Finite Group Databasebeta

← C13×#3370 #13112428

Subgroups — C13×#3370 #13112428

Order 1664.

358 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#559C211yesmaximal, characteristic, complemented
2C13×#554C211yesmaximal, characteristic, complemented
3C13×#490C211yesmaximal, characteristic, complemented
4C13×#489C211yesmaximal, characteristic, complemented
5C13×#488C211yesmaximal, characteristic, complemented
6C13×#479C211yesmaximal, characteristic, complemented
7C13×#478C211yesmaximal, characteristic, complemented
8C13×#474C211yesmaximal, characteristic, complemented
9C13×#463C211yesmaximal, characteristic, complemented
10C13×#463C211yesmaximal, characteristic, complemented
11C13×#459C211yesmaximal, characteristic
12C13×#446C211yesmaximal, characteristic, complemented
13C13×#442C211yesmaximal, characteristic, complemented
14C13×#440C211yesmaximal, characteristic, complemented
15C4×C13×D8C211yesmaximal, characteristic, complemented
16C2×C13×SD16C2211yescharacteristic
17C2×C13×D8C2211yescharacteristic
18C2×C13×D8C2211yescharacteristic
19C13×C4⋊Q8C2211yescharacteristic
20C13×#127C2211yescharacteristic
21C13×#125C2211yescharacteristic
22C13×#125C2211yescharacteristic
23C13×#124—21no—
24C13×#124C2211yescharacteristic
25C13×#124C2211yescharacteristic
26C13×#123—21no—
27C13×#123—21no—
28C13×C22⋊Q8—21no—
29C13×C22⋊Q8—21no—
30C13×C22⋊Q8—21no—
31C4×Q8×C13C2211yescharacteristic
32C4×Q8×C13C2211yescharacteristic
33C4×D4×C13—21no—
34C4×D4×C13C2211yescharacteristic
35C4×D4×C13C2211yescharacteristic
36C4×D4×C13C2211yescharacteristic
37C4×D4×C13C2211yescharacteristic
38C4×D4×C13C2211yescharacteristic
39C2×C13×C4⋊C4—21no—
40C13×#107C2211yescharacteristic
41C13×#107C2211yescharacteristic
42C13×#106C2211yescharacteristic
43C13×C4⋊C8C2211yescharacteristic
44C13×C4⋊C8C2211yescharacteristic
45C13×C4⋊C8C2211yescharacteristic
46C13×#103C2211yescharacteristic
47C13×#103C2211yescharacteristic
48C13×#103C2211yescharacteristic
49C13×#102C2211yescharacteristic
50C13×#102C2211yescharacteristic
51C13×#102C2211yescharacteristic
52C13×#102C2211yescharacteristic
53C13×#102C2211yescharacteristic
54C13×#102C2211yescharacteristic
55C13×#102C2211yescharacteristic
56C13×#97C2211yescharacteristic
57C13×#97C2211yescharacteristic
58C4×C8×C13C2211yescharacteristic
59C2×Q8×C13—21no—
60C2×Q8×C13D411yescharacteristic
61C2×Q8×C13C2311yescharacteristic
62C2×D4×C13—21no—
63C2×D4×C13—21no—
64C2×D4×C13C2311yescharacteristic
65C2×D4×C13C2311yescharacteristic
66C2×D4×C13C2311yescharacteristic
67C22×C4×C13—21no—
68C22×C4×C13—21no—
69C22×C4×C13—21no—
70C22×C4×C13—21no—
71C22×C4×C13—21no—
72C13×SD16—22no—
73C13×D8—22no—
74C13×D8—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⋊C4—21no—
84C13×C4⋊C4—21no—
85C13×C4⋊C4D411yescharacteristic
86C13×C4⋊C4D411yescharacteristic
87C13×C4⋊C4D411yescharacteristic
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⋊C4—21no—
98C13×C22⋊C4—21no—
99C13×C22⋊C4—21no—
100C13×C22⋊C4—21no—
101C42×C13—21no—
102C42×C13C2311yescharacteristic
103C42×C13C2311yescharacteristic
104C42×C13C2311yescharacteristic
105#3370C1311yesmaximal, characteristic, direct product factor, Sylow
106C23×C13—21no—
107C23×C13—21no—
108C23×C13—21no—
109Q8×C13—21no—
110Q8×C13—21no—
111Q8×C13—41no—
112Q8×C13—81no—
113D4×C13—21no—
114D4×C13—21no—
115D4×C13—21no—
116D4×C13—21no—
117D4×C13—21no—
118D4×C13—42no—
119D4×C13—81no—
120D4×C13#4112yes—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13—21no—
124C2×C4×C13—21no—
125C2×C4×C13—21no—
126C2×C4×C13—42no—
127C2×C4×C13—81no—
128C2×C4×C13—81no—
129C2×C4×C13—81no—
130C2×C4×C13—81no—
131C2×C4×C13C2×D411yescharacteristic
132C2×C4×C13C2×D411yescharacteristic
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—21no—
142#559C2×C1311yescharacteristic, complemented
143#554C2×C1311yescharacteristic, complemented
144#490C2×C1311yescharacteristic, complemented
145#489C2×C1311yescharacteristic, complemented
146#488C2×C1311yescharacteristic, complemented
147#479C2×C1311yescharacteristic, complemented
148#478C2×C1311yescharacteristic, complemented
149#474C2×C1311yescharacteristic, complemented
150#463C2×C1311yescharacteristic, complemented
151#463C2×C1311yescharacteristic, complemented
152#459C2×C1311yescharacteristic
153#446C2×C1311yescharacteristic, complemented
154#442C2×C1311yescharacteristic, complemented
155#440C2×C1311yescharacteristic, complemented
156C4×D8C2×C1311yescharacteristic, complemented
157C22×C13—22no—
158C22×C13—41no—
159C22×C13—41no—
160C22×C13—41no—
161C22×C13—41no—
162C22×C13—41no—
163C22×C13—41no—
164C22×C13—41no—
165C22×C13—41no—
166C22×C13C22×D411yescharacteristic
167C4×C13—21no—
168C4×C13—21no—
169C4×C13—21no—
170C4×C13—21no—
171C4×C13—21no—
172C4×C13—21no—
173C4×C13—41no—
174C4×C13—41no—
175C4×C13—41no—
176C4×C13—41no—
177C4×C13—41no—
178C4×C13C2×#4111yescharacteristic
179C4×C132−1+411yescharacteristic
180C2×SD16C22×C1311yescharacteristic
181C2×D8C22×C1311yescharacteristic
182C2×D8C22×C1311yescharacteristic
183C4⋊Q8C22×C1311yescharacteristic
184#127C22×C1311yescharacteristic
185#125C22×C1311yescharacteristic
186#125C22×C1311yescharacteristic
187#124—21no—
188#124C22×C1311yescharacteristic
189#124C22×C1311yescharacteristic
190#123—21no—
191#123—21no—
192C22⋊Q8—21no—
193C22⋊Q8—21no—
194C22⋊Q8—21no—
195C4×Q8C22×C1311yescharacteristic
196C4×Q8C22×C1311yescharacteristic
197C4×D4—21no—
198C4×D4C22×C1311yescharacteristic
199C4×D4C22×C1311yescharacteristic
200C4×D4C22×C1311yescharacteristic
201C4×D4C22×C1311yescharacteristic
202C4×D4C22×C1311yescharacteristic
203C2×C4⋊C4—21no—
204#107C22×C1311yescharacteristic
205#107C22×C1311yescharacteristic
206#106C22×C1311yescharacteristic
207C4⋊C8C22×C1311yescharacteristic
208C4⋊C8C22×C1311yescharacteristic
209C4⋊C8C22×C1311yescharacteristic
210#103C22×C1311yescharacteristic
211#103C22×C1311yescharacteristic
212#103C22×C1311yescharacteristic
213#102C22×C1311yescharacteristic
214#102C22×C1311yescharacteristic
215#102C22×C1311yescharacteristic
216#102C22×C1311yescharacteristic
217#102C22×C1311yescharacteristic
218#102C22×C1311yescharacteristic
219#102C22×C1311yescharacteristic
220#97C22×C1311yescharacteristic
221#97C22×C1311yescharacteristic
222C4×C8C22×C1311yescharacteristic
223C2×C13—42no—
224C2×C13—81no—
225C2×C13—81no—
226C2×C13#54811yescharacteristic
227C2×C13#57511yescharacteristic
228C2×C13#57611yescharacteristic
229C2×Q8—21no—
230C2×Q8D4×C1311yescharacteristic
231C2×Q8C23×C1311yescharacteristic
232C2×D4—21no—
233C2×D4—21no—
234C2×D4C23×C1311yescharacteristic
235C2×D4C23×C1311yescharacteristic
236C2×D4C23×C1311yescharacteristic
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—21no—
242SD16—22no—
243D8—22no—
244D8—22no—
245C2×C8C23×C1311yescharacteristic
246C2×C8C23×C1311yescharacteristic
247C2×C8C23×C1311yescharacteristic
248C2×C8C23×C1311yescharacteristic
249C4⋊C4—21no—
250C4⋊C4—21no—
251C4⋊C4—21no—
252C4⋊C4—21no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4D4×C1311yescharacteristic
256C4⋊C4D4×C1311yescharacteristic
257C4⋊C4D4×C1311yescharacteristic
258C4⋊C4C23×C1311yescharacteristic
259C4⋊C4C23×C1311yescharacteristic
260C4⋊C4C23×C1311yescharacteristic
261C4⋊C4C23×C1311yescharacteristic
262C22⋊C4—21no—
263C22⋊C4—21no—
264C22⋊C4—21no—
265C22⋊C4—21no—
266C22⋊C4—21no—
267C22⋊C4—21no—
268C22⋊C4—21no—
269C22⋊C4—21no—
270C22⋊C4—21no—
271C42—21no—
272C42C23×C1311yescharacteristic
273C42C23×C1311yescharacteristic
274C42C23×C1311yescharacteristic
275C13#337011yescharacteristic, direct product factor, Sylow
276C23—21no—
277C23—21no—
278C23—21no—
279Q8—21no—
280Q8—21no—
281Q8—41no—
282Q8—81no—
283D4—21no—
284D4—21no—
285D4—21no—
286D4—21no—
287D4—21no—
288D4—42no—
289D4—81no—
290D4C13×#4112yes—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—42no—
297C2×C4—81no—
298C2×C4—81no—
299C2×C4—81no—
300C2×C4—81no—
301C2×C4C2×D4×C1311yescharacteristic
302C2×C4C2×D4×C1311yescharacteristic
303C2×C4C2×D4×C1311yescharacteristic
304C2×C4C2×D4×C1311yescharacteristic
305C2×C4C2×D4×C1311yescharacteristic
306C2×C4C2×D4×C1311yescharacteristic
307C2×C4C24×C1311yescharacteristic
308C8—21no—
309C8—21no—
310C8—21no—
311C8—21no—
312C22—22no—
313C22—41no—
314C22—41no—
315C22—41no—
316C22—41no—
317C22—41no—
318C22—41no—
319C22—41no—
320C22—41no—
321C22C22×D4×C1311yescharacteristic
322C4—21no—
323C4—21no—
324C4—21no—
325C4—21no—
326C4—21no—
327C4—21no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—41no—
332C4—41no—
333C4C2×C13×#4111yescharacteristic
334C4C13×2−1+411yescharacteristic
335C2—42no—
336C2—81no—
337C2—81no—
338C2C13×#54811yescharacteristic
339C2C13×#57511yescharacteristic
340C2C13×#57611yescharacteristic
subgroupG/H
center, socleC22×C13C22×D4
commutator, Frattini, cosocleC2×C4C24×C13
prime radicalC13×#459C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C4×Q8×C13 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×#559C2semidirect
2. C13×#554C2semidirect
3. C13×#490C2semidirect
4. C13×#489C2semidirect
5. C13×#488C2semidirect
6. C13×#479C2semidirect
7. C13×#478C2semidirect
8. C13×#474C2semidirect
9. C13×#463C2semidirect
10. C13×#463C2semidirect
12. C13×#446C2semidirect
13. C13×#442C2semidirect
14. C13×#440C2semidirect
15. C4×C13×D8C2semidirect
105. #3370C13direct (N × H)
142. #559C2×C13semidirect
143. #554C2×C13semidirect
144. #490C2×C13semidirect
145. #489C2×C13semidirect
146. #488C2×C13semidirect
147. #479C2×C13semidirect
148. #478C2×C13semidirect
149. #474C2×C13semidirect
150. #463C2×C13semidirect
151. #463C2×C13semidirect
153. #446C2×C13semidirect
154. #442C2×C13semidirect
155. #440C2×C13semidirect
156. C4×D8C2×C13semidirect
275. C13#3370direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#5592
C13×#5542
C13×#4902
C13×#4892
C13×#4882
C13×#4792
C13×#4782
C13×#4742
C13×#4632
C13×#4592
C13×#4462
C13×#4422
C13×#4402
C4×C13×D82
#337013