Finite Group Databasebeta

← C13×#9376 #15695715

Subgroups — C13×#9376 #15695715

Order 3328.

430 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3218C211yesmaximal, characteristic
2C13×#2992C211yesmaximal, characteristic
3C13×#1987C211yesmaximal, characteristic, complemented
4C13×#1556C211yesmaximal, characteristic, complemented
5C13×#1509C211yesmaximal, characteristic
6C13×#1290C211yesmaximal, characteristic, complemented
7C13×#1285C211yesmaximal, characteristic, complemented
8C2×C13×C4⋊Q8C2211yescharacteristic
9C13×#529C2211yescharacteristic
10C13×#497C412yescomplemented
11C13×#491C412yescomplemented
12C13×#462—21no—
13C13×#461—21no—
14C13×#451—21no—
15C13×#448—21no—
16C13×#446—21no—
17C13×#435—21no—
18C13×#435—21no—
19C8×D4×C13—21no—
20C13×#433—21no—
21C13×#432C2211yescharacteristic
22C13×#432C2211yescharacteristic
23C13×#432C2211yescharacteristic
24C13×#424—21no—
25C2×C13×C4⋊C8C2211yescharacteristic
26C4×C13×C4⋊C4C2211yescharacteristic
27C13×#340—21no—
28C13×#340—21no—
29C13×#332—21no—
30C13×#332—21no—
31C13×#328—21no—
32C13×#327—21no—
33C22×Q8×C13—21no—
34C2×C13×Q16—22no—
35C2×C13×SD16—22no—
36C2×C13×M16—21no—
37C22×C8×C13—21no—
38C22×C8×C13D411yescharacteristic
39C22×C8×C13D411yescharacteristic
40C13×C4⋊Q8—21no—
41C13×C4⋊Q8—21no—
42C13×C4⋊Q8—21no—
43C13×C4⋊Q8C2×C412yes—
44C13×#126—21no—
45C13×#125C2×C411yescharacteristic
46C13×#124C2×C411yescharacteristic
47C13×#123—21no—
48C13×C22⋊Q8D411yescharacteristic
49C13×#121D411yescharacteristic
50C4×Q8×C13D411yescharacteristic
51C4×D4×C13—21no—
52C4×D4×C13D411yescharacteristic
53C13×#117—21no—
54C2×C13×C4⋊C4—21no—
55C2×C13×C4⋊C4—21no—
56C2×C13×C4⋊C4—21no—
57C2×C42×C13—21no—
58C2×C42×C13C2311yescharacteristic
59C13×C4⋊C8—21no—
60C13×C4⋊C8—21no—
61C13×C4⋊C8—21no—
62C13×C4⋊C8—21no—
63C13×C4⋊C8—21no—
64C13×C4⋊C8—21no—
65C13×C4⋊C8D411yescharacteristic
66C13×C4⋊C8D411yescharacteristic
67C13×#103—22no—
68C13×#103—22no—
69C13×C22⋊C8—21no—
70C13×C22⋊C8—21no—
71C13×C22⋊C8—21no—
72C13×C22⋊C8—21no—
73C13×C22⋊C8—21no—
74C13×#97—21no—
75C13×#97—21no—
76C13×#97—21no—
77C13×#97C2×C412yes—
78C4×C8×C13—21no—
79C13×#95—21no—
80#9376C1311yesmaximal, characteristic, direct product factor, Sylow
81C2×Q8×C13—22no—
82C2×Q8×C13—41no—
83C2×Q8×C13—82no—
84C2×Q8×C13C22⋊C411yescharacteristic
85C2×D4×C13—21no—
86C2×D4×C13C22⋊C411yescharacteristic
87C22×C4×C13—21no—
88C22×C4×C13—41no—
89C22×C4×C13—41no—
90C22×C4×C13C2×D411yescharacteristic
91C22×C4×C13C2×D411yescharacteristic
92C22×C4×C13#4111yescharacteristic
93C13×Q16—82no—
94C13×SD16—82no—
95C13×M16—81no—
96C2×C8×C13—22no—
97C2×C8×C13—21no—
98C2×C8×C13—21no—
99C2×C8×C13—21no—
100C2×C8×C13—21no—
101C2×C8×C13—41no—
102C2×C8×C13—41no—
103C2×C8×C13—41no—
104C2×C8×C13—81no—
105C13×C4⋊C4—21no—
106C13×C4⋊C4—21no—
107C13×C4⋊C4—21no—
108C13×C4⋊C4—21no—
109C13×C4⋊C4—22no—
110C13×C4⋊C4—22no—
111C13×C4⋊C4—22no—
112C13×C4⋊C4—41no—
113C13×C4⋊C4—41no—
114C13×C4⋊C4—41no—
115C13×C4⋊C4C22⋊C411yescharacteristic
116C13×C4⋊C4C22⋊C411yescharacteristic
117C13×C22⋊C4—21no—
118C13×C22⋊C4—21no—
119C13×C22⋊C4—21no—
120C13×C22⋊C4—21no—
121C13×C22⋊C4—21no—
122C42×C13—21no—
123C42×C13—81no—
124C42×C13C22×C411yescharacteristic
125C42×C13C2×D411yescharacteristic
126C42×C13C2×D411yescharacteristic
127C42×C13#4111yescharacteristic
128#3218C2×C1311yescharacteristic
129#2992C2×C1311yescharacteristic
130#1987C2×C1311yescharacteristic, complemented
131#1556C2×C1311yescharacteristic, complemented
132#1509C2×C1311yescharacteristic
133#1290C2×C1311yescharacteristic, complemented
134#1285C2×C1311yescharacteristic, complemented
135C23×C13—21no—
136C23×C13#12111yescharacteristic
137Q8×C13—41no—
138Q8×C13—42no—
139Q8×C13—42no—
140Q8×C13—82no—
141D4×C13—41no—
142D4×C13—41no—
143D4×C13—41no—
144C2×C4×C13—21no—
145C2×C4×C13—21no—
146C2×C4×C13—21no—
147C2×C4×C13—21no—
148C2×C4×C13—21no—
149C2×C4×C13—21no—
150C2×C4×C13—21no—
151C2×C4×C13—41no—
152C2×C4×C13—41no—
153C2×C4×C13—41no—
154C2×C4×C13—42no—
155C2×C4×C13—42no—
156C2×C4×C13—81no—
157C2×C4×C13—82no—
158C2×C4×C13—81no—
159C2×C4×C13C2×C22⋊C411yescharacteristic
160C2×C4×C13C4×D411yescharacteristic
161C2×C4×C13C4×D411yescharacteristic
162C2×C4×C13#12011yescharacteristic
163C2×C4×C13#12111yescharacteristic
164C2×C4×C13#12311yescharacteristic
165C8×C13—42no—
166C8×C13—41no—
167C8×C13—41no—
168C8×C13—41no—
169C8×C13—41no—
170C8×C13—81no—
171C2×C4⋊Q8C22×C1311yescharacteristic
172#529C22×C1311yescharacteristic
173#497C4×C1312yescomplemented
174#491C4×C1312yescomplemented
175#462—21no—
176#461—21no—
177#451—21no—
178#448—21no—
179#446—21no—
180#435—21no—
181#435—21no—
182C8×D4—21no—
183#433—21no—
184#432C22×C1311yescharacteristic
185#432C22×C1311yescharacteristic
186#432C22×C1311yescharacteristic
187#424—21no—
188C2×C4⋊C8C22×C1311yescharacteristic
189C4×C4⋊C4C22×C1311yescharacteristic
190#340—21no—
191#340—21no—
192#332—21no—
193#332—21no—
194#328—21no—
195#327—21no—
196C22×C13—21no—
197C22×C13—21no—
198C22×C13—41no—
199C22×C13—41no—
200C22×C13—41no—
201C22×C13#38611yescharacteristic
202C22×C13#47111yescharacteristic
203C22×C13#47311yescharacteristic
204C4×C13—21no—
205C4×C13—21no—
206C4×C13—21no—
207C4×C13—21no—
208C4×C13—21no—
209C4×C13—41no—
210C4×C13—41no—
211C4×C13—41no—
212C4×C13—82no—
213C4×C13—82no—
214C4×C13#45511yescharacteristic
215C4×C13#45611yescharacteristic
216C22×Q8—21no—
217C2×Q16—22no—
218C2×SD16—22no—
219C2×M16—21no—
220C22×C8—21no—
221C22×C8D4×C1311yescharacteristic
222C22×C8D4×C1311yescharacteristic
223C4⋊Q8—21no—
224C4⋊Q8—21no—
225C4⋊Q8—21no—
226C4⋊Q8C2×C4×C1312yes—
227#126—21no—
228#125C2×C4×C1311yescharacteristic
229#124C2×C4×C1311yescharacteristic
230#123—21no—
231C22⋊Q8D4×C1311yescharacteristic
232#121D4×C1311yescharacteristic
233C4×Q8D4×C1311yescharacteristic
234C4×D4—21no—
235C4×D4D4×C1311yescharacteristic
236#117—21no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—21no—
240C2×C42—21no—
241C2×C42C23×C1311yescharacteristic
242C4⋊C8—21no—
243C4⋊C8—21no—
244C4⋊C8—21no—
245C4⋊C8—21no—
246C4⋊C8—21no—
247C4⋊C8—21no—
248C4⋊C8D4×C1311yescharacteristic
249C4⋊C8D4×C1311yescharacteristic
250#103—22no—
251#103—22no—
252C22⋊C8—21no—
253C22⋊C8—21no—
254C22⋊C8—21no—
255C22⋊C8—21no—
256C22⋊C8—21no—
257#97—21no—
258#97—21no—
259#97—21no—
260#97C2×C4×C1312yes—
261C4×C8—21no—
262#95—21no—
263C2×C13—21no—
264C2×C13—21no—
265C2×C13—81no—
266C2×C13#188211yescharacteristic
267C2×C13#190811yescharacteristic
268C2×C13#191011yescharacteristic
269C2×Q8—22no—
270C2×Q8—41no—
271C2×Q8—82no—
272C2×Q8C13×C22⋊C411yescharacteristic
273C2×D4—21no—
274C2×D4C13×C22⋊C411yescharacteristic
275C22×C4—21no—
276C22×C4—41no—
277C22×C4—41no—
278C22×C4C2×D4×C1311yescharacteristic
279C22×C4C2×D4×C1311yescharacteristic
280C22×C4C13×#4111yescharacteristic
281Q16—82no—
282SD16—82no—
283M16—81no—
284C2×C8—22no—
285C2×C8—21no—
286C2×C8—21no—
287C2×C8—21no—
288C2×C8—21no—
289C2×C8—41no—
290C2×C8—41no—
291C2×C8—41no—
292C2×C8—81no—
293C4⋊C4—21no—
294C4⋊C4—21no—
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—22no—
298C4⋊C4—22no—
299C4⋊C4—22no—
300C4⋊C4—41no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C4⋊C4C13×C22⋊C411yescharacteristic
304C4⋊C4C13×C22⋊C411yescharacteristic
305C22⋊C4—21no—
306C22⋊C4—21no—
307C22⋊C4—21no—
308C22⋊C4—21no—
309C22⋊C4—21no—
310C42—21no—
311C42—81no—
312C42C22×C4×C1311yescharacteristic
313C42C2×D4×C1311yescharacteristic
314C42C2×D4×C1311yescharacteristic
315C42C13×#4111yescharacteristic
316C13#937611yescharacteristic, direct product factor, Sylow
317C23—21no—
318C23C13×#12111yescharacteristic
319Q8—41no—
320Q8—42no—
321Q8—42no—
322Q8—82no—
323D4—41no—
324D4—41no—
325D4—41no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—42no—
337C2×C4—42no—
338C2×C4—81no—
339C2×C4—82no—
340C2×C4—81no—
341C2×C4C2×C13×C22⋊C411yescharacteristic
342C2×C4C4×D4×C1311yescharacteristic
343C2×C4C4×D4×C1311yescharacteristic
344C2×C4C13×#12011yescharacteristic
345C2×C4C13×#12111yescharacteristic
346C2×C4C13×#12311yescharacteristic
347C8—42no—
348C8—41no—
349C8—41no—
350C8—41no—
351C8—41no—
352C8—81no—
353C22—21no—
354C22—21no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22C13×#38611yescharacteristic
359C22C13×#47111yescharacteristic
360C22C13×#47311yescharacteristic
361C4—21no—
362C4—21no—
363C4—21no—
364C4—21no—
365C4—21no—
366C4—41no—
367C4—41no—
368C4—41no—
369C4—82no—
370C4—82no—
371C4C13×#45511yescharacteristic
372C4C13×#45611yescharacteristic
373C2—21no—
374C2—21no—
375C2—81no—
376C2C13×#188211yescharacteristic
377C2C13×#190811yescharacteristic
378C2C13×#191011yescharacteristic
subgroupG/H
center, socleC22×C13#386
commutatorC42C22×C4×C13
Frattini, cosocleC2×C42C23×C13
prime radicalC13×#121D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G

Complements

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

NH ≅ G/Ntype
3. C13×#1987C2semidirect
4. C13×#1556C2semidirect
6. C13×#1290C2semidirect
7. C13×#1285C2semidirect
10. C13×#497C4semidirect
11. C13×#491C4semidirect
80. #9376C13direct (N × H)
130. #1987C2×C13semidirect
131. #1556C2×C13semidirect
133. #1290C2×C13semidirect
134. #1285C2×C13semidirect
173. #497C4×C13semidirect
174. #491C4×C13semidirect
316. C13#9376direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#32182
C13×#29922
C13×#19872
C13×#15562
C13×#15092
C13×#12902
C13×#12852
#937613