Finite Group Databasebeta

← C13×#10205 #15696544

Subgroups — C13×#10205 #15696544

Order 3328.

512 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×#3246C211yesmaximal, characteristic
2C13×#3226C211yesmaximal, characteristic
3C13×#3139C211yesmaximal, characteristic, complemented
4C13×#1988C211yesmaximal, characteristic, complemented
5C13×#1980C211yesmaximal, characteristic
6C13×#1503C211yesmaximal, characteristic, complemented
7C13×#1283C211yesmaximal, characteristic, complemented
8C13×#533C2211yescharacteristic
9C13×#532C2211yescharacteristic
10C2×C13×C4⋊Q8C2211yescharacteristic
11C13×#500—21no—
12C13×#491—22no—
13C13×#487—21no—
14C13×#487—21no—
15C13×#486—21no—
16C13×#480—22no—
17C13×#476—21no—
18C13×#475—21no—
19C13×#474—22no—
20C13×#465—22no—
21C13×#461—21no—
22C13×#460—21no—
23C13×#431C2211yescharacteristic
24C2×C13×C4⋊C8C2211yescharacteristic
25C2×C13×#104—22no—
26C13×#419—22no—
27C4×C13×M16C2211yescharacteristic
28C4×C13×C4⋊C4C2211yescharacteristic
29C13×#340—22no—
30C13×#328—22no—
31C2×C13×#41—21no—
32C22×Q8×C13—21no—
33C2×C13×SD16—22no—
34C2×C13×M16D412yes—
35C22×C8×C13D412yes—
36C13×C4⋊Q8—21no—
37C13×C4⋊Q8—21no—
38C13×C4⋊Q8—21no—
39C13×C4⋊Q8D411yescharacteristic
40C13×C4⋊Q8D412yes—
41C13×C4⋊Q8D411yescharacteristic
42C13×C4⋊Q8D411yescharacteristic
43C13×#127D411yescharacteristic
44C13×#125—21no—
45C13×#124—21no—
46C13×C22⋊Q8—21no—
47C13×C22⋊Q8—21no—
48C13×#121—21no—
49C13×#121—21no—
50C4×Q8×C13—21no—
51C4×Q8×C13—21no—
52C4×D4×C13—21no—
53C4×D4×C13—21no—
54C13×#117—21no—
55C2×C13×C4⋊C4—21no—
56C2×C13×C4⋊C4—21no—
57C2×C13×C4⋊C4—21no—
58C2×C42×C13—21no—
59C2×C42×C13C2311yescharacteristic
60C13×#107—24no—
61C13×#106—22no—
62C13×C4⋊C8—21no—
63C13×C4⋊C8—21no—
64C13×C4⋊C8—21no—
65C13×#104—44no—
66C13×#103—24no—
67C13×#103—24no—
68C13×#103—22no—
69C13×#102—22no—
70C13×#102—24no—
71C13×C22⋊C8D412yes—
72C13×#97—21no—
73C4×C8×C13—21no—
74C4×C8×C13—21no—
75C13×#95—21no—
76#10205C1311yesmaximal, characteristic, direct product factor, Sylow
77C13×#41—42no—
78C13×#41—42no—
79C2×Q8×C13—22no—
80C2×Q8×C13—21no—
81C2×Q8×C13—21no—
82C2×Q8×C13—21no—
83C2×Q8×C13—41no—
84C2×Q8×C13—42no—
85C2×Q8×C13—42no—
86C2×D4×C13—21no—
87C2×D4×C13—21no—
88C2×D4×C13—21no—
89C2×D4×C13—41no—
90C22×C4×C13—41no—
91C22×C4×C13—41no—
92C22×C4×C13—41no—
93C22×C4×C13C2×D411yescharacteristic
94C22×C4×C13C2×D411yescharacteristic
95C22×C4×C13C2×D411yescharacteristic
96C13×SD16—82no—
97C13×M16—22no—
98C13×M16—22no—
99C2×C8×C13—22no—
100C2×C8×C13—22no—
101C2×C8×C13—22no—
102C2×C8×C13—42no—
103C13×C4⋊C4—22no—
104C13×C4⋊C4—21no—
105C13×C4⋊C4—22no—
106C13×C4⋊C4—21no—
107C13×C4⋊C4—21no—
108C13×C4⋊C4—21no—
109C13×C4⋊C4—21no—
110C13×C4⋊C4—22no—
111C13×C4⋊C4—21no—
112C13×C4⋊C4—41no—
113C13×C4⋊C4—41no—
114C13×C4⋊C4—41no—
115C13×C4⋊C4—41no—
116C13×C4⋊C4—41no—
117C13×C22⋊C4—41no—
118C13×C22⋊C4—41no—
119C13×C22⋊C4—41no—
120C42×C13—41no—
121C42×C13—42no—
122C42×C13C2×D411yescharacteristic
123C42×C13C2×D411yescharacteristic
124C42×C13C2×D411yescharacteristic
125C42×C13#4111yescharacteristic
126#3246C2×C1311yescharacteristic
127#3226C2×C1311yescharacteristic
128#3139C2×C1311yescharacteristic, complemented
129#1988C2×C1311yescharacteristic, complemented
130#1980C2×C1311yescharacteristic
131#1503C2×C1311yescharacteristic, complemented
132#1283C2×C1311yescharacteristic, complemented
133C23×C13—41no—
134C23×C13#12711yescharacteristic
135Q8×C13—44no—
136Q8×C13—41no—
137Q8×C13—41no—
138Q8×C13—42no—
139Q8×C13—81no—
140Q8×C13—82no—
141D4×C13—42no—
142D4×C13—41no—
143D4×C13—41no—
144D4×C13—42no—
145D4×C13—81no—
146D4×C13—81no—
147C2×C4×C13—21no—
148C2×C4×C13—21no—
149C2×C4×C13—41no—
150C2×C4×C13—42no—
151C2×C4×C13—41no—
152C2×C4×C13—41no—
153C2×C4×C13—41no—
154C2×C4×C13—42no—
155C2×C4×C13—81no—
156C2×C4×C13—81no—
157C2×C4×C13—81no—
158C2×C4×C13—81no—
159C2×C4×C13—82no—
160C2×C4×C13#12011yescharacteristic
161C2×C4×C13#12011yescharacteristic
162C2×C4×C13#12011yescharacteristic
163C2×C4×C13#12111yescharacteristic
164C2×C4×C13#12111yescharacteristic
165C2×C4×C13#12111yescharacteristic
166C2×C4×C13#13512yes—
167C2×C4×C13AGL(1,ℤ/8)12yes—
168C8×C13—42no—
169C8×C13—42no—
170C8×C13—42no—
171#533C22×C1311yescharacteristic
172#532C22×C1311yescharacteristic
173C2×C4⋊Q8C22×C1311yescharacteristic
174#500—21no—
175#491—22no—
176#487—21no—
177#487—21no—
178#486—21no—
179#480—22no—
180#476—21no—
181#475—21no—
182#474—22no—
183#465—22no—
184#461—21no—
185#460—21no—
186#431C22×C1311yescharacteristic
187C2×C4⋊C8C22×C1311yescharacteristic
188C2×#104—22no—
189#419—22no—
190C4×M16C22×C1311yescharacteristic
191C4×C4⋊C4C22×C1311yescharacteristic
192#340—22no—
193#328—22no—
194C22×C13—21no—
195C22×C13—21no—
196C22×C13—81no—
197C22×C13—81no—
198C22×C13—81no—
199C22×C13#39211yescharacteristic
200C22×C13#49511yescharacteristic
201C22×C13#49611yescharacteristic
202C4×C13—21no—
203C4×C13—21no—
204C4×C13—21no—
205C4×C13—82no—
206C4×C13—81no—
207C4×C13—81no—
208C4×C13—81no—
209C4×C13—82no—
210C4×C13#44912yes—
211C4×C13#45511yescharacteristic
212C4×C13#45611yescharacteristic
213C4×C13#46312yes—
214C2×#41—21no—
215C22×Q8—21no—
216C2×SD16—22no—
217C2×M16D4×C1312yes—
218C22×C8D4×C1312yes—
219C4⋊Q8—21no—
220C4⋊Q8—21no—
221C4⋊Q8—21no—
222C4⋊Q8D4×C1312yes—
223C4⋊Q8D4×C1311yescharacteristic
224C4⋊Q8D4×C1311yescharacteristic
225C4⋊Q8D4×C1311yescharacteristic
226#127D4×C1311yescharacteristic
227#125—21no—
228#124—21no—
229C22⋊Q8—21no—
230C22⋊Q8—21no—
231#121—21no—
232#121—21no—
233C4×Q8—21no—
234C4×Q8—21no—
235C4×D4—21no—
236C4×D4—21no—
237#117—21no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—21no—
241C2×C42—21no—
242C2×C42C23×C1311yescharacteristic
243#107—24no—
244#106—22no—
245C4⋊C8—21no—
246C4⋊C8—21no—
247C4⋊C8—21no—
248#104—44no—
249#103—24no—
250#103—24no—
251#103—22no—
252#102—22no—
253#102—24no—
254C22⋊C8D4×C1312yes—
255#97—21no—
256C4×C8—21no—
257C4×C8—21no—
258#95—21no—
259C2×C13—21no—
260C2×C13—21no—
261C2×C13—161no—
262C2×C13#200711yescharacteristic
263C2×C13#200911yescharacteristic
264C2×C13#201211yescharacteristic
265#41—42no—
266#41—42no—
267C2×Q8—22no—
268C2×Q8—21no—
269C2×Q8—21no—
270C2×Q8—21no—
271C2×Q8—41no—
272C2×Q8—42no—
273C2×Q8—42no—
274C2×D4—21no—
275C2×D4—21no—
276C2×D4—21no—
277C2×D4—41no—
278C22×C4—41no—
279C22×C4—41no—
280C22×C4—41no—
281C22×C4C2×D4×C1311yescharacteristic
282C22×C4C2×D4×C1311yescharacteristic
283C22×C4C2×D4×C1311yescharacteristic
284SD16—82no—
285M16—22no—
286M16—22no—
287C2×C8—22no—
288C2×C8—22no—
289C2×C8—22no—
290C2×C8—42no—
291C4⋊C4—22no—
292C4⋊C4—21no—
293C4⋊C4—22no—
294C4⋊C4—21no—
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—21no—
298C4⋊C4—22no—
299C4⋊C4—21no—
300C4⋊C4—41no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4—41no—
305C22⋊C4—41no—
306C22⋊C4—41no—
307C22⋊C4—41no—
308C42—41no—
309C42—42no—
310C42C2×D4×C1311yescharacteristic
311C42C2×D4×C1311yescharacteristic
312C42C2×D4×C1311yescharacteristic
313C42C13×#4111yescharacteristic
314C13#1020511yescharacteristic, direct product factor, Sylow
315C23—41no—
316C23C13×#12711yescharacteristic
317Q8—44no—
318Q8—41no—
319Q8—41no—
320Q8—42no—
321Q8—81no—
322Q8—82no—
323D4—42no—
324D4—41no—
325D4—41no—
326D4—42no—
327D4—81no—
328D4—81no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—41no—
332C2×C4—42no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—42no—
337C2×C4—81no—
338C2×C4—81no—
339C2×C4—81no—
340C2×C4—81no—
341C2×C4—82no—
342C2×C4C13×#12011yescharacteristic
343C2×C4C13×#12011yescharacteristic
344C2×C4C13×#12011yescharacteristic
345C2×C4C13×#12111yescharacteristic
346C2×C4C13×#12111yescharacteristic
347C2×C4C13×#12111yescharacteristic
348C2×C4C13×#13512yes—
349C2×C4C13×AGL(1,ℤ/8)12yes—
350C8—42no—
351C8—42no—
352C8—42no—
353C22—21no—
354C22—21no—
355C22—81no—
356C22—81no—
357C22—81no—
358C22C13×#39211yescharacteristic
359C22C13×#49511yescharacteristic
360C22C13×#49611yescharacteristic
361C4—21no—
362C4—21no—
363C4—21no—
364C4—82no—
365C4—81no—
366C4—81no—
367C4—81no—
368C4—82no—
369C4C13×#44912yes—
370C4C13×#45511yescharacteristic
371C4C13×#45611yescharacteristic
372C4C13×#46312yes—
373C2—21no—
374C2—21no—
375C2—161no—
376C2C13×#200711yescharacteristic
377C2C13×#200911yescharacteristic
378C2C13×#201211yescharacteristic
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
3. C13×#3139C2semidirect
4. C13×#1988C2semidirect
6. C13×#1503C2semidirect
7. C13×#1283C2semidirect
76. #10205C13direct (N × H)
128. #3139C2×C13semidirect
129. #1988C2×C13semidirect
131. #1503C2×C13semidirect
132. #1283C2×C13semidirect
314. C13#10205direct (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×#32262
C13×#31392
C13×#19882
C13×#19802
C13×#15032
C13×#12832
#1020513