Finite Group Databasebeta

← C13×#2719 #13111777

Subgroups — C13×#2719 #13111777

Order 1664.

400 conjugacy classes of subgroups.

The subgroup lattice has 326 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#125C211yesmaximal, characteristic
2C2×C13×#125C211yesmaximal, characteristic
3C13×#400C211yesmaximal, characteristic
4C13×#400C211yesmaximal, characteristic
5C13×#400C211yesmaximal, characteristic
6C13×#398C211yesmaximal, characteristic
7C13×#398C211yesmaximal, characteristic
8C13×#398C211yesmaximal, characteristic
9C13×#389C211yesmaximal, characteristic
10C13×#389C211yesmaximal, characteristic
11C13×#387C211yesmaximal, characteristic
12C13×#387C211yesmaximal, characteristic
13C13×#387C211yesmaximal, characteristic
14C13×#387C211yesmaximal, characteristic
15C13×#382C211yesmaximal, characteristic
16C13×#125—24no—
17C13×#125—24no—
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×C13×C4⋊C4C2211yescharacteristic
29C2×C13×C4⋊C4C2211yescharacteristic
30C2×C13×C4⋊C4C2211yescharacteristic
31C2×C13×C4⋊C4C2211yescharacteristic
32C2×C13×C4⋊C4C2211yescharacteristic
33C2×C13×C4⋊C4C2211yescharacteristic
34C2×C42×C13C2211yescharacteristic
35C2×C42×C13C2211yescharacteristic
36C2×C42×C13C2211yescharacteristic
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
51C13×#95C2211yescharacteristic
52C13×#95C2211yescharacteristic
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
66C22×C4×C13C2311yescharacteristic
67C22×C4×C13C2311yescharacteristic
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—22no—
75C13×C4⋊C4—22no—
76C13×C4⋊C4—22no—
77C13×C4⋊C4—22no—
78C13×C4⋊C4—22no—
79C13×C4⋊C4—22no—
80C13×C4⋊C4—22no—
81C13×C4⋊C4—22no—
82C13×C4⋊C4—22no—
83C13×C4⋊C4D414yes—
84C42×C13—22no—
85C42×C13—22no—
86C42×C13—22no—
87#2719C1311yesmaximal, characteristic, direct product factor, Sylow
88C23×C13C2411yescharacteristic
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—21no—
126C2×C4×C13—21no—
127C2×C4×C13—21no—
128C2×C4×C13—21no—
129C2×C4×C13C2×D412yes—
130C2×C4×C13C2×D412yes—
131C2×C4×C13C2×D412yes—
132C2×C4×C13#4112yes—
133C2×C4×C13#4112yes—
134C2×#125C2×C1311yescharacteristic
135C2×#125C2×C1311yescharacteristic
136#400C2×C1311yescharacteristic
137#400C2×C1311yescharacteristic
138#400C2×C1311yescharacteristic
139#398C2×C1311yescharacteristic
140#398C2×C1311yescharacteristic
141#398C2×C1311yescharacteristic
142#389C2×C1311yescharacteristic
143#389C2×C1311yescharacteristic
144#387C2×C1311yescharacteristic
145#387C2×C1311yescharacteristic
146#387C2×C1311yescharacteristic
147#387C2×C1311yescharacteristic
148#382C2×C1311yescharacteristic
149C22×C13C22×D411yescharacteristic
150C22×C13C2×#4111yescharacteristic
151C22×C13C2×#4111yescharacteristic
152C22×C132−1+411yescharacteristic
153C22×C132−1+411yescharacteristic
154C22×C132−1+411yescharacteristic
155C22×C132−1+411yescharacteristic
156C4×C13—22no—
157C4×C13—22no—
158C4×C13—22no—
159C4×C13—22no—
160C4×C13—22no—
161C4×C13—41no—
162C4×C13—41no—
163C4×C13—41no—
164C4×C13—41no—
165C4×C13—41no—
166C4×C13—41no—
167C4×C13—41no—
168C4×C13—41no—
169C4×C13—41no—
170C4×C13—41no—
171#125—24no—
172#125—24no—
173C2×C4⋊C4C22×C1311yescharacteristic
174C2×C4⋊C4C22×C1311yescharacteristic
175C2×C4⋊C4C22×C1311yescharacteristic
176C2×C4⋊C4C22×C1311yescharacteristic
177C2×C4⋊C4C22×C1311yescharacteristic
178C2×C4⋊C4C22×C1311yescharacteristic
179C2×C4⋊C4C22×C1311yescharacteristic
180C2×C4⋊C4C22×C1311yescharacteristic
181C2×C4⋊C4C22×C1311yescharacteristic
182C2×C4⋊C4C22×C1311yescharacteristic
183C2×C4⋊C4C22×C1311yescharacteristic
184C2×C4⋊C4C22×C1311yescharacteristic
185C2×C4⋊C4C22×C1311yescharacteristic
186C2×C4⋊C4C22×C1311yescharacteristic
187C2×C4⋊C4C22×C1311yescharacteristic
188C2×C4⋊C4C22×C1311yescharacteristic
189C2×C42C22×C1311yescharacteristic
190C2×C42C22×C1311yescharacteristic
191C2×C42C22×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
200#95C22×C1311yescharacteristic
201#95C22×C1311yescharacteristic
202#95C22×C1311yescharacteristic
203#95C22×C1311yescharacteristic
204#95C22×C1311yescharacteristic
205#95C22×C1311yescharacteristic
206#95C22×C1311yescharacteristic
207#95C22×C1311yescharacteristic
208C2×C13#53611yescharacteristic
209C2×C13#54111yescharacteristic
210C2×C13#54111yescharacteristic
211C2×C13#54711yescharacteristic
212C2×C13#54811yescharacteristic
213C2×C13#55211yescharacteristic
214C2×C13#56411yescharacteristic
215C22×C4C23×C1311yescharacteristic
216C22×C4C23×C1311yescharacteristic
217C22×C4C23×C1311yescharacteristic
218C22×C4C23×C1311yescharacteristic
219C22×C4C23×C1311yescharacteristic
220C22×C4C23×C1311yescharacteristic
221C22×C4C23×C1311yescharacteristic
222C22×C4C23×C1311yescharacteristic
223C22×C4C23×C1311yescharacteristic
224C22×C4C23×C1311yescharacteristic
225C22×C4C23×C1311yescharacteristic
226C22×C4C23×C1311yescharacteristic
227C22×C4C23×C1311yescharacteristic
228C22×C4C23×C1311yescharacteristic
229C22×C4C23×C1311yescharacteristic
230C4⋊C4—22no—
231C4⋊C4—22no—
232C4⋊C4—22no—
233C4⋊C4—22no—
234C4⋊C4—22no—
235C4⋊C4—22no—
236C4⋊C4—22no—
237C4⋊C4—22no—
238C4⋊C4—22no—
239C4⋊C4—22no—
240C4⋊C4—22no—
241C4⋊C4—22no—
242C4⋊C4—22no—
243C4⋊C4—22no—
244C4⋊C4—22no—
245C4⋊C4D4×C1314yes—
246C42—22no—
247C42—22no—
248C42—22no—
249C13#271911yescharacteristic, direct product factor, Sylow
250C23C24×C1311yescharacteristic
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×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4C2×D4×C1312yes—
292C2×C4C2×D4×C1312yes—
293C2×C4C2×D4×C1312yes—
294C2×C4C13×#4112yes—
295C2×C4C13×#4112yes—
296C22C22×D4×C1311yescharacteristic
297C22C2×C13×#4111yescharacteristic
298C22C2×C13×#4111yescharacteristic
299C22C13×2−1+411yescharacteristic
300C22C13×2−1+411yescharacteristic
301C22C13×2−1+411yescharacteristic
302C22C13×2−1+411yescharacteristic
303C4—22no—
304C4—22no—
305C4—22no—
306C4—22no—
307C4—22no—
308C4—41no—
309C4—41no—
310C4—41no—
311C4—41no—
312C4—41no—
313C4—41no—
314C4—41no—
315C4—41no—
316C4—41no—
317C4—41no—
318C2C13×#53611yescharacteristic
319C2C13×#54111yescharacteristic
320C2C13×#54111yescharacteristic
321C2C13×#54711yescharacteristic
322C2C13×#54811yescharacteristic
323C2C13×#55211yescharacteristic
324C2C13×#56411yescharacteristic
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
87. #2719C13direct (N × H)
249. C13#2719direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#1252
C13×#4002
C13×#3982
C13×#3892
C13×#3872
C13×#3822
#271913