Finite Group Databasebeta

← C13×#9383 #15695722

Subgroups — C13×#9383 #15695722

Order 3328.

570 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#2972C211yesmaximal, characteristic
2C13×#2564C211yesmaximal, characteristic
3C13×#1799C211yesmaximal, characteristic
4C13×#1520C212yesmaximal, complemented
5C13×#1294C212yesmaximal, complemented
6C2×C13×C22⋊Q8C2211yescharacteristic
7C2×C4×D4×C13C2211yescharacteristic
8C8×D4×C13—24no—
9C13×#431—21no—
10C2×C13×#99—21no—
11C2×C13×C22⋊C8—21no—
12C2×C13×C22⋊C8C2212yes—
13C13×#400C411yescharacteristic, complemented
14C13×#399C411yescharacteristic, complemented
15C13×#395C411yescharacteristic, complemented
16C13×#393C411yescharacteristic, complemented
17C13×#387—21no—
18C13×#386—21no—
19C13×#385—21no—
20C13×#380—21no—
21C13×#380C2212yes—
22C2×C13×#95C2211yescharacteristic
23C13×#342—21no—
24C13×#328—24no—
25C22×Q8×C13C2×C411yescharacteristic
26C22×D4×C13D411yescharacteristic
27C23×C4×C13—21no—
28C23×C4×C13D411yescharacteristic
29C23×C4×C13C2311yescharacteristic
30C22×C8×C13—22no—
31C22×C8×C13—22no—
32C13×C22⋊Q8—22no—
33C13×C22⋊Q8—22no—
34C4×D4×C13—22no—
35C4×D4×C13—22no—
36C2×C13×C4⋊C4—21no—
37C2×C13×C4⋊C4—21no—
38C2×C13×C4⋊C4—21no—
39C2×C13×C4⋊C4—22no—
40C2×C13×C4⋊C4C2×C411yescharacteristic
41C2×C13×C4⋊C4C2×C411yescharacteristic
42C2×C13×C22⋊C4—21no—
43C2×C13×C22⋊C4—21no—
44C2×C13×C22⋊C4—22no—
45C2×C13×C22⋊C4—21no—
46C2×C13×C22⋊C4C2×C411yescharacteristic
47C2×C13×C22⋊C4D411yescharacteristic
48C2×C42×C13D411yescharacteristic
49C13×C4⋊C8—22no—
50C13×#99—42no—
51C13×C22⋊C8—22no—
52C13×C22⋊C8—22no—
53C13×C22⋊C8D414yes—
54C4×C8×C13—22no—
55C13×#95—21no—
56C13×#95—21no—
57C13×#95—21no—
58C13×#95—21no—
59C13×#95—21no—
60C13×#95—22no—
61C13×#95C2×C411yescharacteristic
62C13×#95C2×C411yescharacteristic
63#9383C1311yesmaximal, characteristic, direct product factor, Sylow
64C24×C13C22⋊C411yescharacteristic
65C24×C13C2×D411yescharacteristic
66C2×Q8×C13—22no—
67C2×Q8×C13—81no—
68C2×D4×C13—22no—
69C2×D4×C13—22no—
70C2×D4×C13SD1612yes—
71C2×D4×C13Q1612yes—
72C22×C4×C13—21no—
73C22×C4×C13—21no—
74C22×C4×C13—21no—
75C22×C4×C13—21no—
76C22×C4×C13—21no—
77C22×C4×C13—21no—
78C22×C4×C13—42no—
79C22×C4×C13—42no—
80C22×C4×C13—42no—
81C22×C4×C13—81no—
82C22×C4×C13—81no—
83C22×C4×C13—81no—
84C22×C4×C13C22⋊C411yescharacteristic
85C22×C4×C13C22⋊C411yescharacteristic
86C22×C4×C13C22⋊C411yescharacteristic
87C22×C4×C13C22×C411yescharacteristic
88C22×C4×C13C2×D412yes—
89C22×C4×C13C2×D411yescharacteristic
90C22×C4×C13#4112yes—
91C2×C8×C13—24no—
92C2×C8×C13—82no—
93C2×C8×C13—82no—
94C13×C4⋊C4—22no—
95C13×C4⋊C4—22no—
96C13×C4⋊C4—42no—
97C13×C4⋊C4—41no—
98C13×C4⋊C4—41no—
99C13×C4⋊C4—81no—
100C13×C4⋊C4—82no—
101C13×C22⋊C4—22no—
102C13×C22⋊C4—22no—
103C13×C22⋊C4—42no—
104C13×C22⋊C4—42no—
105C13×C22⋊C4—42no—
106C13×C22⋊C4—42no—
107C13×C22⋊C4—81no—
108C42×C13—21no—
109C42×C13—21no—
110#2972C2×C1311yescharacteristic
111#2564C2×C1311yescharacteristic
112#1799C2×C1311yescharacteristic
113#1520C2×C1312yescomplemented
114#1294C2×C1312yescomplemented
115C23×C13—21no—
116C23×C13—21no—
117C23×C13—41no—
118C23×C13—41no—
119C23×C13—41no—
120C23×C13—41no—
121C23×C13#10312yes—
122C23×C13C2×C22⋊C411yescharacteristic
123C23×C13#12112yes—
124C23×C13C2×SD1611yescharacteristic
125C23×C13C2×Q1611yescharacteristic
126C23×C13#13512yes—
127Q8×C13—82no—
128D4×C13—24no—
129D4×C13—24no—
130C2×C4×C13—21no—
131C2×C4×C13—21no—
132C2×C4×C13—22no—
133C2×C4×C13—21no—
134C2×C4×C13—21no—
135C2×C4×C13—42no—
136C2×C4×C13—42no—
137C2×C4×C13—41no—
138C2×C4×C13—41no—
139C2×C4×C13—42no—
140C2×C4×C13—41no—
141C2×C4×C13—41no—
142C2×C4×C13—41no—
143C2×C4×C13—41no—
144C2×C4×C13—41no—
145C2×C4×C13—41no—
146C2×C4×C13—41no—
147C2×C4×C13—41no—
148C2×C4×C13—41no—
149C2×C4×C13—41no—
150C2×C4×C13—41no—
151C2×C4×C13—41no—
152C2×C4×C13—41no—
153C2×C4×C13—81no—
154C2×C4×C13—84no—
155C2×C4×C13—82no—
156C2×C4×C13—82no—
157C2×C4×C13—82no—
158C2×C4×C13#10312yes—
159C2×C4×C13C4×D412yes—
160C2×C4×C13#12011yescharacteristic
161C2×C4×C13#12311yescharacteristic
162C8×C13—44no—
163C2×C22⋊Q8C22×C1311yescharacteristic
164C2×C4×D4C22×C1311yescharacteristic
165C8×D4—24no—
166#431—21no—
167C2×#99—21no—
168C2×C22⋊C8—21no—
169C2×C22⋊C8C22×C1312yes—
170#400C4×C1311yescharacteristic, complemented
171#399C4×C1311yescharacteristic, complemented
172#395C4×C1311yescharacteristic, complemented
173#393C4×C1311yescharacteristic, complemented
174#387—21no—
175#386—21no—
176#385—21no—
177#380—21no—
178#380C22×C1312yes—
179C2×#95C22×C1311yescharacteristic
180#342—21no—
181#328—24no—
182C22×C13—21no—
183C22×C13—22no—
184C22×C13—21no—
185C22×C13—22no—
186C22×C13—22no—
187C22×C13—42no—
188C22×C13—41no—
189C22×C13—41no—
190C22×C13—42no—
191C22×C13—41no—
192C22×C13—41no—
193C22×C13—81no—
194C22×C13#38611yescharacteristic
195C22×C13C2×#10311yescharacteristic
196C22×C13#41611yescharacteristic
197C22×C13#46512yes—
198C22×C13#46712yes—
199C4×C13—22no—
200C4×C13—21no—
201C4×C13—21no—
202C4×C13—22no—
203C4×C13—42no—
204C4×C13—41no—
205C4×C13—41no—
206C4×C13—81no—
207C4×C13—81no—
208C4×C13—81no—
209C4×C13—162no—
210C22×Q8C2×C4×C1311yescharacteristic
211C22×D4D4×C1311yescharacteristic
212C23×C4—21no—
213C23×C4D4×C1311yescharacteristic
214C23×C4C23×C1311yescharacteristic
215C22×C8—22no—
216C22×C8—22no—
217C22⋊Q8—22no—
218C22⋊Q8—22no—
219C4×D4—22no—
220C4×D4—22no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—22no—
225C2×C4⋊C4C2×C4×C1311yescharacteristic
226C2×C4⋊C4C2×C4×C1311yescharacteristic
227C2×C22⋊C4—21no—
228C2×C22⋊C4—21no—
229C2×C22⋊C4—22no—
230C2×C22⋊C4—21no—
231C2×C22⋊C4C2×C4×C1311yescharacteristic
232C2×C22⋊C4D4×C1311yescharacteristic
233C2×C42D4×C1311yescharacteristic
234C4⋊C8—22no—
235#99—42no—
236C22⋊C8—22no—
237C22⋊C8—22no—
238C22⋊C8D4×C1314yes—
239C4×C8—22no—
240#95—21no—
241#95—21no—
242#95—21no—
243#95—21no—
244#95—21no—
245#95—22no—
246#95C2×C4×C1311yescharacteristic
247#95C2×C4×C1311yescharacteristic
248C2×C13—21no—
249C2×C13—22no—
250C2×C13—21no—
251C2×C13—22no—
252C2×C13—42no—
253C2×C13#188411yescharacteristic
254C2×C13#189211yescharacteristic
255C2×C13#191311yescharacteristic
256C24C13×C22⋊C411yescharacteristic
257C24C2×D4×C1311yescharacteristic
258C2×Q8—22no—
259C2×Q8—81no—
260C2×D4—22no—
261C2×D4—22no—
262C2×D4C13×SD1612yes—
263C2×D4C13×Q1612yes—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—42no—
271C22×C4—42no—
272C22×C4—42no—
273C22×C4—81no—
274C22×C4—81no—
275C22×C4—81no—
276C22×C4C13×C22⋊C411yescharacteristic
277C22×C4C13×C22⋊C411yescharacteristic
278C22×C4C13×C22⋊C411yescharacteristic
279C22×C4C22×C4×C1311yescharacteristic
280C22×C4C2×D4×C1312yes—
281C22×C4C2×D4×C1311yescharacteristic
282C22×C4C13×#4112yes—
283C2×C8—24no—
284C2×C8—82no—
285C2×C8—82no—
286C4⋊C4—22no—
287C4⋊C4—22no—
288C4⋊C4—42no—
289C4⋊C4—41no—
290C4⋊C4—41no—
291C4⋊C4—81no—
292C4⋊C4—82no—
293C22⋊C4—22no—
294C22⋊C4—22no—
295C22⋊C4—42no—
296C22⋊C4—42no—
297C22⋊C4—42no—
298C22⋊C4—42no—
299C22⋊C4—81no—
300C42—21no—
301C42—21no—
302C13#938311yescharacteristic, direct product factor, Sylow
303C23—21no—
304C23—21no—
305C23—41no—
306C23—41no—
307C23—41no—
308C23—41no—
309C23C13×#10312yes—
310C23C2×C13×C22⋊C411yescharacteristic
311C23C13×#12112yes—
312C23C2×C13×SD1611yescharacteristic
313C23C2×C13×Q1611yescharacteristic
314C23C13×#13512yes—
315Q8—82no—
316D4—24no—
317D4—24no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—22no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—42no—
324C2×C4—42no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—42no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—81no—
342C2×C4—84no—
343C2×C4—82no—
344C2×C4—82no—
345C2×C4—82no—
346C2×C4C13×#10312yes—
347C2×C4C4×D4×C1312yes—
348C2×C4C13×#12011yescharacteristic
349C2×C4C13×#12311yescharacteristic
350C8—44no—
351C22—21no—
352C22—22no—
353C22—21no—
354C22—22no—
355C22—22no—
356C22—42no—
357C22—41no—
358C22—41no—
359C22—42no—
360C22—41no—
361C22—41no—
362C22—81no—
363C22C13×#38611yescharacteristic
364C22C2×C13×#10311yescharacteristic
365C22C13×#41611yescharacteristic
366C22C13×#46512yes—
367C22C13×#46712yes—
368C4—22no—
369C4—21no—
370C4—21no—
371C4—22no—
372C4—42no—
373C4—41no—
374C4—41no—
375C4—81no—
376C4—81no—
377C4—81no—
378C4—162no—
379C2—21no—
380C2—22no—
381C2—21no—
382C2—22no—
383C2—42no—
384C2C13×#188411yescharacteristic
385C2C13×#189211yescharacteristic
386C2C13×#191311yescharacteristic
subgroupG/H
center, socleC22×C13#386
commutatorC22×C4C22×C4×C13
Frattini, cosocleC23×C4C23×C13
prime radicalC22×D4×C13D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ C23×C4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
4. C13×#1520C2semidirect
5. C13×#1294C2semidirect
13. C13×#400C4semidirect
14. C13×#399C4semidirect
15. C13×#395C4semidirect
16. C13×#393C4semidirect
63. #9383C13direct (N × H)
113. #1520C2×C13semidirect
114. #1294C2×C13semidirect
170. #400C4×C13semidirect
171. #399C4×C13semidirect
172. #395C4×C13semidirect
173. #393C4×C13semidirect
302. C13#9383direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#29722
C13×#25642
C13×#17992
C13×#15202
C13×#12942
#938313