Finite Group Databasebeta

← C13×#10204 #15696543

Subgroups — C13×#10204 #15696543

Order 3328.

598 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3245C211yesmaximal, characteristic
2C13×#3226C211yesmaximal, characteristic, complemented
3C13×#3152C211yesmaximal, characteristic, complemented
4C13×#1988C211yesmaximal, characteristic, complemented
5C13×#1980C211yesmaximal, characteristic, complemented
6C13×#1502C211yesmaximal, characteristic, complemented
7C13×#1283C211yesmaximal, characteristic, complemented
8C2×C13×#137—22no—
9C13×#532C2211yescharacteristic
10C13×#532C2211yescharacteristic
11C2×C13×C4⋊Q8C2211yescharacteristic
12C13×#500—21no—
13C13×#497—22no—
14C13×#494—21no—
15C13×#492—21no—
16C13×#486—21no—
17C13×#480—22no—
18C13×#474—22no—
19C13×#474—21no—
20C13×#474—21no—
21C13×#466—22no—
22C13×#459—21no—
23C13×#459—21no—
24C13×#431C2211yescharacteristic
25C2×C13×C4⋊C8C2211yescharacteristic
26C2×C13×#104—22no—
27C4×C13×M16C2211yescharacteristic
28C4×C13×C4⋊C4C2211yescharacteristic
29C13×#340—22no—
30C13×#327—22no—
31C2×C13×#41—21no—
32C2×C13×#41—21no—
33C22×Q8×C13—21no—
34C13×#137—44no—
35C13×#137—44no—
36C2×C13×Q16—24no—
37C2×C13×SD16—24no—
38C2×C13×D8—22no—
39C2×C13×M16D412yes—
40C22×C8×C13D412yes—
41C13×C4⋊Q8—21no—
42C13×C4⋊Q8—21no—
43C13×C4⋊Q8—21no—
44C13×C4⋊Q8D411yescharacteristic
45C13×C4⋊Q8D412yes—
46C13×C4⋊Q8D411yescharacteristic
47C13×#127D411yescharacteristic
48C13×#127D411yescharacteristic
49C13×#124—21no—
50C13×#124—21no—
51C13×#121—21no—
52C13×#121—21no—
53C13×#121—21no—
54C13×#121—21no—
55C4×D4×C13—21no—
56C4×D4×C13—21no—
57C4×D4×C13—21no—
58C4×D4×C13—21no—
59C2×C13×C4⋊C4—21no—
60C2×C13×C4⋊C4—21no—
61C2×C13×C4⋊C4—21no—
62C2×C42×C13—21no—
63C2×C42×C13C2311yescharacteristic
64C13×#107—22no—
65C13×#107—24no—
66C13×C4⋊C8—21no—
67C13×C4⋊C8—21no—
68C13×C4⋊C8—21no—
69C13×#104—44no—
70C13×#102—22no—
71C13×#102—22no—
72C13×#102—24no—
73C13×C22⋊C8D412yes—
74C13×#97—21no—
75C4×C8×C13—21no—
76C4×C8×C13—21no—
77C13×#95—21no—
78#10204C1311yesmaximal, characteristic, direct product factor, Sylow
79C13×#41—42no—
80C13×#41—42no—
81C13×#41—42no—
82C13×#41—42no—
83C2×Q8×C13—21no—
84C2×Q8×C13—22no—
85C2×Q8×C13—21no—
86C2×Q8×C13—41no—
87C2×Q8×C13—42no—
88C2×Q8×C13—42no—
89C2×D4×C13—21no—
90C2×D4×C13—21no—
91C2×D4×C13—21no—
92C2×D4×C13—21no—
93C2×D4×C13—21no—
94C2×D4×C13—21no—
95C2×D4×C13—41no—
96C2×D4×C13—41no—
97C22×C4×C13—41no—
98C22×C4×C13—41no—
99C22×C4×C13—41no—
100C22×C4×C13—41no—
101C22×C4×C13C2×D411yescharacteristic
102C22×C4×C13C2×D411yescharacteristic
103C22×C4×C13C2×D411yescharacteristic
104C13×Q16—48no—
105C13×SD16—48no—
106C13×D8—82no—
107C13×M16—22no—
108C13×M16D814yescomplemented
109C2×C8×C13—22no—
110C2×C8×C13—22no—
111C2×C8×C13—22no—
112C2×C8×C13—42no—
113C13×C4⋊C4—22no—
114C13×C4⋊C4—22no—
115C13×C4⋊C4—21no—
116C13×C4⋊C4—21no—
117C13×C4⋊C4—21no—
118C13×C4⋊C4—22no—
119C13×C4⋊C4—21no—
120C13×C4⋊C4—41no—
121C13×C4⋊C4—41no—
122C13×C4⋊C4—41no—
123C13×C22⋊C4—41no—
124C13×C22⋊C4—41no—
125C13×C22⋊C4—41no—
126C13×C22⋊C4—41no—
127C42×C13—42no—
128C42×C13C2×D411yescharacteristic
129C42×C13C2×D411yescharacteristic
130C42×C13C2×D411yescharacteristic
131C42×C13#4111yescharacteristic
132#3245C2×C1311yescharacteristic
133#3226C2×C1311yescharacteristic, complemented
134#3152C2×C1311yescharacteristic, complemented
135#1988C2×C1311yescharacteristic, complemented
136#1980C2×C1311yescharacteristic, complemented
137#1502C2×C1311yescharacteristic, complemented
138#1283C2×C1311yescharacteristic, complemented
139C23×C13—41no—
140C23×C13—41no—
141C23×C13#12711yescharacteristic
142Q8×C13—44no—
143Q8×C13—42no—
144Q8×C13—42no—
145Q8×C13—82no—
146D4×C13—42no—
147D4×C13—42no—
148D4×C13—41no—
149D4×C13—41no—
150D4×C13—41no—
151D4×C13—41no—
152D4×C13—42no—
153D4×C13—81no—
154D4×C13—81no—
155D4×C13—81no—
156D4×C13—81no—
157D4×C13—81no—
158C2×C4×C13—21no—
159C2×C4×C13—21no—
160C2×C4×C13—41no—
161C2×C4×C13—42no—
162C2×C4×C13—41no—
163C2×C4×C13—41no—
164C2×C4×C13—42no—
165C2×C4×C13—81no—
166C2×C4×C13—81no—
167C2×C4×C13—81no—
168C2×C4×C13—81no—
169C2×C4×C13—82no—
170C2×C4×C13—82no—
171C2×C4×C13#12011yescharacteristic
172C2×C4×C13#12011yescharacteristic
173C2×C4×C13#12011yescharacteristic
174C2×C4×C13#12111yescharacteristic
175C2×C4×C13#12111yescharacteristic
176C2×C4×C13#12111yescharacteristic
177C2×C4×C13C2×D812yes—
178C2×C4×C13AGL(1,ℤ/8)12yes—
179C8×C13—24no—
180C8×C13—42no—
181C8×C13—42no—
182C2×#137—22no—
183#532C22×C1311yescharacteristic
184#532C22×C1311yescharacteristic
185C2×C4⋊Q8C22×C1311yescharacteristic
186#500—21no—
187#497—22no—
188#494—21no—
189#492—21no—
190#486—21no—
191#480—22no—
192#474—22no—
193#474—21no—
194#474—21no—
195#466—22no—
196#459—21no—
197#459—21no—
198#431C22×C1311yescharacteristic
199C2×C4⋊C8C22×C1311yescharacteristic
200C2×#104—22no—
201C4×M16C22×C1311yescharacteristic
202C4×C4⋊C4C22×C1311yescharacteristic
203#340—22no—
204#327—22no—
205C22×C13—21no—
206C22×C13—21no—
207C22×C13—81no—
208C22×C13—81no—
209C22×C13—81no—
210C22×C13—81no—
211C22×C13—81no—
212C22×C13—81no—
213C22×C13#39211yescharacteristic
214C22×C13#49311yescharacteristic
215C22×C13#49611yescharacteristic
216C4×C13—21no—
217C4×C13—21no—
218C4×C13—21no—
219C4×C13—82no—
220C4×C13—81no—
221C4×C13—81no—
222C4×C13—82no—
223C4×C13#44712yes—
224C4×C13#45511yescharacteristic
225C4×C13#45611yescharacteristic
226C4×C13#45912yes—
227C2×#41—21no—
228C2×#41—21no—
229C22×Q8—21no—
230#137—44no—
231#137—44no—
232C2×Q16—24no—
233C2×SD16—24no—
234C2×D8—22no—
235C2×M16D4×C1312yes—
236C22×C8D4×C1312yes—
237C4⋊Q8—21no—
238C4⋊Q8—21no—
239C4⋊Q8—21no—
240C4⋊Q8D4×C1312yes—
241C4⋊Q8D4×C1311yescharacteristic
242C4⋊Q8D4×C1311yescharacteristic
243#127D4×C1311yescharacteristic
244#127D4×C1311yescharacteristic
245#124—21no—
246#124—21no—
247#121—21no—
248#121—21no—
249#121—21no—
250#121—21no—
251C4×D4—21no—
252C4×D4—21no—
253C4×D4—21no—
254C4×D4—21no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—21no—
258C2×C42—21no—
259C2×C42C23×C1311yescharacteristic
260#107—22no—
261#107—24no—
262C4⋊C8—21no—
263C4⋊C8—21no—
264C4⋊C8—21no—
265#104—44no—
266#102—22no—
267#102—22no—
268#102—24no—
269C22⋊C8D4×C1312yes—
270#97—21no—
271C4×C8—21no—
272C4×C8—21no—
273#95—21no—
274C2×C13—21no—
275C2×C13—21no—
276C2×C13—161no—
277C2×C13—161no—
278C2×C13#200711yescharacteristic
279C2×C13#200911yescharacteristic
280C2×C13#201111yescharacteristic
281#41—42no—
282#41—42no—
283#41—42no—
284#41—42no—
285C2×Q8—21no—
286C2×Q8—22no—
287C2×Q8—21no—
288C2×Q8—41no—
289C2×Q8—42no—
290C2×Q8—42no—
291C2×D4—21no—
292C2×D4—21no—
293C2×D4—21no—
294C2×D4—21no—
295C2×D4—21no—
296C2×D4—21no—
297C2×D4—41no—
298C2×D4—41no—
299C22×C4—41no—
300C22×C4—41no—
301C22×C4—41no—
302C22×C4—41no—
303C22×C4C2×D4×C1311yescharacteristic
304C22×C4C2×D4×C1311yescharacteristic
305C22×C4C2×D4×C1311yescharacteristic
306Q16—48no—
307SD16—48no—
308D8—82no—
309M16—22no—
310M16C13×D814yescomplemented
311C2×C8—22no—
312C2×C8—22no—
313C2×C8—22no—
314C2×C8—42no—
315C4⋊C4—22no—
316C4⋊C4—22no—
317C4⋊C4—21no—
318C4⋊C4—21no—
319C4⋊C4—21no—
320C4⋊C4—22no—
321C4⋊C4—21no—
322C4⋊C4—41no—
323C4⋊C4—41no—
324C4⋊C4—41no—
325C22⋊C4—41no—
326C22⋊C4—41no—
327C22⋊C4—41no—
328C22⋊C4—41no—
329C42—42no—
330C42C2×D4×C1311yescharacteristic
331C42C2×D4×C1311yescharacteristic
332C42C2×D4×C1311yescharacteristic
333C42C13×#4111yescharacteristic
334C13#1020411yescharacteristic, direct product factor, Sylow
335C23—41no—
336C23—41no—
337C23C13×#12711yescharacteristic
338Q8—44no—
339Q8—42no—
340Q8—42no—
341Q8—82no—
342D4—42no—
343D4—42no—
344D4—41no—
345D4—41no—
346D4—41no—
347D4—41no—
348D4—42no—
349D4—81no—
350D4—81no—
351D4—81no—
352D4—81no—
353D4—81no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—41no—
357C2×C4—42no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—42no—
361C2×C4—81no—
362C2×C4—81no—
363C2×C4—81no—
364C2×C4—81no—
365C2×C4—82no—
366C2×C4—82no—
367C2×C4C13×#12011yescharacteristic
368C2×C4C13×#12011yescharacteristic
369C2×C4C13×#12011yescharacteristic
370C2×C4C13×#12111yescharacteristic
371C2×C4C13×#12111yescharacteristic
372C2×C4C13×#12111yescharacteristic
373C2×C4C2×C13×D812yes—
374C2×C4C13×AGL(1,ℤ/8)12yes—
375C8—24no—
376C8—42no—
377C8—42no—
378C22—21no—
379C22—21no—
380C22—81no—
381C22—81no—
382C22—81no—
383C22—81no—
384C22—81no—
385C22—81no—
386C22C13×#39211yescharacteristic
387C22C13×#49311yescharacteristic
388C22C13×#49611yescharacteristic
389C4—21no—
390C4—21no—
391C4—21no—
392C4—82no—
393C4—81no—
394C4—81no—
395C4—82no—
396C4C13×#44712yes—
397C4C13×#45511yescharacteristic
398C4C13×#45611yescharacteristic
399C4C13×#45912yes—
400C2—21no—
401C2—21no—
402C2—161no—
403C2—161no—
404C2C13×#200711yescharacteristic
405C2C13×#200911yescharacteristic
406C2C13×#201111yescharacteristic
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×#3226C2semidirect
3. C13×#3152C2semidirect
4. C13×#1988C2semidirect
5. C13×#1980C2semidirect
6. C13×#1502C2semidirect
7. C13×#1283C2semidirect
78. #10204C13direct (N × H)
108. C13×M16D8semidirect
133. #3226C2×C13semidirect
134. #3152C2×C13semidirect
135. #1988C2×C13semidirect
136. #1980C2×C13semidirect
137. #1502C2×C13semidirect
138. #1283C2×C13semidirect
310. M16C13×D8semidirect
334. C13#10204direct (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×#32262
C13×#31522
C13×#19882
C13×#19802
C13×#15022
C13×#12832
#1020413