Finite Group Databasebeta

← C13×#10206 #15696545

Subgroups — C13×#10206 #15696545

Order 3328.

560 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3246C211yesmaximal, characteristic
2C13×#3229C211yesmaximal, characteristic, complemented
3C13×#3152C211yesmaximal, characteristic
4C13×#1988C211yesmaximal, characteristic, complemented
5C13×#1986C211yesmaximal, characteristic, complemented
6C13×#1502C211yesmaximal, characteristic
7C13×#1283C211yesmaximal, characteristic, complemented
8C2×C13×#137—22no—
9C13×#533C2211yescharacteristic
10C13×#532C2211yescharacteristic
11C2×C13×C4⋊Q8C2211yescharacteristic
12C13×#498—21no—
13C13×#497—22no—
14C13×#494—21no—
15C13×#492—21no—
16C13×#487—21no—
17C13×#483—22no—
18C13×#476—21no—
19C13×#475—22no—
20C13×#475—21no—
21C13×#465—22no—
22C13×#461—21no—
23C13×#460—21no—
24C13×#431C2211yescharacteristic
25C2×C13×C4⋊C8C2211yescharacteristic
26C4×C13×M16C2211yescharacteristic
27C4×C13×C4⋊C4C2211yescharacteristic
28C13×#340—22no—
29C13×#339—22no—
30C13×#327—22no—
31C2×C13×#41—21no—
32C22×Q8×C13—21no—
33C13×#137—44no—
34C13×#137—44no—
35C2×C13×Q16—24no—
36C2×C13×SD16—24no—
37C2×C13×SD16—22no—
38C2×C13×M16D412yes—
39C22×C8×C13D412yes—
40C13×C4⋊Q8—21no—
41C13×C4⋊Q8—21no—
42C13×C4⋊Q8—21no—
43C13×C4⋊Q8D411yescharacteristic
44C13×C4⋊Q8D411yescharacteristic
45C13×C4⋊Q8D412yes—
46C13×C4⋊Q8D411yescharacteristic
47C13×#127D411yescharacteristic
48C13×#125—21no—
49C13×#124—21no—
50C13×C22⋊Q8—21no—
51C13×C22⋊Q8—21no—
52C13×#121—21no—
53C13×#121—21no—
54C4×Q8×C13—21no—
55C4×Q8×C13—21no—
56C4×D4×C13—21no—
57C4×D4×C13—21no—
58C13×#117—21no—
59C2×C13×C4⋊C4—21no—
60C2×C13×C4⋊C4—21no—
61C2×C13×C4⋊C4—21no—
62C2×C42×C13—21no—
63C2×C42×C13C2311yescharacteristic
64C13×#106—22no—
65C13×#106—24no—
66C13×C4⋊C8—21no—
67C13×C4⋊C8—21no—
68C13×C4⋊C8—21no—
69C13×#103—22no—
70C13×#103—24no—
71C13×#102—22no—
72C13×C22⋊C8D412yes—
73C13×#97—21no—
74C4×C8×C13—21no—
75C4×C8×C13—21no—
76C13×#95—21no—
77#10206C1311yesmaximal, characteristic, direct product factor, Sylow
78C13×#41—42no—
79C13×#41—42no—
80C2×Q8×C13—21no—
81C2×Q8×C13—21no—
82C2×Q8×C13—21no—
83C2×Q8×C13—22no—
84C2×Q8×C13—41no—
85C2×Q8×C13—42no—
86C2×Q8×C13—42no—
87C2×D4×C13—21no—
88C2×D4×C13—21no—
89C2×D4×C13—21no—
90C2×D4×C13—41no—
91C22×C4×C13—41no—
92C22×C4×C13—41no—
93C22×C4×C13—41no—
94C22×C4×C13C2×D411yescharacteristic
95C22×C4×C13C2×D411yescharacteristic
96C22×C4×C13C2×D411yescharacteristic
97C13×Q16—48no—
98C13×SD16—48no—
99C13×SD16—82no—
100C13×M16—22no—
101C13×M16SD1614yescomplemented
102C2×C8×C13—22no—
103C2×C8×C13—22no—
104C2×C8×C13—22no—
105C2×C8×C13—42no—
106C13×C4⋊C4—22no—
107C13×C4⋊C4—21no—
108C13×C4⋊C4—22no—
109C13×C4⋊C4—21no—
110C13×C4⋊C4—21no—
111C13×C4⋊C4—22no—
112C13×C4⋊C4—21no—
113C13×C4⋊C4—21no—
114C13×C4⋊C4—21no—
115C13×C4⋊C4—41no—
116C13×C4⋊C4—41no—
117C13×C4⋊C4—41no—
118C13×C4⋊C4—41no—
119C13×C4⋊C4—41no—
120C13×C22⋊C4—41no—
121C13×C22⋊C4—41no—
122C13×C22⋊C4—41no—
123C42×C13—41no—
124C42×C13—42no—
125C42×C13C2×D411yescharacteristic
126C42×C13C2×D411yescharacteristic
127C42×C13C2×D411yescharacteristic
128C42×C13#4111yescharacteristic
129#3246C2×C1311yescharacteristic
130#3229C2×C1311yescharacteristic, complemented
131#3152C2×C1311yescharacteristic
132#1988C2×C1311yescharacteristic, complemented
133#1986C2×C1311yescharacteristic, complemented
134#1502C2×C1311yescharacteristic
135#1283C2×C1311yescharacteristic, complemented
136C23×C13—41no—
137C23×C13#12711yescharacteristic
138Q8×C13—42no—
139Q8×C13—44no—
140Q8×C13—42no—
141Q8×C13—41no—
142Q8×C13—41no—
143Q8×C13—82no—
144D4×C13—42no—
145D4×C13—41no—
146D4×C13—41no—
147D4×C13—81no—
148D4×C13—81no—
149D4×C13—81no—
150C2×C4×C13—21no—
151C2×C4×C13—21no—
152C2×C4×C13—41no—
153C2×C4×C13—42no—
154C2×C4×C13—41no—
155C2×C4×C13—41no—
156C2×C4×C13—41no—
157C2×C4×C13—42no—
158C2×C4×C13—81no—
159C2×C4×C13—81no—
160C2×C4×C13—81no—
161C2×C4×C13—81no—
162C2×C4×C13—82no—
163C2×C4×C13#12011yescharacteristic
164C2×C4×C13#12011yescharacteristic
165C2×C4×C13#12011yescharacteristic
166C2×C4×C13#12111yescharacteristic
167C2×C4×C13#12111yescharacteristic
168C2×C4×C13#12111yescharacteristic
169C2×C4×C13C2×SD1612yes—
170C2×C4×C13AGL(1,ℤ/8)12yes—
171C8×C13—24no—
172C8×C13—42no—
173C8×C13—42no—
174C2×#137—22no—
175#533C22×C1311yescharacteristic
176#532C22×C1311yescharacteristic
177C2×C4⋊Q8C22×C1311yescharacteristic
178#498—21no—
179#497—22no—
180#494—21no—
181#492—21no—
182#487—21no—
183#483—22no—
184#476—21no—
185#475—22no—
186#475—21no—
187#465—22no—
188#461—21no—
189#460—21no—
190#431C22×C1311yescharacteristic
191C2×C4⋊C8C22×C1311yescharacteristic
192C4×M16C22×C1311yescharacteristic
193C4×C4⋊C4C22×C1311yescharacteristic
194#340—22no—
195#339—22no—
196#327—22no—
197C22×C13—21no—
198C22×C13—21no—
199C22×C13—81no—
200C22×C13—81no—
201C22×C13—81no—
202C22×C13#39211yescharacteristic
203C22×C13#49211yescharacteristic
204C22×C13#49611yescharacteristic
205C4×C13—21no—
206C4×C13—21no—
207C4×C13—21no—
208C4×C13—82no—
209C4×C13—81no—
210C4×C13—81no—
211C4×C13—81no—
212C4×C13—82no—
213C4×C13#45012yes—
214C4×C13#45511yescharacteristic
215C4×C13#45611yescharacteristic
216C4×C13#46012yes—
217C2×#41—21no—
218C22×Q8—21no—
219#137—44no—
220#137—44no—
221C2×Q16—24no—
222C2×SD16—24no—
223C2×SD16—22no—
224C2×M16D4×C1312yes—
225C22×C8D4×C1312yes—
226C4⋊Q8—21no—
227C4⋊Q8—21no—
228C4⋊Q8—21no—
229C4⋊Q8D4×C1312yes—
230C4⋊Q8D4×C1311yescharacteristic
231C4⋊Q8D4×C1311yescharacteristic
232C4⋊Q8D4×C1311yescharacteristic
233#127D4×C1311yescharacteristic
234#125—21no—
235#124—21no—
236C22⋊Q8—21no—
237C22⋊Q8—21no—
238#121—21no—
239#121—21no—
240C4×Q8—21no—
241C4×Q8—21no—
242C4×D4—21no—
243C4×D4—21no—
244#117—21no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—21no—
248C2×C42—21no—
249C2×C42C23×C1311yescharacteristic
250#106—22no—
251#106—24no—
252C4⋊C8—21no—
253C4⋊C8—21no—
254C4⋊C8—21no—
255#103—22no—
256#103—24no—
257#102—22no—
258C22⋊C8D4×C1312yes—
259#97—21no—
260C4×C8—21no—
261C4×C8—21no—
262#95—21no—
263C2×C13—21no—
264C2×C13—21no—
265C2×C13—161no—
266C2×C13#200711yescharacteristic
267C2×C13#200911yescharacteristic
268C2×C13#201411yescharacteristic
269#41—42no—
270#41—42no—
271C2×Q8—21no—
272C2×Q8—21no—
273C2×Q8—21no—
274C2×Q8—22no—
275C2×Q8—41no—
276C2×Q8—42no—
277C2×Q8—42no—
278C2×D4—21no—
279C2×D4—21no—
280C2×D4—21no—
281C2×D4—41no—
282C22×C4—41no—
283C22×C4—41no—
284C22×C4—41no—
285C22×C4C2×D4×C1311yescharacteristic
286C22×C4C2×D4×C1311yescharacteristic
287C22×C4C2×D4×C1311yescharacteristic
288Q16—48no—
289SD16—48no—
290SD16—82no—
291M16—22no—
292M16C13×SD1614yescomplemented
293C2×C8—22no—
294C2×C8—22no—
295C2×C8—22no—
296C2×C8—42no—
297C4⋊C4—22no—
298C4⋊C4—21no—
299C4⋊C4—22no—
300C4⋊C4—21no—
301C4⋊C4—21no—
302C4⋊C4—22no—
303C4⋊C4—21no—
304C4⋊C4—21no—
305C4⋊C4—21no—
306C4⋊C4—41no—
307C4⋊C4—41no—
308C4⋊C4—41no—
309C4⋊C4—41no—
310C4⋊C4—41no—
311C22⋊C4—41no—
312C22⋊C4—41no—
313C22⋊C4—41no—
314C42—41no—
315C42—42no—
316C42C2×D4×C1311yescharacteristic
317C42C2×D4×C1311yescharacteristic
318C42C2×D4×C1311yescharacteristic
319C42C13×#4111yescharacteristic
320C13#1020611yescharacteristic, direct product factor, Sylow
321C23—41no—
322C23C13×#12711yescharacteristic
323Q8—42no—
324Q8—44no—
325Q8—42no—
326Q8—41no—
327Q8—41no—
328Q8—82no—
329D4—42no—
330D4—41no—
331D4—41no—
332D4—81no—
333D4—81no—
334D4—81no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—41no—
338C2×C4—42no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—42no—
343C2×C4—81no—
344C2×C4—81no—
345C2×C4—81no—
346C2×C4—81no—
347C2×C4—82no—
348C2×C4C13×#12011yescharacteristic
349C2×C4C13×#12011yescharacteristic
350C2×C4C13×#12011yescharacteristic
351C2×C4C13×#12111yescharacteristic
352C2×C4C13×#12111yescharacteristic
353C2×C4C13×#12111yescharacteristic
354C2×C4C2×C13×SD1612yes—
355C2×C4C13×AGL(1,ℤ/8)12yes—
356C8—24no—
357C8—42no—
358C8—42no—
359C22—21no—
360C22—21no—
361C22—81no—
362C22—81no—
363C22—81no—
364C22C13×#39211yescharacteristic
365C22C13×#49211yescharacteristic
366C22C13×#49611yescharacteristic
367C4—21no—
368C4—21no—
369C4—21no—
370C4—82no—
371C4—81no—
372C4—81no—
373C4—81no—
374C4—82no—
375C4C13×#45012yes—
376C4C13×#45511yescharacteristic
377C4C13×#45611yescharacteristic
378C4C13×#46012yes—
379C2—21no—
380C2—21no—
381C2—161no—
382C2C13×#200711yescharacteristic
383C2C13×#200911yescharacteristic
384C2C13×#201411yescharacteristic
subgroupG/H
center, socleC22×C13#392
commutator, Frattini, cosocleC2×C42C23×C13
prime radicalC13×#532C22
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C13×#3229C2semidirect
4. C13×#1988C2semidirect
5. C13×#1986C2semidirect
7. C13×#1283C2semidirect
77. #10206C13direct (N × H)
101. C13×M16SD16semidirect
130. #3229C2×C13semidirect
132. #1988C2×C13semidirect
133. #1986C2×C13semidirect
135. #1283C2×C13semidirect
292. M16C13×SD16semidirect
320. C13#10206direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#32462
C13×#32292
C13×#31522
C13×#19882
C13×#19862
C13×#15022
C13×#12832
#1020613