Finite Group Databasebeta

← C13×#20475 #15706814

Subgroups — C13×#20475 #15706814

Order 3328.

906 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#433C211yesmaximal, characteristic
2C2×C13×#405C211yesmaximal, characteristic
3C13×#2298C211yesmaximal, characteristic
4C13×#1771C212yesmaximal, complemented
5C13×#1770C212yesmaximal, complemented
6C13×#1753C212yesmaximal
7C13×#1752C212yesmaximal
8C13×#1746C211yesmaximal, characteristic, complemented
9C13×#1745C211yesmaximal, characteristic, complemented
10C13×#1726C211yesmaximal, characteristic, complemented
11C4×C13×#97C211yesmaximal, characteristic, complemented
12C22×C13×M16C2211yescharacteristic
13C23×C8×C13C2211yescharacteristic
14C2×C13×#117C2211yescharacteristic
15C13×#433C418yescomplemented
16C2×C13×C4⋊C8C2212yes—
17C2×C13×C22⋊C8C2212yes—
18C13×#405C418yescomplemented
19C2×C13×#97C2212yes—
20C2×C13×#97C2212yes—
21C2×C13×#97C2212yes—
22C2×C13×#97C2211yescharacteristic
23C2×C13×#97C2211yescharacteristic
24C2×C13×#97C2211yescharacteristic
25C2×C4×C8×C13C2212yes—
26C2×C4×C8×C13C2211yescharacteristic
27C2×C4×C8×C13C2211yescharacteristic
28C2×C4×C8×C13C2211yescharacteristic
29C13×#388C414yes—
30C13×#387C414yes—
31C4×C13×C4⋊C4C2212yes—
32C4×C13×C22⋊C4C2212yes—
33C13×#376C2211yescharacteristic
34C43×C13C2211yescharacteristic
35C13×#336C2212yes—
36C13×#336C2212yes—
37C13×#336C2212yes—
38C13×#336C2212yes—
39C23×C4×C13C2311yescharacteristic
40C2×C13×M16—24no—
41C2×C13×M16C2×C414yes—
42C22×C8×C13—24no—
43C22×C8×C13C2×C414yes—
44C22×C8×C13C2312yes—
45C22×C8×C13C2312yes—
46C22×C8×C13C2311yescharacteristic
47C22×C8×C13C2311yescharacteristic
48C22×C8×C13C2311yescharacteristic
49C22×C8×C13C2311yescharacteristic
50C13×#117C2×C414yes—
51C13×#117C2×C414yes—
52C2×C13×C4⋊C4C2×C414yes—
53C2×C13×C4⋊C4C2×C412yes—
54C2×C13×C22⋊C4C2×C414yes—
55C2×C13×C22⋊C4C2×C412yes—
56C2×C42×C13C2×C414yes—
57C2×C42×C13C2312yes—
58C2×C42×C13C2312yes—
59C2×C42×C13C2311yescharacteristic
60C2×C42×C13C2311yescharacteristic
61C13×C4⋊C8C2×C418yes—
62C13×C22⋊C8C2×C418yes—
63C13×#97—24no—
64C13×#97—24no—
65C13×#97—24no—
66C13×#97C2×C414yes—
67C13×#97C2×C414yes—
68C13×#97C2×C414yes—
69C4×C8×C13—24no—
70C4×C8×C13C2×C414yes—
71C4×C8×C13C2×C414yes—
72C4×C8×C13C2×C414yes—
73C13×#95C2×C414yes—
74C13×#95C2×C414yes—
75C13×#95C2×C414yes—
76#20475C1311yesmaximal, characteristic, direct product factor, Sylow
77C24×C13C22×C411yescharacteristic
78C22×C4×C13—22no—
79C22×C4×C13—22no—
80C22×C4×C13C22×C414yes—
81C22×C4×C13C22×C414yes—
82C22×C4×C13C22×C411yescharacteristic
83C22×C4×C13C22×C412yes—
84C22×C4×C13C22×C412yes—
85C22×C4×C13C22×C412yes—
86C22×C4×C13C22×C412yes—
87C22×C4×C13C2411yescharacteristic
88C13×M16—28no—
89C2×C8×C13—22no—
90C2×C8×C13—22no—
91C2×C8×C13—22no—
92C2×C8×C13—22no—
93C2×C8×C13—22no—
94C2×C8×C13—22no—
95C2×C8×C13—28no—
96C2×C8×C13C22×C412yes—
97C2×C8×C13C22×C414yes—
98C2×C8×C13C22×C412yes—
99C2×C8×C13C22×C414yes—
100C2×C8×C13C22×C412yes—
101C2×C8×C13C22×C412yes—
102C2×C8×C13#4114yes—
103C2×C8×C13#4114yes—
104C13×C4⋊C4—44no—
105C13×C4⋊C4C4218yes—
106C13×C22⋊C4—44no—
107C13×C22⋊C4C4218yes—
108C42×C13—22no—
109C42×C13—22no—
110C42×C13—22no—
111C42×C13—22no—
112C42×C13—44no—
113C42×C13C22×C412yes—
114C42×C13C22×C412yes—
115C42×C13C22×C412yes—
116C42×C13C22×C412yes—
117C2×#433C2×C1311yescharacteristic
118C2×#405C2×C1311yescharacteristic
119#2298C2×C1311yescharacteristic
120#1771C2×C1312yescomplemented
121#1770C2×C1312yescomplemented
122#1753C2×C1312yes—
123#1752C2×C1312yes—
124#1746C2×C1311yescharacteristic, complemented
125#1745C2×C1311yescharacteristic, complemented
126#1726C2×C1311yescharacteristic, complemented
127C4×#97C2×C1311yescharacteristic, complemented
128C23×C13—22no—
129C23×C13—24no—
130C23×C13C2×C4212yes—
131C23×C13C23×C411yescharacteristic
132C2×C4×C13—22no—
133C2×C4×C13—24no—
134C2×C4×C13—24no—
135C2×C4×C13—22no—
136C2×C4×C13—22no—
137C2×C4×C13—24no—
138C2×C4×C13—24no—
139C2×C4×C13—24no—
140C2×C4×C13—24no—
141C2×C4×C13—24no—
142C2×C4×C13—24no—
143C2×C4×C13—24no—
144C2×C4×C13C2×C4214yes—
145C2×C4×C13C2×C4214yes—
146C2×C4×C13C2×C4212yes—
147C2×C4×C13C23×C411yescharacteristic
148C2×C4×C13C23×C411yescharacteristic
149C2×C4×C13C2×#4112yes—
150C2×C4×C13C2×#4112yes—
151C8×C13—22no—
152C8×C13—22no—
153C8×C13—24no—
154C8×C13—24no—
155C8×C13#11714yes—
156C8×C13#11714yes—
157C22×M16C22×C1311yescharacteristic
158C23×C8C22×C1311yescharacteristic
159C2×#117C22×C1311yescharacteristic
160#433C4×C1318yescomplemented
161C2×C4⋊C8C22×C1312yes—
162C2×C22⋊C8C22×C1312yes—
163#405C4×C1318yescomplemented
164C2×#97C22×C1312yes—
165C2×#97C22×C1312yes—
166C2×#97C22×C1312yes—
167C2×#97C22×C1311yescharacteristic
168C2×#97C22×C1311yescharacteristic
169C2×#97C22×C1311yescharacteristic
170C2×C4×C8C22×C1312yes—
171C2×C4×C8C22×C1311yescharacteristic
172C2×C4×C8C22×C1311yescharacteristic
173C2×C4×C8C22×C1311yescharacteristic
174#388C4×C1314yes—
175#387C4×C1314yes—
176C4×C4⋊C4C22×C1312yes—
177C4×C22⋊C4C22×C1312yes—
178#376C22×C1311yescharacteristic
179C43C22×C1311yescharacteristic
180#336C22×C1312yes—
181#336C22×C1312yes—
182#336C22×C1312yes—
183#336C22×C1312yes—
184C22×C13—24no—
185C22×C13—22no—
186C22×C13—44no—
187C22×C13C22×C4211yescharacteristic
188C22×C13C4×#4112yes—
189C22×C13#56814yes—
190C4×C13—24no—
191C4×C13—24no—
192C4×C13—22no—
193C4×C13—44no—
194C4×C13—44no—
195C4×C13C2×#11711yescharacteristic
196C4×C13C2×#11711yescharacteristic
197C4×C13C4×#4112yes—
198C23×C4C23×C1311yescharacteristic
199C2×M16—24no—
200C2×M16C2×C4×C1314yes—
201C22×C8—24no—
202C22×C8C2×C4×C1314yes—
203C22×C8C23×C1311yescharacteristic
204C22×C8C23×C1311yescharacteristic
205C22×C8C23×C1312yes—
206C22×C8C23×C1312yes—
207C22×C8C23×C1311yescharacteristic
208C22×C8C23×C1311yescharacteristic
209#117C2×C4×C1314yes—
210#117C2×C4×C1314yes—
211C2×C4⋊C4C2×C4×C1314yes—
212C2×C4⋊C4C2×C4×C1312yes—
213C2×C22⋊C4C2×C4×C1314yes—
214C2×C22⋊C4C2×C4×C1312yes—
215C2×C42C2×C4×C1314yes—
216C2×C42C23×C1312yes—
217C2×C42C23×C1312yes—
218C2×C42C23×C1311yescharacteristic
219C2×C42C23×C1311yescharacteristic
220C4⋊C8C2×C4×C1318yes—
221C22⋊C8C2×C4×C1318yes—
222#97—24no—
223#97—24no—
224#97—24no—
225#97C2×C4×C1314yes—
226#97C2×C4×C1314yes—
227#97C2×C4×C1314yes—
228C4×C8—24no—
229C4×C8C2×C4×C1314yes—
230C4×C8C2×C4×C1314yes—
231C4×C8C2×C4×C1314yes—
232#95C2×C4×C1314yes—
233#95C2×C4×C1314yes—
234#95C2×C4×C1314yes—
235C2×C13—42no—
236C2×C13C4×#11711yescharacteristic
237C2×C13#287512yes—
238C2×C13#296714yes—
239C24C22×C4×C1311yescharacteristic
240C22×C4—22no—
241C22×C4—22no—
242C22×C4C22×C4×C1314yes—
243C22×C4C22×C4×C1314yes—
244C22×C4C22×C4×C1311yescharacteristic
245C22×C4C22×C4×C1312yes—
246C22×C4C22×C4×C1312yes—
247C22×C4C22×C4×C1312yes—
248C22×C4C22×C4×C1312yes—
249C22×C4C24×C1311yescharacteristic
250M16—28no—
251C2×C8—22no—
252C2×C8—22no—
253C2×C8—22no—
254C2×C8—22no—
255C2×C8—22no—
256C2×C8—22no—
257C2×C8—28no—
258C2×C8C22×C4×C1312yes—
259C2×C8C22×C4×C1314yes—
260C2×C8C22×C4×C1312yes—
261C2×C8C22×C4×C1314yes—
262C2×C8C22×C4×C1312yes—
263C2×C8C22×C4×C1312yes—
264C2×C8C13×#4114yes—
265C2×C8C13×#4114yes—
266C4⋊C4—44no—
267C4⋊C4C42×C1318yes—
268C22⋊C4—44no—
269C22⋊C4C42×C1318yes—
270C42—22no—
271C42—22no—
272C42—22no—
273C42—22no—
274C42—44no—
275C42C22×C4×C1312yes—
276C42C22×C4×C1312yes—
277C42C22×C4×C1312yes—
278C42C22×C4×C1312yes—
279C13#2047511yescharacteristic, direct product factor, Sylow
280C23—22no—
281C23—24no—
282C23C2×C42×C1312yes—
283C23C23×C4×C1311yescharacteristic
284C2×C4—22no—
285C2×C4—24no—
286C2×C4—24no—
287C2×C4—22no—
288C2×C4—22no—
289C2×C4—24no—
290C2×C4—24no—
291C2×C4—24no—
292C2×C4—24no—
293C2×C4—24no—
294C2×C4—24no—
295C2×C4—24no—
296C2×C4C2×C42×C1314yes—
297C2×C4C2×C42×C1314yes—
298C2×C4C2×C42×C1312yes—
299C2×C4C23×C4×C1311yescharacteristic
300C2×C4C23×C4×C1311yescharacteristic
301C2×C4C2×C13×#4112yes—
302C2×C4C2×C13×#4112yes—
303C8—22no—
304C8—22no—
305C8—24no—
306C8—24no—
307C8C13×#11714yes—
308C8C13×#11714yes—
309C22—22no—
310C22—24no—
311C22—44no—
312C22C22×C42×C1311yescharacteristic
313C22C4×C13×#4112yes—
314C22C13×#56814yes—
315C4—22no—
316C4—24no—
317C4—24no—
318C4—44no—
319C4—44no—
320C4C2×C13×#11711yescharacteristic
321C4C2×C13×#11711yescharacteristic
322C4C4×C13×#4112yes—
323C2—42no—
324C2C4×C13×#11711yescharacteristic
325C2C13×#287512yes—
326C2C13×#296714yes—
subgroupG/H
centerC22×C4×C13C24
commutatorC22C22×C42×C13
Frattini, cosocleC22×C4C24×C13
socleC23×C13C23×C4
prime radicalC24×C13C22×C4
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
4. C13×#1771C2semidirect
5. C13×#1770C2semidirect
8. C13×#1746C2semidirect
9. C13×#1745C2semidirect
10. C13×#1726C2semidirect
11. C4×C13×#97C2semidirect
15. C13×#433C4semidirect
18. C13×#405C4semidirect
76. #20475C13direct (N × H)
120. #1771C2×C13semidirect
121. #1770C2×C13semidirect
124. #1746C2×C13semidirect
125. #1745C2×C13semidirect
126. #1726C2×C13semidirect
127. C4×#97C2×C13semidirect
160. #433C4×C13semidirect
163. #405C4×C13semidirect
279. C13#20475direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#4332
C2×C13×#4052
C13×#22982
C13×#17712
C13×#17702
C13×#17532
C13×#17522
C13×#17462
C13×#17452
C13×#17262
C4×C13×#972
#2047513