Finite Group Databasebeta

← C13×#19006 #15705345

Subgroups — C13×#19006 #15705345

Order 3328.

938 conjugacy classes of subgroups; only the 222 normal subgroups are shown.

normal subgroups only

This group has 938 conjugacy classes of subgroups — too many to draw. Only its 222 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
1C2×C13×#562C211yesmaximal, characteristic
2C13×#3215C212yesmaximal, complemented
3C13×#3166C211yesmaximal, characteristic, complemented
4C13×#1661C218yesmaximal, complemented
5C13×#1534C211yesmaximal, characteristic, complemented
6C13×#1527C212yesmaximal, complemented
7C13×#562—22no—
8C13×#562—24no—
9C13×#562C2214yes—
10C13×#533C2211yescharacteristic
11C2×C13×#125C2211yescharacteristic
12C2×C13×#124C2212yes—
13C2×C13×#123—22no—
14C2×C13×C22⋊Q8—22no—
15C2×C13×#121—22no—
16C13×#501C2214yescomplemented
17C13×#499—22no—
18C13×#497C2214yescomplemented
19C13×#489C2214yescomplemented
20C13×#464—24no—
21C13×#451—22no—
22C13×#450—22no—
23C13×#432C2212yes—
24C13×#428—22no—
25C4×C13×M16C2211yescharacteristic
26C13×#330C2214yescomplemented
27C13×#329C2218yescomplemented
28C22×Q8×C13D412yes—
29C22×D4×C13—22no—
30C22×D4×C13D412yes—
31C23×C4×C13—22no—
32C2×C13×Q16—24no—
33C2×C13×SD16—24no—
34C2×C13×M16—21no—
35C13×C4⋊Q8C2312yes—
36C13×#125—22no—
37C13×#125—21no—
38C13×#125D412yes—
39C13×#125C2312yes—
40C13×#124—22no—
41C13×#124—22no—
42C13×#124D414yes—
43C13×#124C2314yes—
44C13×#123—28no—
45C13×#123—28no—
46C13×C22⋊Q8—28no—
47C13×C22⋊Q8—28no—
48C13×C22⋊Q8—22no—
49C13×#121—28no—
50C13×#121—28no—
51C4×Q8×C13—22no—
52C13×#117—21no—
53C2×C13×C4⋊C4—22no—
54C2×C13×C4⋊C4—22no—
55C2×C13×C4⋊C4D412yes—
56C2×C13×C22⋊C4—22no—
57C2×C13×C22⋊C4—22no—
58C2×C13×C22⋊C4—22no—
59C2×C42×C13C2311yescharacteristic
60C13×#107—24no—
61C13×#106—24no—
62C13×C4⋊C8—22no—
63C13×#103—24no—
64C13×#102—24no—
65C13×C22⋊C8—22no—
66C13×#97C2312yes—
67C13×#97C2314yes—
68C4×C8×C13—21no—
69#19006C1311yesmaximal, characteristic, direct product factor, Sylow
70C24×C13—22no—
71C2×Q8×C13—22no—
72C2×Q8×C13—22no—
73C2×Q8×C13—82no—
74C2×Q8×C13C2×D414yes—
75C2×D4×C13—28no—
76C2×D4×C13—22no—
77C2×D4×C13—82no—
78C2×D4×C13—84no—
79C2×D4×C13C2×D414yes—
80C22×C4×C13—22no—
81C22×C4×C13—22no—
82C22×C4×C13—28no—
83C22×C4×C13—84no—
84C22×C4×C13C2×D411yescharacteristic
85C22×C4×C13C2×D412yes—
86C13×Q16—84no—
87C13×SD16—84no—
88C13×M16—24no—
89C2×C8×C13—22no—
90C2×C8×C13—24no—
91C13×C4⋊C4—28no—
92C13×C4⋊C4—24no—
93C13×C4⋊C4—22no—
94C13×C4⋊C4—24no—
95C13×C4⋊C4—22no—
96C13×C4⋊C4—22no—
97C13×C4⋊C4—42no—
98C13×C4⋊C4C2×D414yes—
99C13×C22⋊C4—28no—
100C13×C22⋊C4—24no—
101C13×C22⋊C4—24no—
102C13×C22⋊C4—24no—
103C13×C22⋊C4—24no—
104C13×C22⋊C4—41no—
105C42×C13—41no—
106C42×C13C2×D411yescharacteristic
107C42×C13C2×D412yes—
108C42×C13C2411yescharacteristic
109C2×#562C2×C1311yescharacteristic
110#3215C2×C1312yescomplemented
111#3166C2×C1311yescharacteristic, complemented
112#1661C2×C1318yescomplemented
113#1534C2×C1311yescharacteristic, complemented
114#1527C2×C1312yescomplemented
115C23×C13—24no—
116C23×C13—44no—
117C23×C13—44no—
118C23×C13—44no—
119C23×C13#12011yescharacteristic
120Q8×C13—44no—
121Q8×C13—44no—
122Q8×C13—82no—
123D4×C13—44no—
124D4×C13—82no—
125D4×C13—88no—
126C2×C4×C13—22no—
127C2×C4×C13—24no—
128C2×C4×C13—24no—
129C2×C4×C13—42no—
130C2×C4×C13—44no—
131C2×C4×C13—44no—
132C2×C4×C13—42no—
133C2×C4×C13—88no—
134C2×C4×C13#12011yescharacteristic
135C2×C4×C13#12012yes—
136C2×C4×C13C22×D411yescharacteristic
137C2×C4×C13C22×D412yes—
138C8×C13—24no—
139C8×C13—44no—
140#562—22no—
141#562—24no—
142#562C22×C1314yes—
143#533C22×C1311yescharacteristic
144C2×#125C22×C1311yescharacteristic
145C2×#124C22×C1312yes—
146C2×#123—22no—
147C2×C22⋊Q8—22no—
148C2×#121—22no—
149#501C22×C1314yescomplemented
150#499—22no—
151#497C22×C1314yescomplemented
152#489C22×C1314yescomplemented
153#464—24no—
154#451—22no—
155#450—22no—
156#432C22×C1312yes—
157#428—22no—
158C4×M16C22×C1311yescharacteristic
159#330C22×C1314yescomplemented
160#329C22×C1318yescomplemented
161C22×C13—22no—
162C22×C13—44no—
163C22×C13—44no—
164C22×C13—44no—
165C22×C13—88no—
166C22×C13#45612yes—
167C22×C13C2×#12011yescharacteristic
168C4×C13—21no—
169C4×C13—21no—
170C4×C13—22no—
171C4×C13—22no—
172C4×C13—44no—
173C4×C13—44no—
174C4×C13—82no—
175C22×Q8D4×C1312yes—
176C22×D4—22no—
177C22×D4D4×C1312yes—
178C23×C4—22no—
179C2×Q16—24no—
180C2×SD16—24no—
181C2×M16—21no—
182C4⋊Q8C23×C1312yes—
183#125—22no—
184#125—21no—
185#125D4×C1312yes—
186#125C23×C1312yes—
187#124—22no—
188#124—22no—
189#124D4×C1314yes—
190#124C23×C1314yes—
191#123—28no—
192#123—28no—
193C22⋊Q8—28no—
194C22⋊Q8—28no—
195C22⋊Q8—22no—
196#121—28no—
197#121—28no—
198C4×Q8—22no—
199#117—21no—
200C2×C4⋊C4—22no—
201C2×C4⋊C4—22no—
202C2×C4⋊C4D4×C1312yes—
203C2×C22⋊C4—22no—
204C2×C22⋊C4—22no—
205C2×C22⋊C4—22no—
206C2×C42C23×C1311yescharacteristic
207#107—24no—
208#106—24no—
209C4⋊C8—22no—
210#103—24no—
211#102—24no—
212C22⋊C8—22no—
213#97C23×C1312yes—
214#97C23×C1314yes—
215C4×C8—21no—
216C2×C13—22no—
217C2×C13—84no—
218C2×C13C2×#45611yescharacteristic
219C2×C13#301912yes—
220C24—22no—
221C2×Q8—22no—
222C2×Q8—22no—
223C2×Q8—82no—
224C2×Q8C2×D4×C1314yes—
225C2×D4—28no—
226C2×D4—22no—
227C2×D4—82no—
228C2×D4—84no—
229C2×D4C2×D4×C1314yes—
230C22×C4—22no—
231C22×C4—22no—
232C22×C4—28no—
233C22×C4—84no—
234C22×C4C2×D4×C1311yescharacteristic
235C22×C4C2×D4×C1312yes—
236Q16—84no—
237SD16—84no—
238M16—24no—
239C2×C8—22no—
240C2×C8—24no—
241C4⋊C4—28no—
242C4⋊C4—24no—
243C4⋊C4—22no—
244C4⋊C4—24no—
245C4⋊C4—22no—
246C4⋊C4—22no—
247C4⋊C4—42no—
248C4⋊C4C2×D4×C1314yes—
249C22⋊C4—28no—
250C22⋊C4—24no—
251C22⋊C4—24no—
252C22⋊C4—24no—
253C22⋊C4—24no—
254C22⋊C4—41no—
255C42—41no—
256C42C2×D4×C1311yescharacteristic
257C42C2×D4×C1312yes—
258C42C24×C1311yescharacteristic
259C13#1900611yescharacteristic, direct product factor, Sylow
260C23—24no—
261C23—44no—
262C23—44no—
263C23—44no—
264C23C13×#12011yescharacteristic
265Q8—44no—
266Q8—44no—
267Q8—82no—
268D4—44no—
269D4—82no—
270D4—88no—
271C2×C4—22no—
272C2×C4—24no—
273C2×C4—24no—
274C2×C4—42no—
275C2×C4—44no—
276C2×C4—44no—
277C2×C4—42no—
278C2×C4—88no—
279C2×C4C13×#12011yescharacteristic
280C2×C4C13×#12012yes—
281C2×C4C22×D4×C1311yescharacteristic
282C2×C4C22×D4×C1312yes—
283C8—24no—
284C8—44no—
285C22—22no—
286C22—44no—
287C22—44no—
288C22—44no—
289C22—88no—
290C22C13×#45612yes—
291C22C2×C13×#12011yescharacteristic
292C4—21no—
293C4—21no—
294C4—22no—
295C4—22no—
296C4—44no—
297C4—44no—
298C4—82no—
299C2—22no—
300C2—84no—
301C2C2×C13×#45611yescharacteristic
302C2C13×#301912yes—
subgroupG/H
center, socleC22×C13C2×#120
commutator, Frattini, cosocleC42C24×C13
prime radicalC2×C13×#562C2
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×#3215C2semidirect
3. C13×#3166C2semidirect
4. C13×#1661C2semidirect
5. C13×#1534C2semidirect
6. C13×#1527C2semidirect
16. C13×#501C22semidirect
18. C13×#497C22semidirect
19. C13×#489C22semidirect
26. C13×#330C22semidirect
27. C13×#329C22semidirect
69. #19006C13direct (N × H)
110. #3215C2×C13semidirect
111. #3166C2×C13semidirect
112. #1661C2×C13semidirect
113. #1534C2×C13semidirect
114. #1527C2×C13semidirect
149. #501C22×C13semidirect
151. #497C22×C13semidirect
152. #489C22×C13semidirect
159. #330C22×C13semidirect
160. #329C22×C13semidirect
259. C13#19006direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#5622
C13×#32152
C13×#31662
C13×#16612
C13×#15342
C13×#15272
#1900613