Finite Group Databasebeta

← C13×#3241 #13112299

Subgroups — C13×#3241 #13112299

Order 1664.

332 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#544C211yesmaximal, characteristic, complemented
2C13×#540C211yesmaximal, characteristic
3C13×#501C211yesmaximal, characteristic, complemented
4C13×#499C211yesmaximal, characteristic, complemented
5C13×#490C211yesmaximal, characteristic, complemented
6C13×#486C211yesmaximal, characteristic, complemented
7C13×#482C211yesmaximal, characteristic, complemented
8C13×#482C211yesmaximal, characteristic, complemented
9C13×#481C211yesmaximal, characteristic, complemented
10C13×#480C211yesmaximal, characteristic, complemented
11C13×#478C211yesmaximal, characteristic, complemented
12C13×#478C211yesmaximal, characteristic, complemented
13C13×#476C211yesmaximal, characteristic, complemented
14C13×#474C211yesmaximal, characteristic, complemented
15C13×#433C211yesmaximal, characteristic, complemented
16C13×C4⋊Q8—21no—
17C13×C4⋊Q8C2211yescharacteristic
18C13×C4⋊Q8C2211yescharacteristic
19C13×#127C2211yescharacteristic
20C13×#125—21no—
21C13×#125C2211yescharacteristic
22C13×#125C2211yescharacteristic
23C13×#125C2211yescharacteristic
24C13×#123—21no—
25C13×#123—21no—
26C13×C22⋊Q8—21no—
27C13×C22⋊Q8—21no—
28C13×#121—21no—
29C13×#121—21no—
30C13×#121C2211yescharacteristic
31C13×#121C2211yescharacteristic
32C4×D4×C13C2211yescharacteristic
33C4×D4×C13C2211yescharacteristic
34C13×#117C2211yescharacteristic
35C13×#117C2211yescharacteristic
36C2×C13×C4⋊C4C2211yescharacteristic
37C13×#107C2211yescharacteristic
38C13×#107C2211yescharacteristic
39C13×#107C2211yescharacteristic
40C13×#107C2211yescharacteristic
41C13×#106C2211yescharacteristic
42C13×#106C2211yescharacteristic
43C13×#106C2211yescharacteristic
44C13×#106C2211yescharacteristic
45C13×C4⋊C8C2211yescharacteristic
46C13×C4⋊C8C2211yescharacteristic
47C13×#102C2211yescharacteristic
48C13×#102C2211yescharacteristic
49C13×#102C2211yescharacteristic
50C13×#102C2211yescharacteristic
51C13×#102C2211yescharacteristic
52C13×#102C2211yescharacteristic
53C13×#102C2211yescharacteristic
54C13×#102C2211yescharacteristic
55C13×C22⋊C8C2211yescharacteristic
56C13×C22⋊C8C2211yescharacteristic
57C13×#97C2211yescharacteristic
58C4×C8×C13C2211yescharacteristic
59C2×Q8×C13—21no—
60C2×Q8×C13—21no—
61C2×D4×C13—21no—
62C2×D4×C13—21no—
63C2×D4×C13—21no—
64C2×D4×C13—21no—
65C2×D4×C13C2311yescharacteristic
66C2×D4×C13C2311yescharacteristic
67C22×C4×C13—21no—
68C22×C4×C13—21no—
69C22×C4×C13—21no—
70C22×C4×C13C2311yescharacteristic
71C2×C8×C13C2311yescharacteristic
72C2×C8×C13C2311yescharacteristic
73C2×C8×C13C2311yescharacteristic
74C2×C8×C13C2311yescharacteristic
75C13×C4⋊C4—21no—
76C13×C4⋊C4—21no—
77C13×C4⋊C4—21no—
78C13×C4⋊C4—21no—
79C13×C4⋊C4—21no—
80C13×C4⋊C4—21no—
81C13×C4⋊C4—21no—
82C13×C4⋊C4—21no—
83C13×C4⋊C4—21no—
84C13×C4⋊C4D411yescharacteristic
85C13×C4⋊C4D411yescharacteristic
86C13×C4⋊C4C2311yescharacteristic
87C13×C4⋊C4C2311yescharacteristic
88C13×C4⋊C4C2311yescharacteristic
89C13×C4⋊C4C2311yescharacteristic
90C13×C4⋊C4C2311yescharacteristic
91C13×C4⋊C4C2311yescharacteristic
92C13×C22⋊C4—21no—
93C13×C22⋊C4—21no—
94C13×C22⋊C4—21no—
95C13×C22⋊C4—21no—
96C13×C22⋊C4—21no—
97C13×C22⋊C4D411yescharacteristic
98C13×C22⋊C4D411yescharacteristic
99C42×C13—21no—
100C42×C13C2311yescharacteristic
101C42×C13C2311yescharacteristic
102#3241C1311yesmaximal, characteristic, direct product factor, Sylow
103C23×C13—21no—
104C23×C13—21no—
105C23×C13C2×D411yescharacteristic
106Q8×C13—81no—
107Q8×C13—81no—
108D4×C13—21no—
109D4×C13—21no—
110D4×C13—21no—
111D4×C13—21no—
112D4×C13—81no—
113D4×C13—81no—
114D4×C13—81no—
115D4×C13—81no—
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—81no—
125C2×C4×C13—81no—
126C2×C4×C13—81no—
127C2×C4×C13C2×D411yescharacteristic
128C2×C4×C13C2×D411yescharacteristic
129C2×C4×C13C2×D411yescharacteristic
130C2×C4×C13C2×D411yescharacteristic
131C2×C4×C13C2×D411yescharacteristic
132C2×C4×C13C2411yescharacteristic
133C8×C13—21no—
134C8×C13—21no—
135C8×C13—21no—
136C8×C13—21no—
137#544C2×C1311yescharacteristic, complemented
138#540C2×C1311yescharacteristic
139#501C2×C1311yescharacteristic, complemented
140#499C2×C1311yescharacteristic, complemented
141#490C2×C1311yescharacteristic, complemented
142#486C2×C1311yescharacteristic, complemented
143#482C2×C1311yescharacteristic, complemented
144#482C2×C1311yescharacteristic, complemented
145#481C2×C1311yescharacteristic, complemented
146#480C2×C1311yescharacteristic, complemented
147#478C2×C1311yescharacteristic, complemented
148#478C2×C1311yescharacteristic, complemented
149#476C2×C1311yescharacteristic, complemented
150#474C2×C1311yescharacteristic, complemented
151#433C2×C1311yescharacteristic, complemented
152C22×C13—21no—
153C22×C13—21no—
154C22×C13—21no—
155C22×C13—41no—
156C22×C13—41no—
157C22×C13—41no—
158C22×C13—41no—
159C22×C13—41no—
160C22×C13—41no—
161C22×C13C22×D411yescharacteristic
162C4×C13—21no—
163C4×C13—21no—
164C4×C13—21no—
165C4×C13—21no—
166C4×C13—21no—
167C4×C13—41no—
168C4×C13—41no—
169C4×C13—41no—
170C4×C13—41no—
171C4×C13—41no—
172C4×C13—41no—
173C4×C132−1+411yescharacteristic
174C4×C132−1+411yescharacteristic
175C4⋊Q8—21no—
176C4⋊Q8C22×C1311yescharacteristic
177C4⋊Q8C22×C1311yescharacteristic
178#127C22×C1311yescharacteristic
179#125—21no—
180#125C22×C1311yescharacteristic
181#125C22×C1311yescharacteristic
182#125C22×C1311yescharacteristic
183#123—21no—
184#123—21no—
185C22⋊Q8—21no—
186C22⋊Q8—21no—
187#121—21no—
188#121—21no—
189#121C22×C1311yescharacteristic
190#121C22×C1311yescharacteristic
191C4×D4C22×C1311yescharacteristic
192C4×D4C22×C1311yescharacteristic
193#117C22×C1311yescharacteristic
194#117C22×C1311yescharacteristic
195C2×C4⋊C4C22×C1311yescharacteristic
196#107C22×C1311yescharacteristic
197#107C22×C1311yescharacteristic
198#107C22×C1311yescharacteristic
199#107C22×C1311yescharacteristic
200#106C22×C1311yescharacteristic
201#106C22×C1311yescharacteristic
202#106C22×C1311yescharacteristic
203#106C22×C1311yescharacteristic
204C4⋊C8C22×C1311yescharacteristic
205C4⋊C8C22×C1311yescharacteristic
206#102C22×C1311yescharacteristic
207#102C22×C1311yescharacteristic
208#102C22×C1311yescharacteristic
209#102C22×C1311yescharacteristic
210#102C22×C1311yescharacteristic
211#102C22×C1311yescharacteristic
212#102C22×C1311yescharacteristic
213#102C22×C1311yescharacteristic
214C22⋊C8C22×C1311yescharacteristic
215C22⋊C8C22×C1311yescharacteristic
216#97C22×C1311yescharacteristic
217C4×C8C22×C1311yescharacteristic
218C2×C13—41no—
219C2×C13—81no—
220C2×C13—81no—
221C2×C13#53611yescharacteristic
222C2×C13#57611yescharacteristic
223C2×C13#57711yescharacteristic
224C2×Q8—21no—
225C2×Q8—21no—
226C2×D4—21no—
227C2×D4—21no—
228C2×D4—21no—
229C2×D4—21no—
230C2×D4C23×C1311yescharacteristic
231C2×D4C23×C1311yescharacteristic
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4C23×C1311yescharacteristic
236C2×C8C23×C1311yescharacteristic
237C2×C8C23×C1311yescharacteristic
238C2×C8C23×C1311yescharacteristic
239C2×C8C23×C1311yescharacteristic
240C4⋊C4—21no—
241C4⋊C4—21no—
242C4⋊C4—21no—
243C4⋊C4—21no—
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—21no—
247C4⋊C4—21no—
248C4⋊C4—21no—
249C4⋊C4D4×C1311yescharacteristic
250C4⋊C4D4×C1311yescharacteristic
251C4⋊C4C23×C1311yescharacteristic
252C4⋊C4C23×C1311yescharacteristic
253C4⋊C4C23×C1311yescharacteristic
254C4⋊C4C23×C1311yescharacteristic
255C4⋊C4C23×C1311yescharacteristic
256C4⋊C4C23×C1311yescharacteristic
257C22⋊C4—21no—
258C22⋊C4—21no—
259C22⋊C4—21no—
260C22⋊C4—21no—
261C22⋊C4—21no—
262C22⋊C4D4×C1311yescharacteristic
263C22⋊C4D4×C1311yescharacteristic
264C42—21no—
265C42C23×C1311yescharacteristic
266C42C23×C1311yescharacteristic
267C13#324111yescharacteristic, direct product factor, Sylow
268C23—21no—
269C23—21no—
270C23C2×D4×C1311yescharacteristic
271Q8—81no—
272Q8—81no—
273D4—21no—
274D4—21no—
275D4—21no—
276D4—21no—
277D4—81no—
278D4—81no—
279D4—81no—
280D4—81no—
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—81no—
290C2×C4—81no—
291C2×C4—81no—
292C2×C4C2×D4×C1311yescharacteristic
293C2×C4C2×D4×C1311yescharacteristic
294C2×C4C2×D4×C1311yescharacteristic
295C2×C4C2×D4×C1311yescharacteristic
296C2×C4C2×D4×C1311yescharacteristic
297C2×C4C24×C1311yescharacteristic
298C8—21no—
299C8—21no—
300C8—21no—
301C8—21no—
302C22—21no—
303C22—21no—
304C22—21no—
305C22—41no—
306C22—41no—
307C22—41no—
308C22—41no—
309C22—41no—
310C22—41no—
311C22C22×D4×C1311yescharacteristic
312C4—21no—
313C4—21no—
314C4—21no—
315C4—21no—
316C4—21no—
317C4—41no—
318C4—41no—
319C4—41no—
320C4—41no—
321C4—41no—
322C4—41no—
323C4C13×2−1+411yescharacteristic
324C4C13×2−1+411yescharacteristic
325C2—41no—
326C2—81no—
327C2—81no—
328C2C13×#53611yescharacteristic
329C2C13×#57611yescharacteristic
330C2C13×#57711yescharacteristic
subgroupG/H
center, socleC22×C13C22×D4
commutator, Frattini, cosocleC2×C4C24×C13
prime radicalC13×#540C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C13×#117 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×#544C2semidirect
3. C13×#501C2semidirect
4. C13×#499C2semidirect
5. C13×#490C2semidirect
6. C13×#486C2semidirect
7. C13×#482C2semidirect
8. C13×#482C2semidirect
9. C13×#481C2semidirect
10. C13×#480C2semidirect
11. C13×#478C2semidirect
12. C13×#478C2semidirect
13. C13×#476C2semidirect
14. C13×#474C2semidirect
15. C13×#433C2semidirect
102. #3241C13direct (N × H)
137. #544C2×C13semidirect
139. #501C2×C13semidirect
140. #499C2×C13semidirect
141. #490C2×C13semidirect
142. #486C2×C13semidirect
143. #482C2×C13semidirect
144. #482C2×C13semidirect
145. #481C2×C13semidirect
146. #480C2×C13semidirect
147. #478C2×C13semidirect
148. #478C2×C13semidirect
149. #476C2×C13semidirect
150. #474C2×C13semidirect
151. #433C2×C13semidirect
267. C13#3241direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#5442
C13×#5402
C13×#5012
C13×#4992
C13×#4902
C13×#4862
C13×#4822
C13×#4812
C13×#4802
C13×#4782
C13×#4762
C13×#4742
C13×#4332
#324113