45C2×C22⋊C4×C59D411yescharacteristic
46C2×C22⋊C4×C59C2311yescharacteristic
47C2×C42×C59—21no—
48C22⋊C8×C59—22no—
49C22⋊C8×C59—41no—
50#95×C59—21no—
51#95×C59—21no—
52#95×C59—21no—
53#95×C59—21no—
54#95×C59C2×C411yescharacteristic
55#95×C59C2×C411yescharacteristic
56C24×C59—21no—
57C24×C59—21no—
58C24×C59—22no—
59C24×C59—41no—
60C24×C59—42no—
61C24×C59—81no—
62C24×C59C22⋊C411yescharacteristic
63C24×C59C22⋊C411yescharacteristic
64C24×C59C2×D411yescharacteristic
65C2×Q8×C59—41no—
66C2×Q8×C59—81no—
67C22×C4×C59—21no—
68C22×C4×C59—21no—
69C22×C4×C59—21no—
70C22×C4×C59—21no—
71C22×C4×C59—21no—
72C22×C4×C59—21no—
73C22×C4×C59—21no—
74C22×C4×C59—21no—
75C22×C4×C59—42no—
76C22×C4×C59—42no—
77C22×C4×C59—81no—
78C22×C4×C59C22⋊C411yescharacteristic
79C22×C4×C59C22⋊C411yescharacteristic
80C22×C4×C59C22×C411yescharacteristic
81C22×C4×C59C2×D411yescharacteristic
82C2×C8×C59—42no—
83C2×C8×C59—82no—
84C4⋊C4×C59—42no—
85C4⋊C4×C59—41no—
86C22⋊C4×C59—41no—
87C22⋊C4×C59—41no—
88C22⋊C4×C59—41no—
89C22⋊C4×C59—41no—
90C22⋊C4×C59—42no—
91C22⋊C4×C59—42no—
92C22⋊C4×C59—41no—
93C22⋊C4×C59—41no—
94C22⋊C4×C59—42no—
95C22⋊C4×C59—42no—
96C22⋊C4×C59—42no—
97C22⋊C4×C59—81no—
98C22⋊C4×C59—81no—
99C22⋊C4×C59—82no—
100C22⋊C4×C59—82no—
101C42×C59—81no—
102C23×C59—22no—
103C23×C59—21no—
104C23×C59—21no—
105C23×C59—21no—
106C23×C59—21no—
107C23×C59—21no—
108C23×C59—21no—
109C23×C59—21no—
110C23×C59—41no—
111C23×C59—42no—
112C23×C59—42no—
113C23×C59—41no—
114C23×C59—41no—
115C23×C59—41no—
116C23×C59—41no—
117C23×C59—42no—
118C23×C59—42no—
119C23×C59—81no—
120C23×C59—81no—
121C23×C59—84no—
122C23×C59—84no—
123C23×C59#9911yescharacteristic
124C23×C59#9911yescharacteristic
125C23×C59C2×C22⋊C411yescharacteristic
126C23×C59#13512yes—
127Q8×C59—82no—
128C2×C4×C59—21no—
129C2×C4×C59—21no—
130C2×C4×C59—21no—
131C2×C4×C59—21no—
132C2×C4×C59—42no—
133C2×C4×C59—41no—
134C2×C4×C59—41no—
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—41no—
145C2×C4×C59—41no—
146C2×C4×C59—41no—
147C2×C4×C59—41no—
148C2×C4×C59—41no—
149C2×C4×C59—81no—
150C2×C4×C59—81no—
151C2×C4×C59—81no—
152C2×C4×C59—82no—
153C2×C4×C59—82no—
154C2×C4×C59—82no—
155C8×C59—82no—
156#11845C5911yesmaximal, characteristic, direct product factor, Sylow
157C22×C59—21no—
158C22×C59—21no—
159C22×C59—21no—
160C22×C59—21no—
161C22×C59—21no—
162C22×C59—21no—
163C22×C59—22no—
164C22×C59—21no—
165C22×C59—42no—
166C22×C59—42no—
167C22×C59—42no—
168C22×C59—42no—
169C22×C59—41no—
170C22×C59—41no—
171C22×C59—41no—
172C22×C59—41no—
173C22×C59—41no—
174C22×C59—81no—
175C22×C59—84no—
176C22×C59—81no—
177C22×C59—84no—
178C22×C59#35412yes—
179C22×C59C2×#9911yescharacteristic
180C22×C59#41611yescharacteristic
181C22×C59#42111yescharacteristic
182C4×C59—41no—
183C4×C59—41no—
184C4×C59—41no—
185C4×C59—41no—
186C4×C59—81no—
187C4×C59—81no—
188C4×C59—81no—
189C4×C59—81no—
190C4×C59—162no—
191#2561C2×C5911yescharacteristic
192#1819C2×C5911yescharacteristic
193C2×#323C2×C5911yescharacteristic
194#1351C2×C5912yescomplemented
195#1344C2×C5912yescomplemented
196C2×C59—21no—
197C2×C59—21no—
198C2×C59—22no—
199C2×C59—42no—
200C2×C59—41no—
201C2×C59—81no—
202C2×C59#151611yescharacteristic
203C2×C59#212111yescharacteristic
204C2×C59C2×#35411yescharacteristic
205C2×C22⋊Q8C4×C5911yescharacteristic, complemented
206C22×C22⋊C4C22×C5911yescharacteristic
207C2×C22⋊C8—21no—
208#397C4×C5911yescharacteristic, complemented
209#397C22×C5911yescharacteristic
210#393C4×C5911yescharacteristic, complemented
211#393C22×C5911yescharacteristic
212#388—21no—
213#388—21no—
214#381—21no—
215#379—21no—
216#379—21no—
217C4×C22⋊C4C4×C5911yescharacteristic, complemented
218#342—21no—
219#342C22×C5912yes—
220#323—21no—
221#323C22×C5912yes—
222C59#1184511yescharacteristic, direct product factor, Sylow
223C25D4×C5911yescharacteristic
224C22×Q8C2×C4×C5911yescharacteristic
225C23×C4C2×C4×C5911yescharacteristic
226C23×C4D4×C5911yescharacteristic
227C22×C8—41no—
228C22⋊Q8—41no—
229C22⋊Q8—41no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4C2×C4×C5911yescharacteristic
232C2×C22⋊C4—21no—
233C2×C22⋊C4—21no—
234C2×C22⋊C4—21no—
235C2×C22⋊C4—21no—
236C2×C22⋊C4—22no—
237C2×C22⋊C4—21no—
238C2×C22⋊C4—21no—
239C2×C22⋊C4—41no—
240C2×C22⋊C4—41no—
241C2×C22⋊C4—41no—
242C2×C22⋊C4—41no—
243C2×C22⋊C4C2×C4×C5911yescharacteristic
244C2×C22⋊C4D4×C5911yescharacteristic
245C2×C22⋊C4D4×C5911yescharacteristic
246C2×C22⋊C4C23×C5911yescharacteristic
247C2×C42—21no—
248C22⋊C8—22no—
249C22⋊C8—41no—
250#95—21no—
251#95—21no—
252#95—21no—
253#95—21no—
254#95C2×C4×C5911yescharacteristic
255#95C2×C4×C5911yescharacteristic
256C24—21no—
257C24—21no—
258C24—22no—
259C24—41no—
260C24—42no—
261C24—81no—
262C24C22⋊C4×C5911yescharacteristic
263C24C22⋊C4×C5911yescharacteristic
264C24C2×D4×C5911yescharacteristic
265C2×Q8—41no—
266C2×Q8—81no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—42no—
276C22×C4—42no—
277C22×C4—81no—
278C22×C4C22⋊C4×C5911yescharacteristic
279C22×C4C22⋊C4×C5911yescharacteristic
280C22×C4C22×C4×C5911yescharacteristic
281C22×C4C2×D4×C5911yescharacteristic
282C2×C8—42no—
283C2×C8—82no—
284C4⋊C4—41no—
285C4⋊C4—42no—
286C22⋊C4—41no—
287C22⋊C4—41no—
288C22⋊C4—41no—
289C22⋊C4—41no—
290C22⋊C4—42no—
291C22⋊C4—42no—
292C22⋊C4—41no—
293C22⋊C4—41no—
294C22⋊C4—42no—
295C22⋊C4—42no—
296C22⋊C4—42no—
297C22⋊C4—81no—
298C22⋊C4—81no—
299C22⋊C4—82no—
300C22⋊C4—82no—
301C42—81no—
302C23—22no—
303C23—21no—
304C23—21no—
305C23—21no—
306C23—21no—
307C23—21no—
308C23—21no—
309C23—21no—
310C23—41no—
311C23—42no—
312C23—42no—
313C23—41no—
314C23—41no—
315C23—41no—
316C23—41no—
317C23—42no—
318C23—42no—
319C23—81no—
320C23—81no—
321C23—84no—
322C23—84no—
323C23#99×C5911yescharacteristic
324C23#99×C5911yescharacteristic
325C23C2×C22⋊C4×C5911yescharacteristic
326C23#135×C5912yes—
327Q8—82no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—42no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—81no—
350C2×C4—81no—
351C2×C4—81no—
352C2×C4—82no—
353C2×C4—82no—
354C2×C4—82no—
355C8—82no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—22no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—42no—
365C22—42no—
366C22—42no—
367C22—42no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—41no—
372C22—41no—
373C22—81no—
374C22—84no—
375C22—81no—
376C22—84no—
377C22C59×#35412yes—
378C22C2×#99×C5911yescharacteristic
379C22C59×#41611yescharacteristic
380C22C59×#42111yescharacteristic
381C4—41no—
382C4—41no—
383C4—41no—
384C4—41no—
385C4—81no—
386C4—81no—
387C4—81no—
388C4—81no—
389C4—162no—
390C2—21no—
391C2—21no—
392C2—22no—
393C2—42no—
394C2—41no—
395C2—81no—
396C2C59×#151611yescharacteristic
397C2C59×#212111yescharacteristic
398C2C2×C59×#35411yescharacteristic
subgroupG/H
center, socleC22×C59C2×#99
commutatorC22×C4C22×C4×C59
Frattini, cosocleC2×C22⋊C4C23×C59
prime radicalC25×C59D4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C59 ◁ C24×C59 ◁ C22×C22⋊C4×C59 ◁ G

Complements

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

NH ≅ G/Ntype
4. C59×#1351C2semidirect
5. C59×#1344C2semidirect
6. C2×C22⋊Q8×C59C4semidirect
9. C59×#397C4semidirect
11. C59×#393C4semidirect
18. C4×C22⋊C4×C59C4semidirect
156. #11845C59direct (N × H)
194. #1351C2×C59semidirect
195. #1344C2×C59semidirect
205. C2×C22⋊Q8C4×C59semidirect
208. #397C4×C59semidirect
210. #393C4×C59semidirect
217. C4×C22⋊C4C4×C59semidirect
222. C59#11845direct (N × H)

Maximal subgroups

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

subgroupindex
C59×#25612
C59×#18192
C2×C59×#3232
C59×#13512
C59×#13442
#1184559