Finite Group Databasebeta

← C13×#10521 #15696860

Subgroups — C13×#10521 #15696860

Order 3328.

420 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×#1994C211yesmaximal, characteristic, complemented
3C13×#1962C211yesmaximal, characteristic
4C13×#1831C211yesmaximal, characteristic, complemented
5C13×#1550C211yesmaximal, characteristic, complemented
6C13×#1547C211yesmaximal, characteristic
7C13×#1292C211yesmaximal, characteristic, complemented
8C13×#533C2211yescharacteristic
9C13×#532C2211yescharacteristic
10C13×#476—21no—
11C13×#475—21no—
12C13×#465—22no—
13C13×#461—21no—
14C13×#460—21no—
15C13×#423C2211yescharacteristic
16C13×#423C2211yescharacteristic
17C2×C13×C4⋊C8C2211yescharacteristic
18C2×C13×C4⋊C8C2211yescharacteristic
19C2×C13×#104—21no—
20C2×C13×#104—21no—
21C43×C13C2211yescharacteristic
22C13×#339—21no—
23C13×#339—21no—
24C13×#336—22no—
25C13×#333—21no—
26C13×#332—21no—
27C13×#332—21no—
28C13×#331—21no—
29C2×C13×#41—21no—
30C2×C13×SD16—22no—
31C2×C13×M16—21no—
32C2×C13×M16—21no—
33C22×C8×C13—21no—
34C22×C8×C13D412yes—
35C13×C4⋊Q8D411yescharacteristic
36C13×C4⋊Q8D411yescharacteristic
37C13×C4⋊Q8D411yescharacteristic
38C13×#127D411yescharacteristic
39C13×#125—21no—
40C13×#124—21no—
41C13×C22⋊Q8—21no—
42C13×C22⋊Q8—21no—
43C13×#121—21no—
44C13×#121—21no—
45C4×Q8×C13—21no—
46C4×Q8×C13—21no—
47C4×D4×C13—21no—
48C4×D4×C13—21no—
49C13×#117—21no—
50C2×C42×C13—21no—
51C2×C42×C13—21no—
52C2×C42×C13D411yescharacteristic
53C2×C42×C13D411yescharacteristic
54C2×C42×C13C2311yescharacteristic
55C13×#106—22no—
56C13×C4⋊C8—21no—
57C13×C4⋊C8—21no—
58C13×C4⋊C8—21no—
59C13×C4⋊C8—21no—
60C13×C4⋊C8—21no—
61C13×C4⋊C8—21no—
62C13×C4⋊C8—21no—
63C13×C4⋊C8—21no—
64C13×#104—42no—
65C13×#104—42no—
66C13×#103—22no—
67C13×#102—22no—
68#10521C1311yesmaximal, characteristic, direct product factor, Sylow
69C13×#41—41no—
70C13×#41—41no—
71C13×#41—41no—
72C13×#41—41no—
73C2×Q8×C13—21no—
74C2×Q8×C13—21no—
75C2×Q8×C13—21no—
76C2×D4×C13—21no—
77C2×D4×C13—21no—
78C2×D4×C13—21no—
79C2×D4×C13—41no—
80C22×C4×C13—21no—
81C22×C4×C13—21no—
82C22×C4×C13—41no—
83C22×C4×C13C2×D411yescharacteristic
84C22×C4×C13C2×D411yescharacteristic
85C22×C4×C13#4111yescharacteristic
86C13×SD16—82no—
87C13×M16—41no—
88C13×M16—41no—
89C13×M16—41no—
90C13×M16—41no—
91C2×C8×C13—22no—
92C2×C8×C13—42no—
93C2×C8×C13—42no—
94C2×C8×C13—41no—
95C2×C8×C13—41no—
96C2×C8×C13—41no—
97C13×C4⋊C4—21no—
98C13×C4⋊C4—21no—
99C13×C4⋊C4—21no—
100C13×C4⋊C4—21no—
101C13×C4⋊C4—21no—
102C13×C4⋊C4—21no—
103C13×C4⋊C4—41no—
104C13×C4⋊C4—41no—
105C13×C22⋊C4—41no—
106C13×C22⋊C4—41no—
107C13×C22⋊C4—41no—
108C42×C13—21no—
109C42×C13—21no—
110C42×C13—21no—
111C42×C13—41no—
112C42×C13—41no—
113C42×C13—42no—
114C42×C13—41no—
115C42×C13SD1612yescomplemented
116C42×C13C2×D411yescharacteristic
117C42×C13C2×D411yescharacteristic
118C42×C13#4111yescharacteristic
119C42×C13#4111yescharacteristic
120#3246C2×C1311yescharacteristic
121#1994C2×C1311yescharacteristic, complemented
122#1962C2×C1311yescharacteristic
123#1831C2×C1311yescharacteristic, complemented
124#1550C2×C1311yescharacteristic, complemented
125#1547C2×C1311yescharacteristic
126#1292C2×C1311yescharacteristic, complemented
127C23×C13—41no—
128C23×C13#12111yescharacteristic
129Q8×C13—41no—
130Q8×C13—41no—
131Q8×C13—41no—
132Q8×C13—41no—
133Q8×C13—81no—
134D4×C13—41no—
135D4×C13—41no—
136D4×C13—41no—
137D4×C13—41no—
138D4×C13—81no—
139D4×C13—81no—
140D4×C13—81no—
141C2×C4×C13—21no—
142C2×C4×C13—21no—
143C2×C4×C13—22no—
144C2×C4×C13—22no—
145C2×C4×C13—41no—
146C2×C4×C13—41no—
147C2×C4×C13—41no—
148C2×C4×C13—41no—
149C2×C4×C13—41no—
150C2×C4×C13—41no—
151C2×C4×C13—41no—
152C2×C4×C13—41no—
153C2×C4×C13—81no—
154C2×C4×C13—81no—
155C2×C4×C13#12011yescharacteristic
156C2×C4×C13#12111yescharacteristic
157C2×C4×C13#12111yescharacteristic
158C2×C4×C13#12311yescharacteristic
159C2×C4×C13#12311yescharacteristic
160C2×C4×C13#12411yescharacteristic
161C2×C4×C13C2×SD1611yescharacteristic
162C2×C4×C13#13511yescharacteristic
163C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
164C2×C4×C13#13711yescharacteristic
165C8×C13—42no—
166C8×C13—81no—
167C8×C13—81no—
168C8×C13—81no—
169#533C22×C1311yescharacteristic
170#532C22×C1311yescharacteristic
171#476—21no—
172#475—21no—
173#465—22no—
174#461—21no—
175#460—21no—
176#423C22×C1311yescharacteristic
177#423C22×C1311yescharacteristic
178C2×C4⋊C8C22×C1311yescharacteristic
179C2×C4⋊C8C22×C1311yescharacteristic
180C2×#104—21no—
181C2×#104—21no—
182C43C22×C1311yescharacteristic
183#339—21no—
184#339—21no—
185#336—22no—
186#333—21no—
187#332—21no—
188#332—21no—
189#331—21no—
190C22×C13—21no—
191C22×C13—21no—
192C22×C13—81no—
193C22×C13—81no—
194C22×C13—81no—
195C22×C13#39411yescharacteristic
196C22×C13#46511yescharacteristic
197C22×C13#46811yescharacteristic
198C4×C13—21no—
199C4×C13—21no—
200C4×C13—21no—
201C4×C13—42no—
202C4×C13—42no—
203C4×C13—81no—
204C4×C13—81no—
205C4×C13—81no—
206C4×C13#45411yescharacteristic
207C4×C13#45511yescharacteristic
208C4×C13#46011yescharacteristic
209C4×C13#46111yescharacteristic
210C4×C13#46311yescharacteristic
211C4×C13#46411yescharacteristic
212C2×#41—21no—
213C2×SD16—22no—
214C2×M16—21no—
215C2×M16—21no—
216C22×C8—21no—
217C22×C8D4×C1312yes—
218C4⋊Q8D4×C1311yescharacteristic
219C4⋊Q8D4×C1311yescharacteristic
220C4⋊Q8D4×C1311yescharacteristic
221#127D4×C1311yescharacteristic
222#125—21no—
223#124—21no—
224C22⋊Q8—21no—
225C22⋊Q8—21no—
226#121—21no—
227#121—21no—
228C4×Q8—21no—
229C4×Q8—21no—
230C4×D4—21no—
231C4×D4—21no—
232#117—21no—
233C2×C42—21no—
234C2×C42—21no—
235C2×C42D4×C1311yescharacteristic
236C2×C42D4×C1311yescharacteristic
237C2×C42C23×C1311yescharacteristic
238#106—22no—
239C4⋊C8—21no—
240C4⋊C8—21no—
241C4⋊C8—21no—
242C4⋊C8—21no—
243C4⋊C8—21no—
244C4⋊C8—21no—
245C4⋊C8—21no—
246C4⋊C8—21no—
247#104—42no—
248#104—42no—
249#103—22no—
250#102—22no—
251C2×C13—21no—
252C2×C13—21no—
253C2×C13—161no—
254C2×C13#204011yescharacteristic
255C2×C13#205011yescharacteristic
256C2×C13#205511yescharacteristic
257#41—41no—
258#41—41no—
259#41—41no—
260#41—41no—
261C2×Q8—21no—
262C2×Q8—21no—
263C2×Q8—21no—
264C2×D4—21no—
265C2×D4—21no—
266C2×D4—21no—
267C2×D4—41no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—41no—
271C22×C4C2×D4×C1311yescharacteristic
272C22×C4C2×D4×C1311yescharacteristic
273C22×C4C13×#4111yescharacteristic
274SD16—82no—
275M16—41no—
276M16—41no—
277M16—41no—
278M16—41no—
279C2×C8—22no—
280C2×C8—42no—
281C2×C8—42no—
282C2×C8—41no—
283C2×C8—41no—
284C2×C8—41no—
285C4⋊C4—21no—
286C4⋊C4—21no—
287C4⋊C4—21no—
288C4⋊C4—21no—
289C4⋊C4—21no—
290C4⋊C4—21no—
291C4⋊C4—41no—
292C4⋊C4—41no—
293C22⋊C4—41no—
294C22⋊C4—41no—
295C22⋊C4—41no—
296C42—21no—
297C42—21no—
298C42—21no—
299C42—41no—
300C42—41no—
301C42—42no—
302C42—41no—
303C42C13×SD1612yescomplemented
304C42C2×D4×C1311yescharacteristic
305C42C2×D4×C1311yescharacteristic
306C42C13×#4111yescharacteristic
307C42C13×#4111yescharacteristic
308C13#1052111yescharacteristic, direct product factor, Sylow
309C23—41no—
310C23C13×#12111yescharacteristic
311Q8—41no—
312Q8—41no—
313Q8—41no—
314Q8—41no—
315Q8—81no—
316D4—41no—
317D4—41no—
318D4—41no—
319D4—41no—
320D4—81no—
321D4—81no—
322D4—81no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—22no—
326C2×C4—22no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—81no—
336C2×C4—81no—
337C2×C4C13×#12011yescharacteristic
338C2×C4C13×#12111yescharacteristic
339C2×C4C13×#12111yescharacteristic
340C2×C4C13×#12311yescharacteristic
341C2×C4C13×#12311yescharacteristic
342C2×C4C13×#12411yescharacteristic
343C2×C4C2×C13×SD1611yescharacteristic
344C2×C4C13×#13511yescharacteristic
345C2×C4C13×AGL(1,ℤ/8)11yescharacteristic
346C2×C4C13×#13711yescharacteristic
347C8—42no—
348C8—81no—
349C8—81no—
350C8—81no—
351C22—21no—
352C22—21no—
353C22—81no—
354C22—81no—
355C22—81no—
356C22C13×#39411yescharacteristic
357C22C13×#46511yescharacteristic
358C22C13×#46811yescharacteristic
359C4—21no—
360C4—21no—
361C4—21no—
362C4—42no—
363C4—42no—
364C4—81no—
365C4—81no—
366C4—81no—
367C4C13×#45411yescharacteristic
368C4C13×#45511yescharacteristic
369C4C13×#46011yescharacteristic
370C4C13×#46111yescharacteristic
371C4C13×#46311yescharacteristic
372C4C13×#46411yescharacteristic
373C2—21no—
374C2—21no—
375C2—161no—
376C2C13×#204011yescharacteristic
377C2C13×#205011yescharacteristic
378C2C13×#205511yescharacteristic
subgroupG/H
center, socleC22×C13#394
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×#1994C2semidirect
4. C13×#1831C2semidirect
5. C13×#1550C2semidirect
7. C13×#1292C2semidirect
68. #10521C13direct (N × H)
115. C42×C13SD16semidirect
121. #1994C2×C13semidirect
123. #1831C2×C13semidirect
124. #1550C2×C13semidirect
126. #1292C2×C13semidirect
303. C42C13×SD16semidirect
308. C13#10521direct (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×#19942
C13×#19622
C13×#18312
C13×#15502
C13×#15472
C13×#12922
#1052113