Finite Group Databasebeta

← C13×#10221 #15696560

Subgroups — C13×#10221 #15696560

Order 3328.

570 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3227C211yesmaximal, characteristic, complemented
2C13×#3206C211yesmaximal, characteristic, complemented
3C13×#3150C211yesmaximal, characteristic
4C13×#1993C211yesmaximal, characteristic, complemented
5C13×#1517C211yesmaximal, characteristic, complemented
6C13×#1517C211yesmaximal, characteristic, complemented
7C13×#1281C211yesmaximal, characteristic, complemented
8C2×C13×#135—22no—
9C13×#532C2211yescharacteristic
10C13×#532C2211yescharacteristic
11C2×C13×C4⋊Q8C2211yescharacteristic
12C13×#498—21no—
13C13×#497—21no—
14C13×#497—21no—
15C13×#496—21no—
16C13×#496—21no—
17C13×#492—21no—
18C13×#487—21no—
19C13×#486—21no—
20C13×#481—22no—
21C13×#476—22no—
22C13×#461—22no—
23C13×#448—22no—
24C13×#431C2211yescharacteristic
25C13×#431C2211yescharacteristic
26C2×C13×#97C2211yescharacteristic
27C13×#382C2211yescharacteristic
28C13×#340—22no—
29C13×#327—22no—
30C13×#327—22no—
31C2×C13×#41—21no—
32C2×C13×#41—21no—
33C22×Q8×C13—21no—
34C13×#135—44no—
35C13×#135—44no—
36C2×C13×Q16—22no—
37C2×C13×SD16—22no—
38C2×C13×SD16—22no—
39C2×C13×SD16—24no—
40C2×C13×D8—22no—
41C22×C8×C13D412yes—
42C13×C4⋊Q8—21no—
43C13×C4⋊Q8—21no—
44C13×C4⋊Q8—21no—
45C13×C4⋊Q8D412yes—
46C13×C4⋊Q8D411yescharacteristic
47C13×C4⋊Q8D411yescharacteristic
48C13×#127D411yescharacteristic
49C13×#127D411yescharacteristic
50C13×#124—21no—
51C13×#124—21no—
52C13×#121—21no—
53C13×#121—21no—
54C13×#121—21no—
55C13×#121—21no—
56C4×D4×C13—21no—
57C4×D4×C13—21no—
58C4×D4×C13—21no—
59C4×D4×C13—21no—
60C2×C13×C4⋊C4—21no—
61C2×C13×C4⋊C4—21no—
62C2×C13×C4⋊C4—21no—
63C2×C42×C13C2311yescharacteristic
64C13×#106—24no—
65C13×C4⋊C8—21no—
66C13×C4⋊C8—21no—
67C13×#103—24no—
68C13×#102—24no—
69C13×C22⋊C8D412yes—
70C13×C22⋊C8D412yes—
71C13×#97—21no—
72C13×#97—21no—
73C4×C8×C13—21no—
74C4×C8×C13—21no—
75C13×#95—21no—
76C13×#95—21no—
77#10221C1311yesmaximal, characteristic, direct product factor, Sylow
78C13×#41—42no—
79C13×#41—42no—
80C13×#41—42no—
81C13×#41—42no—
82C2×Q8×C13—22no—
83C2×Q8×C13—21no—
84C2×Q8×C13—21no—
85C2×Q8×C13—41no—
86C2×Q8×C13—82no—
87C2×D4×C13—21no—
88C2×D4×C13—21no—
89C2×D4×C13—21no—
90C2×D4×C13—21no—
91C2×D4×C13—21no—
92C2×D4×C13—21no—
93C2×D4×C13—41no—
94C2×D4×C13—41no—
95C22×C4×C13—41no—
96C22×C4×C13—41no—
97C22×C4×C13—41no—
98C22×C4×C13—41no—
99C22×C4×C13C2×D411yescharacteristic
100C22×C4×C13C2×D411yescharacteristic
101C22×C4×C13C2×D411yescharacteristic
102C13×Q16—44no—
103C13×SD16—44no—
104C13×SD16—44no—
105C13×SD16—84no—
106C13×D8—44no—
107C2×C8×C13—22no—
108C2×C8×C13—22no—
109C2×C8×C13—22no—
110C2×C8×C13—22no—
111C2×C8×C13SD1614yescomplemented
112C13×C4⋊C4—22no—
113C13×C4⋊C4—21no—
114C13×C4⋊C4—21no—
115C13×C4⋊C4—22no—
116C13×C4⋊C4—21no—
117C13×C4⋊C4—21no—
118C13×C4⋊C4—41no—
119C13×C4⋊C4—41no—
120C13×C4⋊C4—42no—
121C13×C22⋊C4—41no—
122C13×C22⋊C4—41no—
123C13×C22⋊C4—41no—
124C13×C22⋊C4—41no—
125C42×C13C2×D411yescharacteristic
126C42×C13C2×D411yescharacteristic
127C42×C13C2×D411yescharacteristic
128C42×C13#4111yescharacteristic
129#3227C2×C1311yescharacteristic, complemented
130#3206C2×C1311yescharacteristic, complemented
131#3150C2×C1311yescharacteristic
132#1993C2×C1311yescharacteristic, complemented
133#1517C2×C1311yescharacteristic, complemented
134#1517C2×C1311yescharacteristic, complemented
135#1281C2×C1311yescharacteristic, complemented
136C23×C13—41no—
137C23×C13—41no—
138C23×C13#12711yescharacteristic
139Q8×C13—44no—
140Q8×C13—42no—
141Q8×C13—42no—
142Q8×C13—82no—
143D4×C13—42no—
144D4×C13—42no—
145D4×C13—42no—
146D4×C13—42no—
147D4×C13—81no—
148D4×C13—81no—
149D4×C13—81no—
150D4×C13—81no—
151D4×C13—81no—
152D4×C13—81no—
153C2×C4×C13—41no—
154C2×C4×C13—41no—
155C2×C4×C13—41no—
156C2×C4×C13—41no—
157C2×C4×C13—42no—
158C2×C4×C13—82no—
159C2×C4×C13—82no—
160C2×C4×C13—82no—
161C2×C4×C13—81no—
162C2×C4×C13—81no—
163C2×C4×C13—81no—
164C2×C4×C13#12011yescharacteristic
165C2×C4×C13#12011yescharacteristic
166C2×C4×C13#12011yescharacteristic
167C2×C4×C13#12111yescharacteristic
168C2×C4×C13#12111yescharacteristic
169C2×C4×C13#12111yescharacteristic
170C2×C4×C13C2×SD1612yes—
171C2×C4×C13AGL(1,ℤ/8)12yes—
172C8×C13—24no—
173C8×C13—42no—
174C8×C13—42no—
175C2×#135—22no—
176#532C22×C1311yescharacteristic
177#532C22×C1311yescharacteristic
178C2×C4⋊Q8C22×C1311yescharacteristic
179#498—21no—
180#497—21no—
181#497—21no—
182#496—21no—
183#496—21no—
184#492—21no—
185#487—21no—
186#486—21no—
187#481—22no—
188#476—22no—
189#461—22no—
190#448—22no—
191#431C22×C1311yescharacteristic
192#431C22×C1311yescharacteristic
193C2×#97C22×C1311yescharacteristic
194#382C22×C1311yescharacteristic
195#340—22no—
196#327—22no—
197#327—22no—
198C22×C13—21no—
199C22×C13—21no—
200C22×C13—81no—
201C22×C13—81no—
202C22×C13—81no—
203C22×C13—81no—
204C22×C13—81no—
205C22×C13—81no—
206C22×C13#39211yescharacteristic
207C22×C13#49211yescharacteristic
208C22×C13#49611yescharacteristic
209C4×C13—21no—
210C4×C13—21no—
211C4×C13—21no—
212C4×C13—21no—
213C4×C13—82no—
214C4×C13—81no—
215C4×C13—81no—
216C4×C13—161no—
217C4×C13#45012yes—
218C4×C13#46012yes—
219C2×#41—21no—
220C2×#41—21no—
221C22×Q8—21no—
222#135—44no—
223#135—44no—
224C2×Q16—22no—
225C2×SD16—22no—
226C2×SD16—22no—
227C2×SD16—24no—
228C2×D8—22no—
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×C42C23×C1311yescharacteristic
252#106—24no—
253C4⋊C8—21no—
254C4⋊C8—21no—
255#103—24no—
256#102—24no—
257C22⋊C8D4×C1312yes—
258C22⋊C8D4×C1312yes—
259#97—21no—
260#97—21no—
261C4×C8—21no—
262C4×C8—21no—
263#95—21no—
264#95—21no—
265C2×C13—21no—
266C2×C13—21no—
267C2×C13—161no—
268C2×C13—161no—
269C2×C13#200811yescharacteristic
270C2×C13#200911yescharacteristic
271C2×C13#201411yescharacteristic
272#41—42no—
273#41—42no—
274#41—42no—
275#41—42no—
276C2×Q8—22no—
277C2×Q8—21no—
278C2×Q8—21no—
279C2×Q8—41no—
280C2×Q8—82no—
281C2×D4—21no—
282C2×D4—21no—
283C2×D4—21no—
284C2×D4—21no—
285C2×D4—21no—
286C2×D4—21no—
287C2×D4—41no—
288C2×D4—41no—
289C22×C4—41no—
290C22×C4—41no—
291C22×C4—41no—
292C22×C4—41no—
293C22×C4C2×D4×C1311yescharacteristic
294C22×C4C2×D4×C1311yescharacteristic
295C22×C4C2×D4×C1311yescharacteristic
296Q16—44no—
297SD16—44no—
298SD16—44no—
299SD16—84no—
300D8—44no—
301C2×C8—22no—
302C2×C8—22no—
303C2×C8—22no—
304C2×C8—22no—
305C2×C8C13×SD1614yescomplemented
306C4⋊C4—22no—
307C4⋊C4—21no—
308C4⋊C4—21no—
309C4⋊C4—22no—
310C4⋊C4—21no—
311C4⋊C4—21no—
312C4⋊C4—41no—
313C4⋊C4—41no—
314C4⋊C4—42no—
315C22⋊C4—41no—
316C22⋊C4—41no—
317C22⋊C4—41no—
318C22⋊C4—41no—
319C42C2×D4×C1311yescharacteristic
320C42C2×D4×C1311yescharacteristic
321C42C2×D4×C1311yescharacteristic
322C42C13×#4111yescharacteristic
323C13#1022111yescharacteristic, direct product factor, Sylow
324C23—41no—
325C23—41no—
326C23C13×#12711yescharacteristic
327Q8—44no—
328Q8—42no—
329Q8—42no—
330Q8—82no—
331D4—42no—
332D4—42no—
333D4—42no—
334D4—42no—
335D4—81no—
336D4—81no—
337D4—81no—
338D4—81no—
339D4—81no—
340D4—81no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—42no—
346C2×C4—82no—
347C2×C4—82no—
348C2×C4—82no—
349C2×C4—81no—
350C2×C4—81no—
351C2×C4—81no—
352C2×C4C13×#12011yescharacteristic
353C2×C4C13×#12011yescharacteristic
354C2×C4C13×#12011yescharacteristic
355C2×C4C13×#12111yescharacteristic
356C2×C4C13×#12111yescharacteristic
357C2×C4C13×#12111yescharacteristic
358C2×C4C2×C13×SD1612yes—
359C2×C4C13×AGL(1,ℤ/8)12yes—
360C8—24no—
361C8—42no—
362C8—42no—
363C22—21no—
364C22—21no—
365C22—81no—
366C22—81no—
367C22—81no—
368C22—81no—
369C22—81no—
370C22—81no—
371C22C13×#39211yescharacteristic
372C22C13×#49211yescharacteristic
373C22C13×#49611yescharacteristic
374C4—21no—
375C4—21no—
376C4—21no—
377C4—21no—
378C4—82no—
379C4—81no—
380C4—81no—
381C4—161no—
382C4C13×#45012yes—
383C4C13×#46012yes—
384C2—21no—
385C2—21no—
386C2—161no—
387C2—161no—
388C2C13×#200811yescharacteristic
389C2C13×#200911yescharacteristic
390C2C13×#201411yescharacteristic
subgroupG/H
center, socleC22×C13#392
commutator, Frattini, cosocleC2×C42C23×C13
prime radicalC13×#3150C2
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
1. C13×#3227C2semidirect
2. C13×#3206C2semidirect
4. C13×#1993C2semidirect
5. C13×#1517C2semidirect
6. C13×#1517C2semidirect
7. C13×#1281C2semidirect
77. #10221C13direct (N × H)
111. C2×C8×C13SD16semidirect
129. #3227C2×C13semidirect
130. #3206C2×C13semidirect
132. #1993C2×C13semidirect
133. #1517C2×C13semidirect
134. #1517C2×C13semidirect
135. #1281C2×C13semidirect
305. C2×C8C13×SD16semidirect
323. C13#10221direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#32272
C13×#32062
C13×#31502
C13×#19932
C13×#15172
C13×#12812
#1022113