Finite Group Databasebeta

← C13×#9202 #15695541

Subgroups — C13×#9202 #15695541

Order 3328.

516 conjugacy classes of subgroups; only the 134 normal subgroups are shown.

normal subgroups only

This group has 516 conjugacy classes of subgroups — too many to draw. Only its 134 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×#2627C211yesmaximal, characteristic
2C13×#2313C211yesmaximal, characteristic
3C13×#1520C212yesmaximal
4C2×C13×#324C211yesmaximal, characteristic
5C13×#1289C212yesmaximal
6C2×C13×C22⋊Q8C2211yescharacteristic
7C22×C13×C4⋊C4C2211yescharacteristic
8C2×C13×C22⋊C8C2212yes—
9C13×#400C412yescomplemented
10C13×#398—22no—
11C13×#395C412yescomplemented
12C13×#387—24no—
13C13×#385—21no—
14C13×#381—21no—
15C13×#381—21no—
16C13×#380C2211yescharacteristic
17C13×#380C2212yes—
18C4×C13×C22⋊C4—21no—
19C13×#328—24no—
20C13×#324—22no—
21C22×Q8×C13C2×C411yescharacteristic
22C23×C4×C13D411yescharacteristic
23C23×C4×C13D411yescharacteristic
24C23×C4×C13C2311yescharacteristic
25C22×C8×C13—22no—
26C13×C22⋊Q8—22no—
27C13×C22⋊Q8—22no—
28C2×C13×C4⋊C4—22no—
29C2×C13×C4⋊C4—22no—
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4—22no—
32C2×C13×C4⋊C4—22no—
33C2×C13×C4⋊C4—21no—
34C2×C13×C4⋊C4C2×C411yescharacteristic
35C2×C13×C4⋊C4C2×C412yes—
36C2×C13×C4⋊C4D412yes—
37C2×C13×C22⋊C4—22no—
38C2×C13×C22⋊C4—21no—
39C2×C13×C22⋊C4—21no—
40C2×C42×C13—22no—
41C13×C22⋊C8—22no—
42C13×C22⋊C8—22no—
43C13×#95—22no—
44C13×#95—24no—
45C13×#95—22no—
46C13×#95—22no—
47C13×#95—22no—
48C13×#95C2×C412yes—
49C13×#95D414yes—
50#9202C1311yesmaximal, characteristic, direct product factor, Sylow
51C24×C13C2×D411yescharacteristic
52C2×Q8×C13—22no—
53C2×Q8×C13—81no—
54C22×C4×C13—21no—
55C22×C4×C13—21no—
56C22×C4×C13—21no—
57C22×C4×C13—22no—
58C22×C4×C13—22no—
59C22×C4×C13—21no—
60C22×C4×C13—21no—
61C22×C4×C13—22no—
62C22×C4×C13—21no—
63C22×C4×C13—24no—
64C22×C4×C13—81no—
65C22×C4×C13—81no—
66C22×C4×C13C22⋊C412yes—
67C22×C4×C13C22⋊C412yes—
68C22×C4×C13C22×C411yescharacteristic
69C22×C4×C13C2×D412yes—
70C22×C4×C13C2×D411yescharacteristic
71C22×C4×C13#4112yes—
72C2×C8×C13—42no—
73C2×C8×C13—82no—
74C13×C4⋊C4—24no—
75C13×C4⋊C4—24no—
76C13×C4⋊C4—22no—
77C13×C4⋊C4—42no—
78C13×C4⋊C4—82no—
79C13×C4⋊C4—81no—
80C13×C4⋊C4—82no—
81C13×C22⋊C4—41no—
82C13×C22⋊C4—41no—
83C13×C22⋊C4—42no—
84C13×C22⋊C4—42no—
85C13×C22⋊C4—42no—
86C42×C13—82no—
87#2627C2×C1311yescharacteristic
88#2313C2×C1311yescharacteristic
89#1520C2×C1312yes—
90C2×#324C2×C1311yescharacteristic
91#1289C2×C1312yes—
92C23×C13—41no—
93C23×C13—41no—
94C23×C13C2×C22⋊C411yescharacteristic
95C23×C13#12011yescharacteristic
96C23×C13#12311yescharacteristic
97C23×C13#13512yes—
98C23×C13#13712yes—
99Q8×C13—82no—
100C2×C4×C13—22no—
101C2×C4×C13—22no—
102C2×C4×C13—22no—
103C2×C4×C13—22no—
104C2×C4×C13—41no—
105C2×C4×C13—42no—
106C2×C4×C13—42no—
107C2×C4×C13—41no—
108C2×C4×C13—42no—
109C2×C4×C13—42no—
110C2×C4×C13—42no—
111C2×C4×C13—42no—
112C2×C4×C13—44no—
113C2×C4×C13—42no—
114C2×C4×C13—42no—
115C2×C4×C13—42no—
116C2×C4×C13—44no—
117C2×C4×C13—42no—
118C2×C4×C13—41no—
119C2×C4×C13—41no—
120C2×C4×C13—42no—
121C2×C4×C13—44no—
122C2×C4×C13—81no—
123C2×C4×C13C4×D412yes—
124C2×C4×C13#12112yes—
125C8×C13—82no—
126C2×C22⋊Q8C22×C1311yescharacteristic
127C22×C4⋊C4C22×C1311yescharacteristic
128C2×C22⋊C8C22×C1312yes—
129#400C4×C1312yescomplemented
130#398—22no—
131#395C4×C1312yescomplemented
132#387—24no—
133#385—21no—
134#381—21no—
135#381—21no—
136#380C22×C1311yescharacteristic
137#380C22×C1312yes—
138C4×C22⋊C4—21no—
139#328—24no—
140#324—22no—
141C22×C13—21no—
142C22×C13—21no—
143C22×C13—21no—
144C22×C13—21no—
145C22×C13—21no—
146C22×C13—21no—
147C22×C13—42no—
148C22×C13—42no—
149C22×C13#38611yescharacteristic
150C22×C13#41611yescharacteristic
151C22×C13#41911yescharacteristic
152C22×C13#45212yes—
153C22×C13#48512yes—
154C4×C13—22no—
155C4×C13—22no—
156C4×C13—42no—
157C4×C13—42no—
158C4×C13—82no—
159C4×C13—84no—
160C4×C13—81no—
161C4×C13—81no—
162C22×Q8C2×C4×C1311yescharacteristic
163C23×C4D4×C1311yescharacteristic
164C23×C4D4×C1311yescharacteristic
165C23×C4C23×C1311yescharacteristic
166C22×C8—22no—
167C22⋊Q8—22no—
168C22⋊Q8—22no—
169C2×C4⋊C4—22no—
170C2×C4⋊C4—22no—
171C2×C4⋊C4—21no—
172C2×C4⋊C4—22no—
173C2×C4⋊C4—22no—
174C2×C4⋊C4—21no—
175C2×C4⋊C4C2×C4×C1311yescharacteristic
176C2×C4⋊C4C2×C4×C1312yes—
177C2×C4⋊C4D4×C1312yes—
178C2×C22⋊C4—21no—
179C2×C22⋊C4—22no—
180C2×C22⋊C4—21no—
181C2×C42—22no—
182C22⋊C8—22no—
183C22⋊C8—22no—
184#95—22no—
185#95—24no—
186#95—22no—
187#95—22no—
188#95—22no—
189#95C2×C4×C1312yes—
190#95D4×C1314yes—
191C2×C13—21no—
192C2×C13—22no—
193C2×C13—21no—
194C2×C13—22no—
195C2×C13#187311yescharacteristic
196C2×C13#191211yescharacteristic
197C2×C13#191311yescharacteristic
198C24C2×D4×C1311yescharacteristic
199C2×Q8—22no—
200C2×Q8—81no—
201C22×C4—21no—
202C22×C4—21no—
203C22×C4—21no—
204C22×C4—22no—
205C22×C4—22no—
206C22×C4—21no—
207C22×C4—21no—
208C22×C4—22no—
209C22×C4—21no—
210C22×C4—24no—
211C22×C4—81no—
212C22×C4—81no—
213C22×C4C13×C22⋊C412yes—
214C22×C4C13×C22⋊C412yes—
215C22×C4C22×C4×C1311yescharacteristic
216C22×C4C2×D4×C1312yes—
217C22×C4C2×D4×C1311yescharacteristic
218C22×C4C13×#4112yes—
219C2×C8—42no—
220C2×C8—82no—
221C4⋊C4—24no—
222C4⋊C4—24no—
223C4⋊C4—22no—
224C4⋊C4—42no—
225C4⋊C4—82no—
226C4⋊C4—81no—
227C4⋊C4—82no—
228C22⋊C4—41no—
229C22⋊C4—41no—
230C22⋊C4—42no—
231C22⋊C4—42no—
232C22⋊C4—42no—
233C42—82no—
234C13#920211yescharacteristic, direct product factor, Sylow
235C23—41no—
236C23—41no—
237C23C2×C13×C22⋊C411yescharacteristic
238C23C13×#12011yescharacteristic
239C23C13×#12311yescharacteristic
240C23C13×#13512yes—
241C23C13×#13712yes—
242Q8—82no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—22no—
247C2×C4—41no—
248C2×C4—42no—
249C2×C4—42no—
250C2×C4—41no—
251C2×C4—42no—
252C2×C4—42no—
253C2×C4—42no—
254C2×C4—42no—
255C2×C4—44no—
256C2×C4—42no—
257C2×C4—42no—
258C2×C4—42no—
259C2×C4—44no—
260C2×C4—42no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—42no—
264C2×C4—44no—
265C2×C4—81no—
266C2×C4C4×D4×C1312yes—
267C2×C4C13×#12112yes—
268C8—82no—
269C22—21no—
270C22—21no—
271C22—21no—
272C22—21no—
273C22—21no—
274C22—21no—
275C22—42no—
276C22—42no—
277C22C13×#38611yescharacteristic
278C22C13×#41611yescharacteristic
279C22C13×#41911yescharacteristic
280C22C13×#45212yes—
281C22C13×#48512yes—
282C4—22no—
283C4—22no—
284C4—42no—
285C4—42no—
286C4—82no—
287C4—84no—
288C4—81no—
289C4—81no—
290C2—21no—
291C2—22no—
292C2—21no—
293C2—22no—
294C2C13×#187311yescharacteristic
295C2C13×#191211yescharacteristic
296C2C13×#191311yescharacteristic
subgroupG/H
center, socleC22×C13#386
commutatorC22×C4C22×C4×C13
Frattini, cosocleC23×C4C23×C13
prime radicalC24×C13C2×D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ C23×C4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
9. C13×#400C4semidirect
11. C13×#395C4semidirect
50. #9202C13direct (N × H)
129. #400C4×C13semidirect
131. #395C4×C13semidirect
234. C13#9202direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#26272
C13×#23132
C13×#15202
C2×C13×#3242
C13×#12892
#920213