Finite Group Databasebeta

← C13×#34374 #15720713

Subgroups — C13×#34374 #15720713

Order 3328.

2098 conjugacy classes of subgroups.

The subgroup lattice has 314 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#533C211yesmaximal, characteristic
2C13×#2382C214yesmaximal, complemented
3C13×#2365C214yesmaximal, complemented
4C13×#2355C214yesmaximal, complemented
5Q8×C13×C4⋊C4C214yesmaximal, complemented
6C13×#2323C218yesmaximal
7C13×#2314C214yesmaximal
8C13×#2285C212yesmaximal
9C13×#533C4116yescomplemented
10C2×C13×C4⋊Q8C2212yes—
11C2×C13×#125C2212yes—
12C2×C13×C22⋊Q8C2214yes—
13C2×C4×Q8×C13C2218yes—
14C2×C4×Q8×C13C2214yes—
15C2×C13×#117C2214yes—
16C2×C13×#117C2212yes—
17C22×C42×C13C2211yescharacteristic
18C13×#391C2218yes—
19C13×#389C2218yes—
20C13×#389C22116yes—
21C13×#388C22116yes—
22C13×#387C22116yes—
23C13×#387C22116yes—
24C13×#384C2212yes—
25C13×#384C2212yes—
26C13×#384C2214yes—
27C13×#382C2214yes—
28C13×#382C2214yes—
29C13×#380C2214yes—
30C13×#380C2214yes—
31C4×C13×C4⋊C4C2214yes—
32C4×C13×C4⋊C4C2214yes—
33C4×C13×C4⋊C4C2218yes—
34C4×C13×C4⋊C4C2218yes—
35C22×Q8×C13C2314yes—
36C23×C4×C13C2311yescharacteristic
37C23×C4×C13C2312yes—
38C13×C4⋊Q8C2×C4116yes—
39C13×#125C2×C4116yes—
40C13×C22⋊Q8C2×C4132yes—
41C4×Q8×C13—416no—
42C4×Q8×C13C2×C4132yes—
43C13×#117—48no—
44C13×#117C2×C4116yes—
45C2×C13×C4⋊C4C2314yes—
46C2×C13×C4⋊C4C2314yes—
47C2×C13×C4⋊C4C2314yes—
48C2×C13×C4⋊C4C2314yes—
49C2×C13×C4⋊C4C2314yes—
50C2×C13×C4⋊C4C2314yes—
51C2×C13×C4⋊C4C23116yes—
52C2×C13×C4⋊C4C2314yes—
53C2×C13×C4⋊C4C2314yes—
54C2×C13×C4⋊C4C2318yes—
55C2×C13×C22⋊C4C2318yes—
56C2×C13×C22⋊C4C2314yes—
57C2×C42×C13C2×C418yes—
58C2×C42×C13C2318yes—
59C2×C42×C13C23116yes—
60C2×C42×C13C2311yescharacteristic
61C2×C42×C13C2314yes—
62C2×C42×C13C2312yes—
63C2×C42×C13C2311yescharacteristic
64C13×#95C2318yes—
65C13×#95C2318yes—
66C13×#95C23116yes—
67C13×#95C23116yes—
68#34374C1311yesmaximal, characteristic, direct product factor, Sylow
69C24×C13C2411yescharacteristic
70C2×Q8×C13—28no—
71C2×Q8×C13—28no—
72C2×Q8×C13C22×C4116yes—
73C22×C4×C13—24no—
74C22×C4×C13—22no—
75C22×C4×C13—22no—
76C22×C4×C13—24no—
77C22×C4×C13C22×C414yes—
78C22×C4×C13C22×C418yes—
79C22×C4×C13C2418yes—
80C22×C4×C13C2418yes—
81C22×C4×C13C2411yescharacteristic
82C22×C4×C13C2418yes—
83C22×C4×C13C2412yes—
84C22×C4×C13C2412yes—
85C22×C4×C13C2411yescharacteristic
86C13×C4⋊C4—28no—
87C13×C4⋊C4—28no—
88C13×C4⋊C4—28no—
89C13×C4⋊C4—28no—
90C13×C4⋊C4—44no—
91C13×C4⋊C4—44no—
92C13×C4⋊C4—416no—
93C13×C4⋊C4C22×C4116yes—
94C13×C4⋊C4C22×C4132yes—
95C13×C4⋊C4C22×C4116yes—
96C13×C22⋊C4—48no—
97C13×C22⋊C4C22×C4116yes—
98C42×C13—216no—
99C42×C13—416no—
100C42×C13C22×C418yes—
101C42×C13C22×C414yes—
102C42×C13C22×C414yes—
103C42×C13C22×C4116yes—
104C2×#533C2×C1311yescharacteristic
105#2382C2×C1314yescomplemented
106#2365C2×C1314yescomplemented
107#2355C2×C1314yescomplemented
108Q8×C4⋊C4C2×C1314yescomplemented
109#2323C2×C1318yes—
110#2314C2×C1314yes—
111#2285C2×C1312yes—
112C23×C13—22no—
113C23×C13—21no—
114C23×C13—21no—
115C23×C13—22no—
116C23×C13C23×C412yes—
117C23×C13C2511yescharacteristic
118Q8×C13—232no—
119C2×C4×C13—28no—
120C2×C4×C13—22no—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13—22no—
124C2×C4×C13—28no—
125C2×C4×C13—28no—
126C2×C4×C13—216no—
127C2×C4×C13—28no—
128C2×C4×C13—28no—
129C2×C4×C13—28no—
130C2×C4×C13—28no—
131C2×C4×C13—28no—
132C2×C4×C13—28no—
133C2×C4×C13C23×C412yes—
134C2×C4×C13C23×C414yes—
135C2×C4×C13C23×C4116yes—
136C2×C4×C13C23×C412yes—
137C2×C4×C13C23×C414yes—
138C2×C4×C13H(5,𝔽2)14yes—
139C2×C4×C132−1+412yes—
140C2×C4×C132−1+412yes—
141C2×C4×C132−1+414yes—
142#533C4×C13116yescomplemented
143C2×C4⋊Q8C22×C1312yes—
144C2×#125C22×C1312yes—
145C2×C22⋊Q8C22×C1314yes—
146C2×C4×Q8C22×C1318yes—
147C2×C4×Q8C22×C1314yes—
148C2×#117C22×C1314yes—
149C2×#117C22×C1312yes—
150C22×C42C22×C1311yescharacteristic
151#391C22×C1318yes—
152#389C22×C1318yes—
153#389C22×C13116yes—
154#388C22×C13116yes—
155#387C22×C13116yes—
156#387C22×C13116yes—
157#384C22×C1314yes—
158#384C22×C1312yes—
159#384C22×C1312yes—
160#382C22×C1314yes—
161#382C22×C1314yes—
162#380C22×C1314yes—
163#380C22×C1314yes—
164C4×C4⋊C4C22×C1318yes—
165C4×C4⋊C4C22×C1318yes—
166C4×C4⋊C4C22×C1314yes—
167C4×C4⋊C4C22×C1314yes—
168C22×C13—22no—
169C22×C13—24no—
170C22×C13—41no—
171C22×C13—42no—
172C22×C13—41no—
173C22×C13C24×C411yescharacteristic
174C22×C13C2×H(5,𝔽2)12yes—
175C22×C13C2×2−1+411yescharacteristic
176C22×C13C2×2−1+411yescharacteristic
177C22×C13C2×2−1+412yes—
178C4×C13—22no—
179C4×C13—24no—
180C4×C13—216no—
181C4×C13—48no—
182C4×C13—48no—
183C4×C13#51914yes—
184C4×C13#52018yes—
185C22×Q8C23×C1314yes—
186C23×C4C23×C1312yes—
187C23×C4C23×C1311yescharacteristic
188C4⋊Q8C2×C4×C13116yes—
189#125C2×C4×C13116yes—
190C22⋊Q8C2×C4×C13132yes—
191C4×Q8—416no—
192C4×Q8C2×C4×C13132yes—
193#117—48no—
194#117C2×C4×C13116yes—
195C2×C4⋊C4C23×C1314yes—
196C2×C4⋊C4C23×C1314yes—
197C2×C4⋊C4C23×C1314yes—
198C2×C4⋊C4C23×C1314yes—
199C2×C4⋊C4C23×C1314yes—
200C2×C4⋊C4C23×C1314yes—
201C2×C4⋊C4C23×C13116yes—
202C2×C4⋊C4C23×C1314yes—
203C2×C4⋊C4C23×C1318yes—
204C2×C4⋊C4C23×C1314yes—
205C2×C22⋊C4C23×C1318yes—
206C2×C22⋊C4C23×C1314yes—
207C2×C42C2×C4×C1318yes—
208C2×C42C23×C1318yes—
209C2×C42C23×C13116yes—
210C2×C42C23×C1314yes—
211C2×C42C23×C1312yes—
212C2×C42C23×C1311yescharacteristic
213C2×C42C23×C1311yescharacteristic
214#95C23×C1318yes—
215#95C23×C1318yes—
216#95C23×C13116yes—
217#95C23×C13116yes—
218C2×C13—42no—
219C2×C13C2×#51911yescharacteristic
220C2×C13C2×#52012yes—
221C2×C13#354811yescharacteristic
222C2×C13#355012yes—
223C2×C13#355611yescharacteristic
224C24C24×C1311yescharacteristic
225C2×Q8—28no—
226C2×Q8—28no—
227C2×Q8C22×C4×C13116yes—
228C22×C4—24no—
229C22×C4—22no—
230C22×C4—22no—
231C22×C4—24no—
232C22×C4C22×C4×C1314yes—
233C22×C4C22×C4×C1318yes—
234C22×C4C24×C1318yes—
235C22×C4C24×C1318yes—
236C22×C4C24×C1311yescharacteristic
237C22×C4C24×C1318yes—
238C22×C4C24×C1312yes—
239C22×C4C24×C1312yes—
240C22×C4C24×C1311yescharacteristic
241C4⋊C4—28no—
242C4⋊C4—28no—
243C4⋊C4—28no—
244C4⋊C4—28no—
245C4⋊C4—44no—
246C4⋊C4—44no—
247C4⋊C4—416no—
248C4⋊C4C22×C4×C13116yes—
249C4⋊C4C22×C4×C13132yes—
250C4⋊C4C22×C4×C13116yes—
251C22⋊C4—48no—
252C22⋊C4C22×C4×C13116yes—
253C42—216no—
254C42—416no—
255C42C22×C4×C1318yes—
256C42C22×C4×C1314yes—
257C42C22×C4×C1314yes—
258C42C22×C4×C13116yes—
259C13#3437411yescharacteristic, direct product factor, Sylow
260C23—22no—
261C23—21no—
262C23—21no—
263C23—22no—
264C23C23×C4×C1312yes—
265C23C25×C1311yescharacteristic
266Q8—232no—
267C2×C4—28no—
268C2×C4—22no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—22no—
272C2×C4—28no—
273C2×C4—28no—
274C2×C4—216no—
275C2×C4—28no—
276C2×C4—28no—
277C2×C4—28no—
278C2×C4—28no—
279C2×C4—28no—
280C2×C4—28no—
281C2×C4C23×C4×C1312yes—
282C2×C4C23×C4×C1314yes—
283C2×C4C23×C4×C13116yes—
284C2×C4C23×C4×C1312yes—
285C2×C4C23×C4×C1314yes—
286C2×C4C13×H(5,𝔽2)14yes—
287C2×C4C13×2−1+412yes—
288C2×C4C13×2−1+412yes—
289C2×C4C13×2−1+414yes—
290C22—22no—
291C22—24no—
292C22—41no—
293C22—42no—
294C22—41no—
295C22C24×C4×C1311yescharacteristic
296C22C2×C13×H(5,𝔽2)12yes—
297C22C2×C13×2−1+411yescharacteristic
298C22C2×C13×2−1+411yescharacteristic
299C22C2×C13×2−1+412yes—
300C4—22no—
301C4—24no—
302C4—216no—
303C4—48no—
304C4—48no—
305C4C13×#51914yes—
306C4C13×#52018yes—
307C2—42no—
308C2C2×C13×#51911yescharacteristic
309C2C2×C13×#52012yes—
310C2C13×#354811yescharacteristic
311C2C13×#355012yes—
312C2C13×#355611yescharacteristic
subgroupG/H
center, socleC23×C13C25
commutatorC22C24×C4×C13
Frattini, cosocleC23C25×C13
prime radicalC24×C13C24
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C13×#2382C2semidirect
3. C13×#2365C2semidirect
4. C13×#2355C2semidirect
5. Q8×C13×C4⋊C4C2semidirect
9. C13×#533C4semidirect
68. #34374C13direct (N × H)
105. #2382C2×C13semidirect
106. #2365C2×C13semidirect
107. #2355C2×C13semidirect
108. Q8×C4⋊C4C2×C13semidirect
142. #533C4×C13semidirect
259. C13#34374direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#5332
C13×#23822
C13×#23652
C13×#23552
Q8×C13×C4⋊C42
C13×#23232
C13×#23142
C13×#22852
#3437413