Finite Group Databasebeta

← C13×#36691 #15723030

Subgroups — C13×#36691 #15723030

Order 3328.

1474 conjugacy classes of subgroups.

The subgroup lattice has 322 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#2845C212yesmaximal, complemented
2C13×#2844C212yesmaximal, complemented
3C13×#2843C214yesmaximal, complemented
4C13×#2841C218yesmaximal
5C13×#2402C214yesmaximal, complemented
6C13×#2399C214yesmaximal, complemented
7C13×#2396C214yesmaximal
8C13×#2285C211yesmaximal, characteristic
9C13×#2283C212yesmaximal
10C2×C4×Q8×C13C2214yes—
11C2×C13×#117C2212yes—
12C22×C42×C13C2211yescharacteristic
13C13×#400C2218yes—
14C13×#400C2218yes—
15C13×#400C2214yes—
16C13×#399C2214yes—
17C13×#398C2218yes—
18C13×#398C2218yes—
19C13×#398C2218yes—
20C13×#398C2218yes—
21C13×#398C2218yes—
22C13×#396C2218yes—
23C13×#395C2218yes—
24C13×#395C2218yes—
25C13×#395C2214yes—
26C13×#393C2214yes—
27C13×#384C2212yes—
28C13×#383C2214yes—
29C13×#382C2214yes—
30C13×#382C2211yescharacteristic
31C13×#382C2211yescharacteristic
32C13×#381C2214yes—
33C13×#380C2214yes—
34C13×#380C2214yes—
35C4×C13×C4⋊C4C2212yes—
36C4×C13×C4⋊C4C2212yes—
37C4×C13×C4⋊C4C2214yes—
38C4×C13×C4⋊C4C2218yes—
39C4×C13×C4⋊C4C2214yes—
40C4×C13×C22⋊C4C2214yes—
41C13×#376C2214yes—
42C22×Q8×C13C2314yes—
43C23×C4×C13C2311yescharacteristic
44C23×C4×C13C2312yes—
45C4×Q8×C13—48no—
46C13×#117—44no—
47C2×C13×C4⋊C4C2314yes—
48C2×C13×C4⋊C4C2314yes—
49C2×C13×C4⋊C4C2318yes—
50C2×C13×C4⋊C4C2318yes—
51C2×C13×C4⋊C4C2318yes—
52C2×C13×C4⋊C4C2318yes—
53C2×C13×C4⋊C4C2312yes—
54C2×C13×C4⋊C4C2312yes—
55C2×C13×C4⋊C4C2314yes—
56C2×C13×C4⋊C4C2318yes—
57C2×C13×C22⋊C4C2318yes—
58C2×C13×C22⋊C4C2314yes—
59C2×C42×C13Q818yescomplemented
60C2×C42×C13C2314yes—
61C2×C42×C13C2314yes—
62C2×C42×C13C2314yes—
63C2×C42×C13C2311yescharacteristic
64C2×C42×C13C2311yescharacteristic
65C2×C42×C13C2312yes—
66C13×#95C2318yes—
67C13×#95C2314yes—
68C13×#95C2314yes—
69C13×#95C2314yes—
70C13×#95C2314yes—
71C13×#95C2318yes—
72C13×#95C2314yes—
73C13×#95C2318yes—
74C13×#95C2314yes—
75C13×#95C2318yes—
76C13×#95C2318yes—
77#36691C1311yesmaximal, characteristic, direct product factor, Sylow
78C24×C13C2411yescharacteristic
79C2×Q8×C13—44no—
80C2×Q8×C13—48no—
81C22×C4×C13—22no—
82C22×C4×C13—22no—
83C22×C4×C13—44no—
84C22×C4×C13C2×Q814yes—
85C22×C4×C13C2×Q818yes—
86C22×C4×C13C2418yes—
87C22×C4×C13C2414yes—
88C22×C4×C13C2418yes—
89C22×C4×C13C2414yes—
90C22×C4×C13C2411yescharacteristic
91C22×C4×C13C2412yes—
92C22×C4×C13C2412yes—
93C22×C4×C13C2411yescharacteristic
94C13×C4⋊C4—44no—
95C13×C4⋊C4—48no—
96C13×C4⋊C4—44no—
97C13×C4⋊C4—48no—
98C13×C4⋊C4—48no—
99C13×C4⋊C4—48no—
100C13×C4⋊C4—42no—
101C13×C4⋊C4—42no—
102C13×C4⋊C4—48no—
103C13×C4⋊C4—44no—
104C13×C22⋊C4—48no—
105C13×C22⋊C4—44no—
106C42×C13—28no—
107C42×C13—28no—
108C42×C13—28no—
109C42×C13C2×Q814yes—
110C42×C13C2×Q814yes—
111C42×C13C2×Q818yes—
112#2845C2×C1312yescomplemented
113#2844C2×C1312yescomplemented
114#2843C2×C1314yescomplemented
115#2841C2×C1318yes—
116#2402C2×C1314yescomplemented
117#2399C2×C1314yescomplemented
118#2396C2×C1314yes—
119#2285C2×C1311yescharacteristic
120#2283C2×C1312yes—
121C23×C13—21no—
122C23×C13—21no—
123C23×C13—24no—
124C23×C13C22×Q812yes—
125C23×C13C2511yescharacteristic
126Q8×C13—416no—
127C2×C4×C13—21no—
128C2×C4×C13—21no—
129C2×C4×C13—24no—
130C2×C4×C13—24no—
131C2×C4×C13—28no—
132C2×C4×C13—24no—
133C2×C4×C13—24no—
134C2×C4×C13—28no—
135C2×C4×C13—28no—
136C2×C4×C13—28no—
137C2×C4×C13—28no—
138C2×C4×C13—28no—
139C2×C4×C13—28no—
140C2×C4×C13—28no—
141C2×C4×C13—28no—
142C2×C4×C13—48no—
143C2×C4×C13C22×Q812yes—
144C2×C4×C13C22×Q814yes—
145C2×C4×C13C22×Q814yes—
146C2×C4×C13C22×Q812yes—
147C2×C4×C13H(5,𝔽2)12yes—
148C2×C4×C132−1+412yes—
149C2×C4×Q8C22×C1314yes—
150C2×#117C22×C1312yes—
151C22×C42C22×C1311yescharacteristic
152#400C22×C1318yes—
153#400C22×C1318yes—
154#400C22×C1314yes—
155#399C22×C1314yes—
156#398C22×C1318yes—
157#398C22×C1318yes—
158#398C22×C1318yes—
159#398C22×C1318yes—
160#398C22×C1318yes—
161#396C22×C1318yes—
162#395C22×C1318yes—
163#395C22×C1318yes—
164#395C22×C1314yes—
165#393C22×C1314yes—
166#384C22×C1312yes—
167#383C22×C1314yes—
168#382C22×C1311yescharacteristic
169#382C22×C1314yes—
170#382C22×C1311yescharacteristic
171#381C22×C1314yes—
172#380C22×C1314yes—
173#380C22×C1314yes—
174C4×C4⋊C4C22×C1318yes—
175C4×C4⋊C4C22×C1314yes—
176C4×C4⋊C4C22×C1312yes—
177C4×C4⋊C4C22×C1314yes—
178C4×C4⋊C4C22×C1312yes—
179C4×C22⋊C4C22×C1314yes—
180#376C22×C1314yes—
181C22×C13—22no—
182C22×C13—24no—
183C22×C13—42no—
184C22×C13—42no—
185C22×C13C23×Q811yescharacteristic
186C22×C13C2×H(5,𝔽2)11yescharacteristic
187C22×C13C2×2−1+411yescharacteristic
188C22×C13#58514yes—
189C4×C13—22no—
190C4×C13—24no—
191C4×C13—24no—
192C4×C13—44no—
193C4×C13—44no—
194C4×C13—48no—
195C4×C13—48no—
196C4×C13#54414yes—
197C22×Q8C23×C1314yes—
198C23×C4C23×C1311yescharacteristic
199C23×C4C23×C1312yes—
200C4×Q8—48no—
201#117—44no—
202C2×C4⋊C4C23×C1312yes—
203C2×C4⋊C4C23×C1312yes—
204C2×C4⋊C4C23×C1314yes—
205C2×C4⋊C4C23×C1318yes—
206C2×C4⋊C4C23×C1314yes—
207C2×C4⋊C4C23×C1314yes—
208C2×C4⋊C4C23×C1318yes—
209C2×C4⋊C4C23×C1318yes—
210C2×C4⋊C4C23×C1318yes—
211C2×C4⋊C4C23×C1318yes—
212C2×C22⋊C4C23×C1314yes—
213C2×C22⋊C4C23×C1318yes—
214C2×C42Q8×C1318yescomplemented
215C2×C42C23×C1314yes—
216C2×C42C23×C1314yes—
217C2×C42C23×C1314yes—
218C2×C42C23×C1312yes—
219C2×C42C23×C1311yescharacteristic
220C2×C42C23×C1311yescharacteristic
221#95C23×C1318yes—
222#95C23×C1318yes—
223#95C23×C1318yes—
224#95C23×C1314yes—
225#95C23×C1314yes—
226#95C23×C1314yes—
227#95C23×C1314yes—
228#95C23×C1318yes—
229#95C23×C1314yes—
230#95C23×C1318yes—
231#95C23×C1314yes—
232C2×C13—42no—
233C2×C13C2×#54411yescharacteristic
234C2×C13#345812yes—
235C2×C13#352912yes—
236C2×C13#353112yes—
237C24C24×C1311yescharacteristic
238C2×Q8—44no—
239C2×Q8—48no—
240C22×C4—22no—
241C22×C4—22no—
242C22×C4—44no—
243C22×C4C2×Q8×C1314yes—
244C22×C4C2×Q8×C1318yes—
245C22×C4C24×C1318yes—
246C22×C4C24×C1314yes—
247C22×C4C24×C1318yes—
248C22×C4C24×C1314yes—
249C22×C4C24×C1311yescharacteristic
250C22×C4C24×C1312yes—
251C22×C4C24×C1312yes—
252C22×C4C24×C1311yescharacteristic
253C4⋊C4—42no—
254C4⋊C4—42no—
255C4⋊C4—48no—
256C4⋊C4—44no—
257C4⋊C4—44no—
258C4⋊C4—48no—
259C4⋊C4—44no—
260C4⋊C4—48no—
261C4⋊C4—48no—
262C4⋊C4—48no—
263C22⋊C4—44no—
264C22⋊C4—48no—
265C42—28no—
266C42—28no—
267C42—28no—
268C42C2×Q8×C1314yes—
269C42C2×Q8×C1314yes—
270C42C2×Q8×C1318yes—
271C13#3669111yescharacteristic, direct product factor, Sylow
272C23—21no—
273C23—21no—
274C23—24no—
275C23C22×Q8×C1312yes—
276C23C25×C1311yescharacteristic
277Q8—416no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—24no—
281C2×C4—24no—
282C2×C4—28no—
283C2×C4—24no—
284C2×C4—24no—
285C2×C4—28no—
286C2×C4—28no—
287C2×C4—28no—
288C2×C4—28no—
289C2×C4—28no—
290C2×C4—28no—
291C2×C4—28no—
292C2×C4—28no—
293C2×C4—48no—
294C2×C4C22×Q8×C1312yes—
295C2×C4C22×Q8×C1314yes—
296C2×C4C22×Q8×C1314yes—
297C2×C4C22×Q8×C1312yes—
298C2×C4C13×H(5,𝔽2)12yes—
299C2×C4C13×2−1+412yes—
300C22—22no—
301C22—24no—
302C22—42no—
303C22—42no—
304C22C23×Q8×C1311yescharacteristic
305C22C2×C13×H(5,𝔽2)11yescharacteristic
306C22C2×C13×2−1+411yescharacteristic
307C22C13×#58514yes—
308C4—22no—
309C4—24no—
310C4—24no—
311C4—44no—
312C4—44no—
313C4—48no—
314C4—48no—
315C4C13×#54414yes—
316C2—42no—
317C2C2×C13×#54411yescharacteristic
318C2C13×#345812yes—
319C2C13×#352912yes—
320C2C13×#353112yes—
subgroupG/H
centerC22×C4×C13C24
commutator, Frattini, cosocleC23C25×C13
socleC23×C13C25
prime radicalC24×C13C24
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×#2845C2semidirect
2. C13×#2844C2semidirect
3. C13×#2843C2semidirect
5. C13×#2402C2semidirect
6. C13×#2399C2semidirect
59. C2×C42×C13Q8semidirect
77. #36691C13direct (N × H)
112. #2845C2×C13semidirect
113. #2844C2×C13semidirect
114. #2843C2×C13semidirect
116. #2402C2×C13semidirect
117. #2399C2×C13semidirect
214. C2×C42Q8×C13semidirect
271. C13#36691direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#28452
C13×#28442
C13×#28432
C13×#28412
C13×#24022
C13×#23992
C13×#23962
C13×#22852
C13×#22832
#3669113