Finite Group Databasebeta

← C13×#3347 #13112405

Subgroups — C13×#3347 #13112405

Order 1664.

360 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#555C211yesmaximal, characteristic, complemented
2C13×#553C211yesmaximal, characteristic, complemented
3C13×#501C211yesmaximal, characteristic, complemented
4C13×#482C211yesmaximal, characteristic, complemented
5C13×#482C211yesmaximal, characteristic, complemented
6C13×#482C211yesmaximal, characteristic, complemented
7C13×#480C211yesmaximal, characteristic, complemented
8C13×#478C211yesmaximal, characteristic, complemented
9C13×#474C211yesmaximal, characteristic, complemented
10C13×#469C211yesmaximal, characteristic, complemented
11C13×#466C211yesmaximal, characteristic, complemented
12C13×#442C211yesmaximal, characteristic, complemented
13C13×#435C211yesmaximal, characteristic, complemented
14C13×#428C211yesmaximal, characteristic, complemented
15C13×#427C211yesmaximal, characteristic, complemented
16C2×C13×D8C2211yescharacteristic
17C2×C13×M16C2211yescharacteristic
18C22×C8×C13C2211yescharacteristic
19C13×C4⋊Q8C2211yescharacteristic
20C13×#126—21no—
21C13×#125C2211yescharacteristic
22C13×#124—21no—
23C13×#124—21no—
24C13×#123—21no—
25C13×#121—21no—
26C13×#121—21no—
27C13×#121C2211yescharacteristic
28C13×#121C2211yescharacteristic
29C13×#121C2211yescharacteristic
30C13×#121C2211yescharacteristic
31C4×D4×C13—21no—
32C4×D4×C13C2211yescharacteristic
33C4×D4×C13C2211yescharacteristic
34C4×D4×C13C2211yescharacteristic
35C13×#117—21no—
36C13×#117C2211yescharacteristic
37C13×#117C2211yescharacteristic
38C13×#117C2211yescharacteristic
39C2×C13×C4⋊C4C2211yescharacteristic
40C13×#107C2211yescharacteristic
41C13×#107C2211yescharacteristic
42C13×#107C2211yescharacteristic
43C13×#107C2211yescharacteristic
44C13×#107C2211yescharacteristic
45C13×#106C2211yescharacteristic
46C13×#106C2211yescharacteristic
47C13×#106C2211yescharacteristic
48C13×#106C2211yescharacteristic
49C13×C4⋊C8C2211yescharacteristic
50C13×#102C2211yescharacteristic
51C13×#102C2211yescharacteristic
52C13×#102C2211yescharacteristic
53C13×#102C2211yescharacteristic
54C13×#102C2211yescharacteristic
55C13×#102C2211yescharacteristic
56C13×C22⋊C8C2211yescharacteristic
57C13×C22⋊C8C2211yescharacteristic
58C13×#97C2211yescharacteristic
59C2×Q8×C13—21no—
60C2×D4×C13—21no—
61C2×D4×C13—21no—
62C2×D4×C13—21no—
63C2×D4×C13—21no—
64C2×D4×C13D411yescharacteristic
65C2×D4×C13C2311yescharacteristic
66C2×D4×C13C2311yescharacteristic
67C22×C4×C13—21no—
68C22×C4×C13—21no—
69C22×C4×C13—21no—
70C22×C4×C13C2311yescharacteristic
71C22×C4×C13C2311yescharacteristic
72C13×D8—22no—
73C13×M16—22no—
74C2×C8×C13—22no—
75C2×C8×C13C2311yescharacteristic
76C2×C8×C13C2311yescharacteristic
77C2×C8×C13C2311yescharacteristic
78C2×C8×C13C2311yescharacteristic
79C13×C4⋊C4—21no—
80C13×C4⋊C4—21no—
81C13×C4⋊C4—21no—
82C13×C4⋊C4—21no—
83C13×C4⋊C4D411yescharacteristic
84C13×C4⋊C4C2311yescharacteristic
85C13×C4⋊C4C2311yescharacteristic
86C13×C4⋊C4C2311yescharacteristic
87C13×C4⋊C4C2311yescharacteristic
88C13×C4⋊C4C2311yescharacteristic
89C13×C4⋊C4C2311yescharacteristic
90C13×C22⋊C4—21no—
91C13×C22⋊C4—21no—
92C13×C22⋊C4—21no—
93C13×C22⋊C4—21no—
94C13×C22⋊C4—21no—
95C13×C22⋊C4—21no—
96C13×C22⋊C4—21no—
97C13×C22⋊C4—21no—
98C13×C22⋊C4—21no—
99C13×C22⋊C4D411yescharacteristic
100C13×C22⋊C4D411yescharacteristic
101C42×C13—21no—
102C42×C13—21no—
103C42×C13—21no—
104C42×C13C2311yescharacteristic
105#3347C1311yesmaximal, characteristic, direct product factor, Sylow
106C23×C13—21no—
107C23×C13—21no—
108C23×C13C2×D411yescharacteristic
109C23×C13C2×D411yescharacteristic
110Q8×C13—81no—
111D4×C13—21no—
112D4×C13—21no—
113D4×C13—21no—
114D4×C13—21no—
115D4×C13—41no—
116D4×C13—42no—
117D4×C13—81no—
118D4×C13—81no—
119D4×C13—81no—
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×C13—21no—
130C2×C4×C13—42no—
131C2×C4×C13—81no—
132C2×C4×C13—81no—
133C2×C4×C13C2×D411yescharacteristic
134C2×C4×C13C2×D411yescharacteristic
135C2×C4×C13C2×D411yescharacteristic
136C2×C4×C13C2×D411yescharacteristic
137C2×C4×C13C2411yescharacteristic
138C8×C13—21no—
139C8×C13—21no—
140C8×C13—21no—
141C8×C13#4112yes—
142#555C2×C1311yescharacteristic, complemented
143#553C2×C1311yescharacteristic, complemented
144#501C2×C1311yescharacteristic, complemented
145#482C2×C1311yescharacteristic, complemented
146#482C2×C1311yescharacteristic, complemented
147#482C2×C1311yescharacteristic, complemented
148#480C2×C1311yescharacteristic, complemented
149#478C2×C1311yescharacteristic, complemented
150#474C2×C1311yescharacteristic, complemented
151#469C2×C1311yescharacteristic, complemented
152#466C2×C1311yescharacteristic, complemented
153#442C2×C1311yescharacteristic, complemented
154#435C2×C1311yescharacteristic, complemented
155#428C2×C1311yescharacteristic, complemented
156#427C2×C1311yescharacteristic, complemented
157C22×C13—21no—
158C22×C13—21no—
159C22×C13—21no—
160C22×C13—21no—
161C22×C13—21no—
162C22×C13—21no—
163C22×C13—41no—
164C22×C13—41no—
165C22×C13—41no—
166C22×C13—41no—
167C22×C13—41no—
168C22×C13—41no—
169C22×C13C22×D411yescharacteristic
170C4×C13—21no—
171C4×C13—21no—
172C4×C13—21no—
173C4×C13—21no—
174C4×C13—41no—
175C4×C13—41no—
176C4×C13—41no—
177C4×C13—41no—
178C4×C13—41no—
179C4×C13—41no—
180C4×C13C2×#4111yescharacteristic
181C4×C132−1+411yescharacteristic
182C2×D8C22×C1311yescharacteristic
183C2×M16C22×C1311yescharacteristic
184C22×C8C22×C1311yescharacteristic
185C4⋊Q8C22×C1311yescharacteristic
186#126—21no—
187#125C22×C1311yescharacteristic
188#124—21no—
189#124—21no—
190#123—21no—
191#121—21no—
192#121—21no—
193#121C22×C1311yescharacteristic
194#121C22×C1311yescharacteristic
195#121C22×C1311yescharacteristic
196#121C22×C1311yescharacteristic
197C4×D4—21no—
198C4×D4C22×C1311yescharacteristic
199C4×D4C22×C1311yescharacteristic
200C4×D4C22×C1311yescharacteristic
201#117—21no—
202#117C22×C1311yescharacteristic
203#117C22×C1311yescharacteristic
204#117C22×C1311yescharacteristic
205C2×C4⋊C4C22×C1311yescharacteristic
206#107C22×C1311yescharacteristic
207#107C22×C1311yescharacteristic
208#107C22×C1311yescharacteristic
209#107C22×C1311yescharacteristic
210#107C22×C1311yescharacteristic
211#106C22×C1311yescharacteristic
212#106C22×C1311yescharacteristic
213#106C22×C1311yescharacteristic
214#106C22×C1311yescharacteristic
215C4⋊C8C22×C1311yescharacteristic
216#102C22×C1311yescharacteristic
217#102C22×C1311yescharacteristic
218#102C22×C1311yescharacteristic
219#102C22×C1311yescharacteristic
220#102C22×C1311yescharacteristic
221#102C22×C1311yescharacteristic
222C22⋊C8C22×C1311yescharacteristic
223C22⋊C8C22×C1311yescharacteristic
224#97C22×C1311yescharacteristic
225C2×C13—41no—
226C2×C13—41no—
227C2×C13—81no—
228C2×C13—81no—
229C2×C13#54711yescharacteristic
230C2×C13#57511yescharacteristic
231C2×C13#57611yescharacteristic
232C2×Q8—21no—
233C2×D4—21no—
234C2×D4—21no—
235C2×D4—21no—
236C2×D4—21no—
237C2×D4D4×C1311yescharacteristic
238C2×D4C23×C1311yescharacteristic
239C2×D4C23×C1311yescharacteristic
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4C23×C1311yescharacteristic
244C22×C4C23×C1311yescharacteristic
245D8—22no—
246M16—22no—
247C2×C8—22no—
248C2×C8C23×C1311yescharacteristic
249C2×C8C23×C1311yescharacteristic
250C2×C8C23×C1311yescharacteristic
251C2×C8C23×C1311yescharacteristic
252C4⋊C4—21no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4D4×C1311yescharacteristic
257C4⋊C4C23×C1311yescharacteristic
258C4⋊C4C23×C1311yescharacteristic
259C4⋊C4C23×C1311yescharacteristic
260C4⋊C4C23×C1311yescharacteristic
261C4⋊C4C23×C1311yescharacteristic
262C4⋊C4C23×C1311yescharacteristic
263C22⋊C4—21no—
264C22⋊C4—21no—
265C22⋊C4—21no—
266C22⋊C4—21no—
267C22⋊C4—21no—
268C22⋊C4—21no—
269C22⋊C4—21no—
270C22⋊C4—21no—
271C22⋊C4—21no—
272C22⋊C4D4×C1311yescharacteristic
273C22⋊C4D4×C1311yescharacteristic
274C42—21no—
275C42—21no—
276C42—21no—
277C42C23×C1311yescharacteristic
278C13#334711yescharacteristic, direct product factor, Sylow
279C23—21no—
280C23—21no—
281C23C2×D4×C1311yescharacteristic
282C23C2×D4×C1311yescharacteristic
283Q8—81no—
284D4—21no—
285D4—21no—
286D4—21no—
287D4—21no—
288D4—41no—
289D4—42no—
290D4—81no—
291D4—81no—
292D4—81no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—42no—
304C2×C4—81no—
305C2×C4—81no—
306C2×C4C2×D4×C1311yescharacteristic
307C2×C4C2×D4×C1311yescharacteristic
308C2×C4C2×D4×C1311yescharacteristic
309C2×C4C2×D4×C1311yescharacteristic
310C2×C4C24×C1311yescharacteristic
311C8—21no—
312C8—21no—
313C8—21no—
314C8C13×#4112yes—
315C22—21no—
316C22—21no—
317C22—21no—
318C22—21no—
319C22—21no—
320C22—21no—
321C22—41no—
322C22—41no—
323C22—41no—
324C22—41no—
325C22—41no—
326C22—41no—
327C22C22×D4×C1311yescharacteristic
328C4—21no—
329C4—21no—
330C4—21no—
331C4—21no—
332C4—41no—
333C4—41no—
334C4—41no—
335C4—41no—
336C4—41no—
337C4—41no—
338C4C2×C13×#4111yescharacteristic
339C4C13×2−1+411yescharacteristic
340C2—41no—
341C2—41no—
342C2—81no—
343C2—81no—
344C2C13×#54711yescharacteristic
345C2C13×#57511yescharacteristic
346C2C13×#57611yescharacteristic
subgroupG/H
center, socleC22×C13C22×D4
commutator, Frattini, cosocleC2×C4C24×C13
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C4×D4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×#555C2semidirect
2. C13×#553C2semidirect
3. C13×#501C2semidirect
4. C13×#482C2semidirect
5. C13×#482C2semidirect
6. C13×#482C2semidirect
7. C13×#480C2semidirect
8. C13×#478C2semidirect
9. C13×#474C2semidirect
10. C13×#469C2semidirect
11. C13×#466C2semidirect
12. C13×#442C2semidirect
13. C13×#435C2semidirect
14. C13×#428C2semidirect
15. C13×#427C2semidirect
105. #3347C13direct (N × H)
142. #555C2×C13semidirect
143. #553C2×C13semidirect
144. #501C2×C13semidirect
145. #482C2×C13semidirect
146. #482C2×C13semidirect
147. #482C2×C13semidirect
148. #480C2×C13semidirect
149. #478C2×C13semidirect
150. #474C2×C13semidirect
151. #469C2×C13semidirect
152. #466C2×C13semidirect
153. #442C2×C13semidirect
154. #435C2×C13semidirect
155. #428C2×C13semidirect
156. #427C2×C13semidirect
278. C13#3347direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#5552
C13×#5532
C13×#5012
C13×#4822
C13×#4802
C13×#4782
C13×#4742
C13×#4692
C13×#4662
C13×#4422
C13×#4352
C13×#4282
C13×#4272
#334713