Finite Group Databasebeta

← C13×#3320 #13112378

Subgroups — C13×#3320 #13112378

Order 1664.

388 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#553C211yesmaximal, characteristic
2D4×Q8×C13C211yesmaximal, characteristic, complemented
3C13×#491C211yesmaximal, characteristic, complemented
4C13×#485C211yesmaximal, characteristic, complemented
5C13×#484C211yesmaximal, characteristic, complemented
6C13×#479C211yesmaximal, characteristic, complemented
7C13×#468C211yesmaximal, characteristic, complemented
8C13×#465C211yesmaximal, characteristic, complemented
9C13×#461C211yesmaximal, characteristic, complemented
10C13×#448C211yesmaximal, characteristic, complemented
11C13×#448C211yesmaximal, characteristic, complemented
12C13×#440C211yesmaximal, characteristic, complemented
13C13×#435C211yesmaximal, characteristic, complemented
14C13×#419C211yesmaximal, characteristic, complemented
15C2×C13×#103C211yesmaximal, characteristic, complemented
16C22×Q8×C13C2211yescharacteristic
17C22×Q8×C13C2211yescharacteristic
18C2×C13×SD16C2211yescharacteristic
19C2×C13×SD16C2211yescharacteristic
20C2×C13×SD16C2211yescharacteristic
21C2×C13×M16C2211yescharacteristic
22C22×C8×C13C2211yescharacteristic
23C13×C4⋊Q8—21no—
24C13×C4⋊Q8C2211yescharacteristic
25C13×#126—21no—
26C13×#125C2211yescharacteristic
27C13×#123—21no—
28C13×C22⋊Q8—21no—
29C13×C22⋊Q8—21no—
30C13×C22⋊Q8C2211yescharacteristic
31C13×C22⋊Q8C2211yescharacteristic
32C13×#121—21no—
33C13×#121C2211yescharacteristic
34C13×#121C2211yescharacteristic
35C4×Q8×C13C2211yescharacteristic
36C4×D4×C13—21no—
37C4×D4×C13—21no—
38C4×D4×C13C2211yescharacteristic
39C4×D4×C13C2211yescharacteristic
40C13×#117C2211yescharacteristic
41C2×C13×C4⋊C4C2211yescharacteristic
42C13×#107C2211yescharacteristic
43C13×#107C2211yescharacteristic
44C13×#106C2211yescharacteristic
45C13×C4⋊C8C2211yescharacteristic
46C13×#103C2211yescharacteristic
47C13×#103C2211yescharacteristic
48C13×#103C2211yescharacteristic
49C13×#103C2211yescharacteristic
50C13×#103C2211yescharacteristic
51C13×#103C2211yescharacteristic
52C13×#103C2211yescharacteristic
53C13×#103C2211yescharacteristic
54C13×#103C2211yescharacteristic
55C13×#102C2211yescharacteristic
56C13×C22⋊C8C2211yescharacteristic
57C13×C22⋊C8C2211yescharacteristic
58C13×#97C2211yescharacteristic
59C2×Q8×C13—21no—
60C2×Q8×C13—21no—
61C2×Q8×C13—22no—
62C2×Q8×C13—22no—
63C2×Q8×C13—41no—
64C2×Q8×C13—41no—
65C2×Q8×C13C2311yescharacteristic
66C2×Q8×C13C2311yescharacteristic
67C2×Q8×C13C2311yescharacteristic
68C2×D4×C13—21no—
69C2×D4×C13—21no—
70C2×D4×C13D411yescharacteristic
71C2×D4×C13C2311yescharacteristic
72C22×C4×C13—21no—
73C22×C4×C13—21no—
74C22×C4×C13—21no—
75C22×C4×C13—21no—
76C22×C4×C13C2311yescharacteristic
77C22×C4×C13C2311yescharacteristic
78C13×SD16—22no—
79C13×SD16—41no—
80C13×SD16—41no—
81C13×M16—41no—
82C2×C8×C13—41no—
83C2×C8×C13C2311yescharacteristic
84C2×C8×C13C2311yescharacteristic
85C2×C8×C13C2311yescharacteristic
86C2×C8×C13C2311yescharacteristic
87C13×C4⋊C4—21no—
88C13×C4⋊C4—21no—
89C13×C4⋊C4—21no—
90C13×C4⋊C4—21no—
91C13×C4⋊C4—21no—
92C13×C4⋊C4—21no—
93C13×C4⋊C4—21no—
94C13×C4⋊C4—21no—
95C13×C4⋊C4D411yescharacteristic
96C13×C4⋊C4C2311yescharacteristic
97C13×C4⋊C4C2311yescharacteristic
98C13×C4⋊C4C2311yescharacteristic
99C13×C4⋊C4C2311yescharacteristic
100C13×C22⋊C4—21no—
101C13×C22⋊C4—21no—
102C13×C22⋊C4—21no—
103C13×C22⋊C4—21no—
104C13×C22⋊C4—21no—
105C13×C22⋊C4—21no—
106C13×C22⋊C4D411yescharacteristic
107C13×C22⋊C4D411yescharacteristic
108C42×C13—21no—
109C42×C13—21no—
110C42×C13C2311yescharacteristic
111#3320C1311yesmaximal, characteristic, direct product factor, Sylow
112C23×C13—21no—
113C23×C13C2×D411yescharacteristic
114C23×C13C2×D411yescharacteristic
115Q8×C13—21no—
116Q8×C13—21no—
117Q8×C13—21no—
118Q8×C13—21no—
119Q8×C13—21no—
120Q8×C13—42no—
121Q8×C13—42no—
122Q8×C13#4112yes—
123D4×C13—22no—
124D4×C13—21no—
125D4×C13—21no—
126D4×C13—42no—
127D4×C13—81no—
128C2×C4×C13—21no—
129C2×C4×C13—21no—
130C2×C4×C13—21no—
131C2×C4×C13—21no—
132C2×C4×C13—21no—
133C2×C4×C13—21no—
134C2×C4×C13—21no—
135C2×C4×C13—21no—
136C2×C4×C13—21no—
137C2×C4×C13—21no—
138C2×C4×C13—21no—
139C2×C4×C13—42no—
140C2×C4×C13—42no—
141C2×C4×C13—81no—
142C2×C4×C13—81no—
143C2×C4×C13C2×D411yescharacteristic
144C2×C4×C13C2×D411yescharacteristic
145C2×C4×C13C2×D411yescharacteristic
146C2×C4×C13C2×D411yescharacteristic
147C2×C4×C13C2411yescharacteristic
148C8×C13—21no—
149C8×C13—21no—
150C8×C13—21no—
151C8×C13—21no—
152#553C2×C1311yescharacteristic
153D4×Q8C2×C1311yescharacteristic, complemented
154#491C2×C1311yescharacteristic, complemented
155#485C2×C1311yescharacteristic, complemented
156#484C2×C1311yescharacteristic, complemented
157#479C2×C1311yescharacteristic, complemented
158#468C2×C1311yescharacteristic, complemented
159#465C2×C1311yescharacteristic, complemented
160#461C2×C1311yescharacteristic, complemented
161#448C2×C1311yescharacteristic, complemented
162#448C2×C1311yescharacteristic, complemented
163#440C2×C1311yescharacteristic, complemented
164#435C2×C1311yescharacteristic, complemented
165#419C2×C1311yescharacteristic, complemented
166C2×#103C2×C1311yescharacteristic, complemented
167C22×C13—21no—
168C22×C13—21no—
169C22×C13—21no—
170C22×C13—21no—
171C22×C13—21no—
172C22×C13—41no—
173C22×C13—41no—
174C22×C13—41no—
175C22×C13#13712yes—
176C22×C13C22×D411yescharacteristic
177C4×C13—21no—
178C4×C13—21no—
179C4×C13—22no—
180C4×C13—21no—
181C4×C13—21no—
182C4×C13—41no—
183C4×C13—41no—
184C4×C13—41no—
185C4×C13—41no—
186C4×C13—41no—
187C4×C13—41no—
188C4×C13C2×#4111yescharacteristic
189C4×C13H(5,𝔽2)11yescharacteristic
190C22×Q8C22×C1311yescharacteristic
191C22×Q8C22×C1311yescharacteristic
192C2×SD16C22×C1311yescharacteristic
193C2×SD16C22×C1311yescharacteristic
194C2×SD16C22×C1311yescharacteristic
195C2×M16C22×C1311yescharacteristic
196C22×C8C22×C1311yescharacteristic
197C4⋊Q8—21no—
198C4⋊Q8C22×C1311yescharacteristic
199#126—21no—
200#125C22×C1311yescharacteristic
201#123—21no—
202C22⋊Q8—21no—
203C22⋊Q8—21no—
204C22⋊Q8C22×C1311yescharacteristic
205C22⋊Q8C22×C1311yescharacteristic
206#121—21no—
207#121C22×C1311yescharacteristic
208#121C22×C1311yescharacteristic
209C4×Q8C22×C1311yescharacteristic
210C4×D4—21no—
211C4×D4—21no—
212C4×D4C22×C1311yescharacteristic
213C4×D4C22×C1311yescharacteristic
214#117C22×C1311yescharacteristic
215C2×C4⋊C4C22×C1311yescharacteristic
216#107C22×C1311yescharacteristic
217#107C22×C1311yescharacteristic
218#106C22×C1311yescharacteristic
219C4⋊C8C22×C1311yescharacteristic
220#103C22×C1311yescharacteristic
221#103C22×C1311yescharacteristic
222#103C22×C1311yescharacteristic
223#103C22×C1311yescharacteristic
224#103C22×C1311yescharacteristic
225#103C22×C1311yescharacteristic
226#103C22×C1311yescharacteristic
227#103C22×C1311yescharacteristic
228#103C22×C1311yescharacteristic
229#102C22×C1311yescharacteristic
230C22⋊C8C22×C1311yescharacteristic
231C22⋊C8C22×C1311yescharacteristic
232#97C22×C1311yescharacteristic
233C2×C13—22no—
234C2×C13—41no—
235C2×C13—81no—
236C2×C13#54611yescharacteristic
237C2×C13C2×#13711yescharacteristic
238C2×C13#57711yescharacteristic
239C2×Q8—21no—
240C2×Q8—21no—
241C2×Q8—22no—
242C2×Q8—22no—
243C2×Q8—41no—
244C2×Q8—41no—
245C2×Q8C23×C1311yescharacteristic
246C2×Q8C23×C1311yescharacteristic
247C2×Q8C23×C1311yescharacteristic
248C2×D4—21no—
249C2×D4—21no—
250C2×D4D4×C1311yescharacteristic
251C2×D4C23×C1311yescharacteristic
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4C23×C1311yescharacteristic
257C22×C4C23×C1311yescharacteristic
258SD16—22no—
259SD16—41no—
260SD16—41no—
261M16—41no—
262C2×C8—41no—
263C2×C8C23×C1311yescharacteristic
264C2×C8C23×C1311yescharacteristic
265C2×C8C23×C1311yescharacteristic
266C2×C8C23×C1311yescharacteristic
267C4⋊C4—21no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4—21no—
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4D4×C1311yescharacteristic
276C4⋊C4C23×C1311yescharacteristic
277C4⋊C4C23×C1311yescharacteristic
278C4⋊C4C23×C1311yescharacteristic
279C4⋊C4C23×C1311yescharacteristic
280C22⋊C4—21no—
281C22⋊C4—21no—
282C22⋊C4—21no—
283C22⋊C4—21no—
284C22⋊C4—21no—
285C22⋊C4—21no—
286C22⋊C4D4×C1311yescharacteristic
287C22⋊C4D4×C1311yescharacteristic
288C42—21no—
289C42—21no—
290C42C23×C1311yescharacteristic
291C13#332011yescharacteristic, direct product factor, Sylow
292C23—21no—
293C23C2×D4×C1311yescharacteristic
294C23C2×D4×C1311yescharacteristic
295Q8—21no—
296Q8—21no—
297Q8—21no—
298Q8—21no—
299Q8—21no—
300Q8—42no—
301Q8—42no—
302Q8C13×#4112yes—
303D4—22no—
304D4—21no—
305D4—21no—
306D4—42no—
307D4—81no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—42no—
320C2×C4—42no—
321C2×C4—81no—
322C2×C4—81no—
323C2×C4C2×D4×C1311yescharacteristic
324C2×C4C2×D4×C1311yescharacteristic
325C2×C4C2×D4×C1311yescharacteristic
326C2×C4C2×D4×C1311yescharacteristic
327C2×C4C24×C1311yescharacteristic
328C8—21no—
329C8—21no—
330C8—21no—
331C8—21no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—21no—
336C22—21no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22C13×#13712yes—
341C22C22×D4×C1311yescharacteristic
342C4—21no—
343C4—21no—
344C4—22no—
345C4—21no—
346C4—21no—
347C4—41no—
348C4—41no—
349C4—41no—
350C4—41no—
351C4—41no—
352C4—41no—
353C4C2×C13×#4111yescharacteristic
354C4C13×H(5,𝔽2)11yescharacteristic
355C2—22no—
356C2—41no—
357C2—81no—
358C2C13×#54611yescharacteristic
359C2C2×C13×#13711yescharacteristic
360C2C13×#57711yescharacteristic
subgroupG/H
center, socleC22×C13C22×D4
commutator, Frattini, cosocleC2×C4C24×C13
prime radicalC13×#553C2
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
2. D4×Q8×C13C2semidirect
3. C13×#491C2semidirect
4. C13×#485C2semidirect
5. C13×#484C2semidirect
6. C13×#479C2semidirect
7. C13×#468C2semidirect
8. C13×#465C2semidirect
9. C13×#461C2semidirect
10. C13×#448C2semidirect
11. C13×#448C2semidirect
12. C13×#440C2semidirect
13. C13×#435C2semidirect
14. C13×#419C2semidirect
15. C2×C13×#103C2semidirect
111. #3320C13direct (N × H)
153. D4×Q8C2×C13semidirect
154. #491C2×C13semidirect
155. #485C2×C13semidirect
156. #484C2×C13semidirect
157. #479C2×C13semidirect
158. #468C2×C13semidirect
159. #465C2×C13semidirect
160. #461C2×C13semidirect
161. #448C2×C13semidirect
162. #448C2×C13semidirect
163. #440C2×C13semidirect
164. #435C2×C13semidirect
165. #419C2×C13semidirect
166. C2×#103C2×C13semidirect
291. C13#3320direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#5532
D4×Q8×C132
C13×#4912
C13×#4852
C13×#4842
C13×#4792
C13×#4682
C13×#4652
C13×#4612
C13×#4482
C13×#4402
C13×#4352
C13×#4192
C2×C13×#1032
#332013