Finite Group Databasebeta

← C13×#8529 #15694868

Subgroups — C13×#8529 #15694868

Order 3328.

648 conjugacy classes of subgroups; only the 142 normal subgroups are shown.

normal subgroups only

This group has 648 conjugacy classes of subgroups — too many to draw. Only its 142 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
1C13×#3553C211yesmaximal, characteristic
2C13×#1991C211yesmaximal, characteristic, complemented
3C13×#1534C211yesmaximal, characteristic, complemented
4C13×#1512C212yesmaximal, complemented
5C13×#1494C212yesmaximal, complemented
6C13×#564C411yescharacteristic, complemented
7C13×#563C412yescomplemented
8C13×#562C411yescharacteristic, complemented
9C13×#554—22no—
10C13×#553—22no—
11C13×#552—22no—
12C13×#541—22no—
13C13×#539—22no—
14C13×#539—22no—
15C13×#529C2212yes—
16C2×C13×#125C2211yescharacteristic
17C13×#432C2212yes—
18C2×C4×C8×C13C2211yescharacteristic
19C13×#382C2211yescharacteristic
20C13×#340—22no—
21C13×#330—22no—
22C13×#328—22no—
23C13×#327—22no—
24C13×Q8⋊C8—22no—
25C13×D4⋊C8—22no—
26C22×C8×C13—21no—
27C13×C4⋊Q8—22no—
28C13×#126—22no—
29C13×#126—22no—
30C13×#126—22no—
31C13×#126—22no—
32C13×#126—22no—
33C13×#125—22no—
34C13×#125—22no—
35C13×#125—22no—
36C13×#125—22no—
37C13×#125—22no—
38C13×#125—22no—
39C13×#125C2×C411yescharacteristic
40C13×#125C2×C411yescharacteristic
41C13×#125C2×C412yes—
42C13×#125D412yes—
43C13×#124C2×C412yes—
44C13×#123—22no—
45C13×#123—22no—
46C13×#123—22no—
47C13×#123—22no—
48C13×#123—22no—
49C13×C22⋊Q8—22no—
50C13×C22⋊Q8—22no—
51C13×C22⋊Q8—22no—
52C13×C22⋊Q8—22no—
53C13×C22⋊Q8—22no—
54C13×C22⋊Q8—22no—
55C13×C22⋊Q8D412yes—
56C13×#121—22no—
57C13×#121—22no—
58C13×#121D412yes—
59C4×Q8×C13—22no—
60C4×Q8×C13D412yes—
61C4×D4×C13—22no—
62C4×D4×C13—22no—
63C4×D4×C13—22no—
64C4×D4×C13—22no—
65C4×D4×C13D412yes—
66C13×#117—22no—
67C13×#117—22no—
68C2×C13×C4⋊C4—22no—
69C2×C13×C4⋊C4—22no—
70C2×C13×C4⋊C4—21no—
71C2×C13×C4⋊C4D412yes—
72C2×C42×C13C2311yescharacteristic
73C13×C4⋊C8—22no—
74C13×C22⋊C8—22no—
75C13×#97—22no—
76C4×C8×C13—22no—
77C13×#95—22no—
78#8529C1311yesmaximal, characteristic, direct product factor, Sylow
79C2×Q8×C13—22no—
80C2×Q8×C13C22⋊C412yes—
81C2×D4×C13—22no—
82C2×D4×C13—22no—
83C2×D4×C13C22⋊C412yes—
84C22×C4×C13—22no—
85C22×C4×C13—22no—
86C22×C4×C13—22no—
87C22×C4×C13—22no—
88C22×C4×C13—41no—
89C22×C4×C13C2×D411yescharacteristic
90C22×C4×C13C2×D412yes—
91C2×C8×C13—22no—
92C2×C8×C13—41no—
93C2×C8×C13—41no—
94C2×C8×C13—42no—
95C13×C4⋊C4—22no—
96C13×C4⋊C4—22no—
97C13×C4⋊C4—22no—
98C13×C4⋊C4—22no—
99C13×C4⋊C4—22no—
100C13×C4⋊C4—22no—
101C13×C4⋊C4—22no—
102C13×C4⋊C4—22no—
103C13×C4⋊C4—22no—
104C13×C4⋊C4—22no—
105C13×C4⋊C4—22no—
106C13×C4⋊C4—22no—
107C13×C4⋊C4—22no—
108C13×C4⋊C4—22no—
109C13×C4⋊C4—22no—
110C13×C4⋊C4—42no—
111C13×C4⋊C4C22⋊C412yes—
112C13×C4⋊C4C22⋊C412yes—
113C13×C4⋊C4C22⋊C412yes—
114C13×C4⋊C4C22⋊C412yes—
115C13×C22⋊C4—22no—
116C13×C22⋊C4—22no—
117C13×C22⋊C4—22no—
118C13×C22⋊C4—22no—
119C13×C22⋊C4—22no—
120C13×C22⋊C4—22no—
121C13×C22⋊C4—22no—
122C13×C22⋊C4—22no—
123C13×C22⋊C4—22no—
124C42×C13—22no—
125C42×C13—22no—
126C42×C13—22no—
127C42×C13C22×C411yescharacteristic
128C42×C13C2×D412yes—
129C42×C13C2×D411yescharacteristic
130#3553C2×C1311yescharacteristic
131#1991C2×C1311yescharacteristic, complemented
132#1534C2×C1311yescharacteristic, complemented
133#1512C2×C1312yescomplemented
134#1494C2×C1312yescomplemented
135C23×C13—22no—
136C23×C13#12011yescharacteristic
137Q8×C13—42no—
138Q8×C13—82no—
139D4×C13—42no—
140D4×C13—42no—
141D4×C13—42no—
142D4×C13—82no—
143C2×C4×C13—21no—
144C2×C4×C13—21no—
145C2×C4×C13—22no—
146C2×C4×C13—22no—
147C2×C4×C13—22no—
148C2×C4×C13—22no—
149C2×C4×C13—22no—
150C2×C4×C13—42no—
151C2×C4×C13—82no—
152C2×C4×C13—82no—
153C2×C4×C13—82no—
154C2×C4×C13—82no—
155C2×C4×C13—82no—
156C2×C4×C13—81no—
157C2×C4×C13C2×C22⋊C411yescharacteristic
158C2×C4×C13C2×C22⋊C412yes—
159C2×C4×C13#12012yes—
160C2×C4×C13#12011yescharacteristic
161C8×C13—42no—
162C8×C13—82no—
163#564C4×C1311yescharacteristic, complemented
164#563C4×C1312yescomplemented
165#562C4×C1311yescharacteristic, complemented
166#554—22no—
167#553—22no—
168#552—22no—
169#541—22no—
170#539—22no—
171#539—22no—
172#529C22×C1312yes—
173C2×#125C22×C1311yescharacteristic
174#432C22×C1312yes—
175C2×C4×C8C22×C1311yescharacteristic
176#382C22×C1311yescharacteristic
177#340—22no—
178#330—22no—
179#328—22no—
180#327—22no—
181Q8⋊C8—22no—
182D4⋊C8—22no—
183C22×C13—22no—
184C22×C13—42no—
185C22×C13—42no—
186C22×C13—42no—
187C22×C13#37911yescharacteristic
188C22×C13#45411yescharacteristic
189C22×C13#45611yescharacteristic
190C4×C13—21no—
191C4×C13—21no—
192C4×C13—22no—
193C4×C13—22no—
194C4×C13—42no—
195C4×C13—42no—
196C4×C13—42no—
197C4×C13—42no—
198C4×C13—42no—
199C4×C13—161no—
200C22×C8—21no—
201C4⋊Q8—22no—
202#126—22no—
203#126—22no—
204#126—22no—
205#126—22no—
206#126—22no—
207#125—22no—
208#125—22no—
209#125—22no—
210#125—22no—
211#125—22no—
212#125—22no—
213#125C2×C4×C1311yescharacteristic
214#125C2×C4×C1311yescharacteristic
215#125C2×C4×C1312yes—
216#125D4×C1312yes—
217#124C2×C4×C1312yes—
218#123—22no—
219#123—22no—
220#123—22no—
221#123—22no—
222#123—22no—
223C22⋊Q8—22no—
224C22⋊Q8—22no—
225C22⋊Q8—22no—
226C22⋊Q8—22no—
227C22⋊Q8—22no—
228C22⋊Q8—22no—
229C22⋊Q8D4×C1312yes—
230#121—22no—
231#121—22no—
232#121D4×C1312yes—
233C4×Q8—22no—
234C4×Q8D4×C1312yes—
235C4×D4—22no—
236C4×D4—22no—
237C4×D4—22no—
238C4×D4—22no—
239C4×D4D4×C1312yes—
240#117—22no—
241#117—22no—
242C2×C4⋊C4—22no—
243C2×C4⋊C4—22no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4D4×C1312yes—
246C2×C42C23×C1311yescharacteristic
247C4⋊C8—22no—
248C22⋊C8—22no—
249#97—22no—
250C4×C8—22no—
251#95—22no—
252C2×C13—21no—
253C2×C13—21no—
254C2×C13—82no—
255C2×C13#179311yescharacteristic
256C2×C13#179412yes—
257C2×Q8—22no—
258C2×Q8C13×C22⋊C412yes—
259C2×D4—22no—
260C2×D4—22no—
261C2×D4C13×C22⋊C412yes—
262C22×C4—22no—
263C22×C4—22no—
264C22×C4—22no—
265C22×C4—22no—
266C22×C4—41no—
267C22×C4C2×D4×C1311yescharacteristic
268C22×C4C2×D4×C1312yes—
269C2×C8—22no—
270C2×C8—41no—
271C2×C8—41no—
272C2×C8—42no—
273C4⋊C4—22no—
274C4⋊C4—22no—
275C4⋊C4—22no—
276C4⋊C4—22no—
277C4⋊C4—22no—
278C4⋊C4—22no—
279C4⋊C4—22no—
280C4⋊C4—22no—
281C4⋊C4—22no—
282C4⋊C4—22no—
283C4⋊C4—22no—
284C4⋊C4—22no—
285C4⋊C4—22no—
286C4⋊C4—22no—
287C4⋊C4—22no—
288C4⋊C4—42no—
289C4⋊C4C13×C22⋊C412yes—
290C4⋊C4C13×C22⋊C412yes—
291C4⋊C4C13×C22⋊C412yes—
292C4⋊C4C13×C22⋊C412yes—
293C22⋊C4—22no—
294C22⋊C4—22no—
295C22⋊C4—22no—
296C22⋊C4—22no—
297C22⋊C4—22no—
298C22⋊C4—22no—
299C22⋊C4—22no—
300C22⋊C4—22no—
301C22⋊C4—22no—
302C42—22no—
303C42—22no—
304C42—22no—
305C42C22×C4×C1311yescharacteristic
306C42C2×D4×C1312yes—
307C42C2×D4×C1311yescharacteristic
308C13#852911yescharacteristic, direct product factor, Sylow
309C23—22no—
310C23C13×#12011yescharacteristic
311Q8—42no—
312Q8—82no—
313D4—42no—
314D4—42no—
315D4—42no—
316D4—82no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—22no—
320C2×C4—22no—
321C2×C4—22no—
322C2×C4—22no—
323C2×C4—22no—
324C2×C4—42no—
325C2×C4—82no—
326C2×C4—82no—
327C2×C4—82no—
328C2×C4—82no—
329C2×C4—82no—
330C2×C4—81no—
331C2×C4C2×C13×C22⋊C411yescharacteristic
332C2×C4C2×C13×C22⋊C412yes—
333C2×C4C13×#12012yes—
334C2×C4C13×#12011yescharacteristic
335C8—42no—
336C8—82no—
337C22—22no—
338C22—42no—
339C22—42no—
340C22—42no—
341C22C13×#37911yescharacteristic
342C22C13×#45411yescharacteristic
343C22C13×#45611yescharacteristic
344C4—21no—
345C4—21no—
346C4—22no—
347C4—22no—
348C4—42no—
349C4—42no—
350C4—42no—
351C4—42no—
352C4—42no—
353C4—161no—
354C2—21no—
355C2—21no—
356C2—82no—
357C2C13×#179311yescharacteristic
358C2C13×#179412yes—
subgroupG/H
center, socleC22×C13#379
commutatorC42C22×C4×C13
Frattini, cosocleC2×C42C23×C13
prime radicalC13×#3553C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C13×#1991C2semidirect
3. C13×#1534C2semidirect
4. C13×#1512C2semidirect
5. C13×#1494C2semidirect
6. C13×#564C4semidirect
7. C13×#563C4semidirect
8. C13×#562C4semidirect
78. #8529C13direct (N × H)
131. #1991C2×C13semidirect
132. #1534C2×C13semidirect
133. #1512C2×C13semidirect
134. #1494C2×C13semidirect
163. #564C4×C13semidirect
164. #563C4×C13semidirect
165. #562C4×C13semidirect
308. C13#8529direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#35532
C13×#19912
C13×#15342
C13×#15122
C13×#14942
#852913