Finite Group Databasebeta

← C13×#10200 #15696539

Subgroups — C13×#10200 #15696539

Order 3328.

550 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3245C211yesmaximal, characteristic
2C13×#3227C211yesmaximal, characteristic, complemented
3C13×#3141C211yesmaximal, characteristic, complemented
4C13×#1981C211yesmaximal, characteristic, complemented
5C13×#1980C211yesmaximal, characteristic, complemented
6C13×#1502C211yesmaximal, characteristic, complemented
7C13×#1283C211yesmaximal, characteristic, complemented
8C13×#532C2211yescharacteristic
9C13×#532C2211yescharacteristic
10C2×C13×C4⋊Q8C2211yescharacteristic
11C13×#498—21no—
12C13×#489—22no—
13C13×#487—21no—
14C13×#486—21no—
15C13×#486—21no—
16C13×#481—22no—
17C13×#476—22no—
18C13×#474—21no—
19C13×#474—21no—
20C13×#466—22no—
21C13×#459—21no—
22C13×#459—21no—
23C13×#431C2211yescharacteristic
24C2×C13×C4⋊C8C2211yescharacteristic
25C2×C13×#104—22no—
26C13×#417—22no—
27C2×C13×#103—22no—
28C4×C13×M16C2211yescharacteristic
29C4×C13×C4⋊C4C2211yescharacteristic
30C13×#327—22no—
31C2×C13×#41—21no—
32C2×C13×#41—21no—
33C22×Q8×C13—21no—
34C2×C13×D8—22no—
35C2×C13×M16D412yes—
36C22×C8×C13D412yes—
37C13×C4⋊Q8—21no—
38C13×C4⋊Q8—21no—
39C13×C4⋊Q8—21no—
40C13×C4⋊Q8D411yescharacteristic
41C13×C4⋊Q8D411yescharacteristic
42C13×C4⋊Q8D412yes—
43C13×#127D411yescharacteristic
44C13×#127D411yescharacteristic
45C13×#124—21no—
46C13×#124—21no—
47C13×#121—21no—
48C13×#121—21no—
49C13×#121—21no—
50C13×#121—21no—
51C4×D4×C13—21no—
52C4×D4×C13—21no—
53C4×D4×C13—21no—
54C4×D4×C13—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—22no—
61C13×#106—24no—
62C13×C4⋊C8—21no—
63C13×C4⋊C8—21no—
64C13×C4⋊C8—21no—
65C13×#104—44no—
66C13×#103—24no—
67C13×#103—44no—
68C13×#102—24no—
69C13×#102—22no—
70C13×#102—22no—
71C13×#102—24no—
72C13×C22⋊C8D412yes—
73C13×#97—21no—
74C4×C8×C13—21no—
75C4×C8×C13—21no—
76C13×#95—21no—
77#10200C1311yesmaximal, characteristic, direct product factor, Sylow
78C13×#41—42no—
79C13×#41—42no—
80C13×#41—42no—
81C13×#41—42no—
82C2×Q8×C13—21no—
83C2×Q8×C13—21no—
84C2×Q8×C13—22no—
85C2×Q8×C13—42no—
86C2×Q8×C13—42no—
87C2×Q8×C13—41no—
88C2×D4×C13—21no—
89C2×D4×C13—21no—
90C2×D4×C13—21no—
91C2×D4×C13—21no—
92C2×D4×C13—21no—
93C2×D4×C13—21no—
94C2×D4×C13—41no—
95C2×D4×C13—41no—
96C22×C4×C13—41no—
97C22×C4×C13—41no—
98C22×C4×C13—41no—
99C22×C4×C13—41no—
100C22×C4×C13C2×D411yescharacteristic
101C22×C4×C13C2×D411yescharacteristic
102C22×C4×C13C2×D411yescharacteristic
103C13×D8—82no—
104C13×M16—22no—
105C13×M16—22no—
106C2×C8×C13—22no—
107C2×C8×C13—22no—
108C2×C8×C13—22no—
109C2×C8×C13—42no—
110C13×C4⋊C4—22no—
111C13×C4⋊C4—22no—
112C13×C4⋊C4—22no—
113C13×C4⋊C4—21no—
114C13×C4⋊C4—21no—
115C13×C4⋊C4—21no—
116C13×C4⋊C4—21no—
117C13×C4⋊C4—41no—
118C13×C4⋊C4—41no—
119C13×C4⋊C4—41no—
120C13×C22⋊C4—41no—
121C13×C22⋊C4—41no—
122C13×C22⋊C4—41no—
123C13×C22⋊C4—41no—
124C42×C13—42no—
125C42×C13C2×D411yescharacteristic
126C42×C13C2×D411yescharacteristic
127C42×C13C2×D411yescharacteristic
128C42×C13#4111yescharacteristic
129#3245C2×C1311yescharacteristic
130#3227C2×C1311yescharacteristic, complemented
131#3141C2×C1311yescharacteristic, complemented
132#1981C2×C1311yescharacteristic, complemented
133#1980C2×C1311yescharacteristic, complemented
134#1502C2×C1311yescharacteristic, complemented
135#1283C2×C1311yescharacteristic, complemented
136C23×C13—41no—
137C23×C13—41no—
138C23×C13#12711yescharacteristic
139Q8×C13—44no—
140Q8×C13—42no—
141Q8×C13—42no—
142Q8×C13—81no—
143Q8×C13—81no—
144D4×C13—42no—
145D4×C13—42no—
146D4×C13—41no—
147D4×C13—41no—
148D4×C13—41no—
149D4×C13—41no—
150D4×C13—42no—
151D4×C13—81no—
152D4×C13—81no—
153D4×C13—81no—
154D4×C13—81no—
155D4×C13—81no—
156C2×C4×C13—21no—
157C2×C4×C13—21no—
158C2×C4×C13—41no—
159C2×C4×C13—42no—
160C2×C4×C13—41no—
161C2×C4×C13—41no—
162C2×C4×C13—42no—
163C2×C4×C13—81no—
164C2×C4×C13—82no—
165C2×C4×C13—81no—
166C2×C4×C13—82no—
167C2×C4×C13—82no—
168C2×C4×C13#12011yescharacteristic
169C2×C4×C13#12011yescharacteristic
170C2×C4×C13#12011yescharacteristic
171C2×C4×C13#12111yescharacteristic
172C2×C4×C13#12111yescharacteristic
173C2×C4×C13#12111yescharacteristic
174C2×C4×C13#13512yes—
175C2×C4×C13AGL(1,ℤ/8)12yes—
176C8×C13—42no—
177C8×C13—42no—
178C8×C13—42no—
179#532C22×C1311yescharacteristic
180#532C22×C1311yescharacteristic
181C2×C4⋊Q8C22×C1311yescharacteristic
182#498—21no—
183#489—22no—
184#487—21no—
185#486—21no—
186#486—21no—
187#481—22no—
188#476—22no—
189#474—21no—
190#474—21no—
191#466—22no—
192#459—21no—
193#459—21no—
194#431C22×C1311yescharacteristic
195C2×C4⋊C8C22×C1311yescharacteristic
196C2×#104—22no—
197#417—22no—
198C2×#103—22no—
199C4×M16C22×C1311yescharacteristic
200C4×C4⋊C4C22×C1311yescharacteristic
201#327—22no—
202C22×C13—21no—
203C22×C13—21no—
204C22×C13—81no—
205C22×C13—81no—
206C22×C13—81no—
207C22×C13—81no—
208C22×C13—81no—
209C22×C13—81no—
210C22×C13#39211yescharacteristic
211C22×C13#49511yescharacteristic
212C22×C13#49611yescharacteristic
213C4×C13—21no—
214C4×C13—21no—
215C4×C13—21no—
216C4×C13—82no—
217C4×C13—82no—
218C4×C13—81no—
219C4×C13—81no—
220C4×C13#44912yes—
221C4×C13#45311yescharacteristic
222C4×C13#45411yescharacteristic
223C4×C13#46312yes—
224C2×#41—21no—
225C2×#41—21no—
226C22×Q8—21no—
227C2×D8—22no—
228C2×M16D4×C1312yes—
229C22×C8D4×C1312yes—
230C4⋊Q8—21no—
231C4⋊Q8—21no—
232C4⋊Q8—21no—
233C4⋊Q8D4×C1312yes—
234C4⋊Q8D4×C1311yescharacteristic
235C4⋊Q8D4×C1311yescharacteristic
236#127D4×C1311yescharacteristic
237#127D4×C1311yescharacteristic
238#124—21no—
239#124—21no—
240#121—21no—
241#121—21no—
242#121—21no—
243#121—21no—
244C4×D4—21no—
245C4×D4—21no—
246C4×D4—21no—
247C4×D4—21no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—21no—
251C2×C42—21no—
252C2×C42C23×C1311yescharacteristic
253#107—22no—
254#106—24no—
255C4⋊C8—21no—
256C4⋊C8—21no—
257C4⋊C8—21no—
258#104—44no—
259#103—24no—
260#103—44no—
261#102—24no—
262#102—22no—
263#102—22no—
264#102—24no—
265C22⋊C8D4×C1312yes—
266#97—21no—
267C4×C8—21no—
268C4×C8—21no—
269#95—21no—
270C2×C13—21no—
271C2×C13—21no—
272C2×C13—161no—
273C2×C13—161no—
274C2×C13#200611yescharacteristic
275C2×C13#200911yescharacteristic
276C2×C13#201211yescharacteristic
277#41—42no—
278#41—42no—
279#41—42no—
280#41—42no—
281C2×Q8—21no—
282C2×Q8—21no—
283C2×Q8—22no—
284C2×Q8—42no—
285C2×Q8—42no—
286C2×Q8—41no—
287C2×D4—21no—
288C2×D4—21no—
289C2×D4—21no—
290C2×D4—21no—
291C2×D4—21no—
292C2×D4—21no—
293C2×D4—41no—
294C2×D4—41no—
295C22×C4—41no—
296C22×C4—41no—
297C22×C4—41no—
298C22×C4—41no—
299C22×C4C2×D4×C1311yescharacteristic
300C22×C4C2×D4×C1311yescharacteristic
301C22×C4C2×D4×C1311yescharacteristic
302D8—82no—
303M16—22no—
304M16—22no—
305C2×C8—22no—
306C2×C8—22no—
307C2×C8—22no—
308C2×C8—42no—
309C4⋊C4—22no—
310C4⋊C4—22no—
311C4⋊C4—22no—
312C4⋊C4—21no—
313C4⋊C4—21no—
314C4⋊C4—21no—
315C4⋊C4—21no—
316C4⋊C4—41no—
317C4⋊C4—41no—
318C4⋊C4—41no—
319C22⋊C4—41no—
320C22⋊C4—41no—
321C22⋊C4—41no—
322C22⋊C4—41no—
323C42—42no—
324C42C2×D4×C1311yescharacteristic
325C42C2×D4×C1311yescharacteristic
326C42C2×D4×C1311yescharacteristic
327C42C13×#4111yescharacteristic
328C13#1020011yescharacteristic, direct product factor, Sylow
329C23—41no—
330C23—41no—
331C23C13×#12711yescharacteristic
332Q8—44no—
333Q8—42no—
334Q8—42no—
335Q8—81no—
336Q8—81no—
337D4—42no—
338D4—42no—
339D4—41no—
340D4—41no—
341D4—41no—
342D4—41no—
343D4—42no—
344D4—81no—
345D4—81no—
346D4—81no—
347D4—81no—
348D4—81no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—41no—
352C2×C4—42no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—42no—
356C2×C4—81no—
357C2×C4—82no—
358C2×C4—81no—
359C2×C4—82no—
360C2×C4—82no—
361C2×C4C13×#12011yescharacteristic
362C2×C4C13×#12011yescharacteristic
363C2×C4C13×#12011yescharacteristic
364C2×C4C13×#12111yescharacteristic
365C2×C4C13×#12111yescharacteristic
366C2×C4C13×#12111yescharacteristic
367C2×C4C13×#13512yes—
368C2×C4C13×AGL(1,ℤ/8)12yes—
369C8—42no—
370C8—42no—
371C8—42no—
372C22—21no—
373C22—21no—
374C22—81no—
375C22—81no—
376C22—81no—
377C22—81no—
378C22—81no—
379C22—81no—
380C22C13×#39211yescharacteristic
381C22C13×#49511yescharacteristic
382C22C13×#49611yescharacteristic
383C4—21no—
384C4—21no—
385C4—21no—
386C4—82no—
387C4—82no—
388C4—81no—
389C4—81no—
390C4C13×#44912yes—
391C4C13×#45311yescharacteristic
392C4C13×#45411yescharacteristic
393C4C13×#46312yes—
394C2—21no—
395C2—21no—
396C2—161no—
397C2—161no—
398C2C13×#200611yescharacteristic
399C2C13×#200911yescharacteristic
400C2C13×#201211yescharacteristic
subgroupG/H
center, socleC22×C13#392
commutator, Frattini, cosocleC2×C42C23×C13
prime radicalC13×#3245C2
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×#3227C2semidirect
3. C13×#3141C2semidirect
4. C13×#1981C2semidirect
5. C13×#1980C2semidirect
6. C13×#1502C2semidirect
7. C13×#1283C2semidirect
77. #10200C13direct (N × H)
130. #3227C2×C13semidirect
131. #3141C2×C13semidirect
132. #1981C2×C13semidirect
133. #1980C2×C13semidirect
134. #1502C2×C13semidirect
135. #1283C2×C13semidirect
328. C13#10200direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#32452
C13×#32272
C13×#31412
C13×#19812
C13×#19802
C13×#15022
C13×#12832
#1020013