Finite Group Databasebeta

← C13×#2655 #13111713

Subgroups — C13×#2655 #13111713

Order 1664.

344 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
1C13×#401C211yesmaximal, characteristic
2C13×#400C211yesmaximal, characteristic
3C13×#400C211yesmaximal, characteristic
4C13×#400C211yesmaximal, characteristic
5C13×#400C211yesmaximal, characteristic
6C13×#398C211yesmaximal, characteristic
7C13×#398C211yesmaximal, characteristic
8C13×#398C211yesmaximal, characteristic
9C13×#389C211yesmaximal, characteristic
10C13×#387C211yesmaximal, characteristic
11C13×#387C211yesmaximal, characteristic
12C13×#387C211yesmaximal, characteristic
13C13×#387C211yesmaximal, characteristic
14C13×#387C211yesmaximal, characteristic
15C4×C13×C4⋊C4C211yesmaximal, characteristic
16C2×C13×C4⋊C4C2211yescharacteristic
17C2×C13×C4⋊C4C2211yescharacteristic
18C2×C13×C4⋊C4C2211yescharacteristic
19C2×C13×C4⋊C4C2211yescharacteristic
20C2×C13×C4⋊C4C2211yescharacteristic
21C2×C13×C4⋊C4C2211yescharacteristic
22C2×C13×C4⋊C4C2211yescharacteristic
23C2×C13×C4⋊C4C2211yescharacteristic
24C2×C13×C4⋊C4C2211yescharacteristic
25C2×C13×C4⋊C4C2211yescharacteristic
26C2×C13×C4⋊C4C2211yescharacteristic
27C2×C13×C4⋊C4C2211yescharacteristic
28C2×C42×C13C2211yescharacteristic
29C2×C42×C13C2211yescharacteristic
30C2×C42×C13C2211yescharacteristic
31C13×#95C2211yescharacteristic
32C13×#95C2211yescharacteristic
33C13×#95C2211yescharacteristic
34C13×#95C2211yescharacteristic
35C13×#95C2211yescharacteristic
36C13×#95C2211yescharacteristic
37C13×#95C2211yescharacteristic
38C13×#95C2211yescharacteristic
39C13×#95C2211yescharacteristic
40C13×#95C2211yescharacteristic
41C13×#95C2211yescharacteristic
42C13×#95C2211yescharacteristic
43C13×#95C2211yescharacteristic
44C13×#95C2211yescharacteristic
45C13×#95C2211yescharacteristic
46C13×#95C2211yescharacteristic
47C13×#95C2211yescharacteristic
48C13×#95C2211yescharacteristic
49C13×#95C2211yescharacteristic
50C13×#95C2211yescharacteristic
51C22×C4×C13C2311yescharacteristic
52C22×C4×C13C2311yescharacteristic
53C22×C4×C13C2311yescharacteristic
54C22×C4×C13C2311yescharacteristic
55C22×C4×C13C2311yescharacteristic
56C22×C4×C13C2311yescharacteristic
57C22×C4×C13C2311yescharacteristic
58C22×C4×C13C2311yescharacteristic
59C22×C4×C13C2311yescharacteristic
60C22×C4×C13C2311yescharacteristic
61C22×C4×C13C2311yescharacteristic
62C22×C4×C13C2311yescharacteristic
63C22×C4×C13C2311yescharacteristic
64C22×C4×C13C2311yescharacteristic
65C22×C4×C13C2311yescharacteristic
66C13×C4⋊C4—22no—
67C13×C4⋊C4—22no—
68C13×C4⋊C4—22no—
69C13×C4⋊C4—22no—
70C13×C4⋊C4—22no—
71C13×C4⋊C4—22no—
72C13×C4⋊C4—22no—
73C13×C4⋊C4—22no—
74C13×C4⋊C4—41no—
75C13×C4⋊C4—41no—
76C13×C4⋊C4—41no—
77C13×C4⋊C4—41no—
78C42×C13—22no—
79C42×C13—41no—
80C42×C13—41no—
81#2655C1311yesmaximal, characteristic, direct product factor, Sylow
82C23×C13C2411yescharacteristic
83C2×C4×C13—21no—
84C2×C4×C13—21no—
85C2×C4×C13—21no—
86C2×C4×C13—21no—
87C2×C4×C13—21no—
88C2×C4×C13—21no—
89C2×C4×C13—21no—
90C2×C4×C13—21no—
91C2×C4×C13—21no—
92C2×C4×C13—21no—
93C2×C4×C13—21no—
94C2×C4×C13—21no—
95C2×C4×C13—21no—
96C2×C4×C13—21no—
97C2×C4×C13—21no—
98C2×C4×C13—21no—
99C2×C4×C13—21no—
100C2×C4×C13—21no—
101C2×C4×C13—21no—
102C2×C4×C13—21no—
103C2×C4×C13—21no—
104C2×C4×C13—21no—
105C2×C4×C13—21no—
106C2×C4×C13—21no—
107C2×C4×C13—21no—
108C2×C4×C13—21no—
109C2×C4×C13—21no—
110C2×C4×C13—21no—
111C2×C4×C13—21no—
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13—21no—
124C2×C4×C13—21no—
125C2×C4×C13#4112yes—
126C2×C4×C13#4112yes—
127C2×C4×C13#4112yes—
128#401C2×C1311yescharacteristic
129#400C2×C1311yescharacteristic
130#400C2×C1311yescharacteristic
131#400C2×C1311yescharacteristic
132#400C2×C1311yescharacteristic
133#398C2×C1311yescharacteristic
134#398C2×C1311yescharacteristic
135#398C2×C1311yescharacteristic
136#389C2×C1311yescharacteristic
137#387C2×C1311yescharacteristic
138#387C2×C1311yescharacteristic
139#387C2×C1311yescharacteristic
140#387C2×C1311yescharacteristic
141#387C2×C1311yescharacteristic
142C4×C4⋊C4C2×C1311yescharacteristic
143C22×C13C2×#4111yescharacteristic
144C22×C13C2×#4111yescharacteristic
145C22×C13C2×#4111yescharacteristic
146C22×C13H(5,𝔽2)11yescharacteristic
147C22×C132−1+411yescharacteristic
148C22×C132−1+411yescharacteristic
149C22×C132−1+411yescharacteristic
150C4×C13—22no—
151C4×C13—22no—
152C4×C13—22no—
153C4×C13—41no—
154C4×C13—41no—
155C4×C13—41no—
156C4×C13—41no—
157C4×C13—41no—
158C4×C13—41no—
159C4×C13—41no—
160C4×C13—41no—
161C4×C13—41no—
162C4×C13—41no—
163C4×C13—41no—
164C4×C13—41no—
165C2×C4⋊C4C22×C1311yescharacteristic
166C2×C4⋊C4C22×C1311yescharacteristic
167C2×C4⋊C4C22×C1311yescharacteristic
168C2×C4⋊C4C22×C1311yescharacteristic
169C2×C4⋊C4C22×C1311yescharacteristic
170C2×C4⋊C4C22×C1311yescharacteristic
171C2×C4⋊C4C22×C1311yescharacteristic
172C2×C4⋊C4C22×C1311yescharacteristic
173C2×C4⋊C4C22×C1311yescharacteristic
174C2×C4⋊C4C22×C1311yescharacteristic
175C2×C4⋊C4C22×C1311yescharacteristic
176C2×C4⋊C4C22×C1311yescharacteristic
177C2×C42C22×C1311yescharacteristic
178C2×C42C22×C1311yescharacteristic
179C2×C42C22×C1311yescharacteristic
180#95C22×C1311yescharacteristic
181#95C22×C1311yescharacteristic
182#95C22×C1311yescharacteristic
183#95C22×C1311yescharacteristic
184#95C22×C1311yescharacteristic
185#95C22×C1311yescharacteristic
186#95C22×C1311yescharacteristic
187#95C22×C1311yescharacteristic
188#95C22×C1311yescharacteristic
189#95C22×C1311yescharacteristic
190#95C22×C1311yescharacteristic
191#95C22×C1311yescharacteristic
192#95C22×C1311yescharacteristic
193#95C22×C1311yescharacteristic
194#95C22×C1311yescharacteristic
195#95C22×C1311yescharacteristic
196#95C22×C1311yescharacteristic
197#95C22×C1311yescharacteristic
198#95C22×C1311yescharacteristic
199#95C22×C1311yescharacteristic
200C2×C13#52911yescharacteristic
201C2×C13#53911yescharacteristic
202C2×C13#53911yescharacteristic
203C2×C13#54111yescharacteristic
204C2×C13#54111yescharacteristic
205C2×C13#54111yescharacteristic
206C2×C13#54211yescharacteristic
207C22×C4C23×C1311yescharacteristic
208C22×C4C23×C1311yescharacteristic
209C22×C4C23×C1311yescharacteristic
210C22×C4C23×C1311yescharacteristic
211C22×C4C23×C1311yescharacteristic
212C22×C4C23×C1311yescharacteristic
213C22×C4C23×C1311yescharacteristic
214C22×C4C23×C1311yescharacteristic
215C22×C4C23×C1311yescharacteristic
216C22×C4C23×C1311yescharacteristic
217C22×C4C23×C1311yescharacteristic
218C22×C4C23×C1311yescharacteristic
219C22×C4C23×C1311yescharacteristic
220C22×C4C23×C1311yescharacteristic
221C22×C4C23×C1311yescharacteristic
222C4⋊C4—22no—
223C4⋊C4—22no—
224C4⋊C4—22no—
225C4⋊C4—22no—
226C4⋊C4—22no—
227C4⋊C4—22no—
228C4⋊C4—22no—
229C4⋊C4—22no—
230C4⋊C4—41no—
231C4⋊C4—41no—
232C4⋊C4—41no—
233C4⋊C4—41no—
234C42—22no—
235C42—41no—
236C42—41no—
237C13#265511yescharacteristic, direct product factor, Sylow
238C23C24×C1311yescharacteristic
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4C13×#4112yes—
282C2×C4C13×#4112yes—
283C2×C4C13×#4112yes—
284C22C2×C13×#4111yescharacteristic
285C22C2×C13×#4111yescharacteristic
286C22C2×C13×#4111yescharacteristic
287C22C13×H(5,𝔽2)11yescharacteristic
288C22C13×2−1+411yescharacteristic
289C22C13×2−1+411yescharacteristic
290C22C13×2−1+411yescharacteristic
291C4—22no—
292C4—22no—
293C4—22no—
294C4—41no—
295C4—41no—
296C4—41no—
297C4—41no—
298C4—41no—
299C4—41no—
300C4—41no—
301C4—41no—
302C4—41no—
303C4—41no—
304C4—41no—
305C4—41no—
306C2C13×#52911yescharacteristic
307C2C13×#53911yescharacteristic
308C2C13×#53911yescharacteristic
309C2C13×#54111yescharacteristic
310C2C13×#54111yescharacteristic
311C2C13×#54111yescharacteristic
312C2C13×#54211yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C13C24
commutator, Frattini, cosocleC23C24×C13
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C13 ◁ G

Complements

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

NH ≅ G/Ntype
81. #2655C13direct (N × H)
237. C13#2655direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#4012
C13×#4002
C13×#3982
C13×#3892
C13×#3872
C4×C13×C4⋊C42
#265513