Finite Group Databasebeta

← C13×#9302 #15695641

Subgroups — C13×#9302 #15695641

Order 3328.

480 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3227C211yesmaximal, characteristic
2C13×#2331C211yesmaximal, characteristic, complemented
3C13×#1963C211yesmaximal, characteristic
4C13×#1549C211yesmaximal, characteristic, complemented
5C13×#1517C211yesmaximal, characteristic
6C13×#1286C211yesmaximal, characteristic, complemented
7C13×#1274C211yesmaximal, characteristic, complemented
8C13×#532C2211yescharacteristic
9C2×C13×C4⋊Q8C2211yescharacteristic
10C13×#498C412yescomplemented
11C13×#486C412yescomplemented
12C13×#481—22no—
13C13×#476—22no—
14C13×#431C2211yescharacteristic
15C13×#431C2211yescharacteristic
16C13×#423C2211yescharacteristic
17C2×C13×#104—21no—
18C2×C13×#104—21no—
19C13×#391—22no—
20C13×#389—21no—
21C13×#387—22no—
22C13×#382C2211yescharacteristic
23C4×C13×C4⋊C4—21no—
24C13×#376C2211yescharacteristic
25C13×#332—22no—
26C13×#327—22no—
27C2×C13×#41—21no—
28C22×Q8×C13—21no—
29C2×C13×M16—21no—
30C13×C4⋊Q8—21no—
31C13×C4⋊Q8—21no—
32C13×C4⋊Q8C2×C411yescharacteristic
33C13×C4⋊Q8C2×C412yes—
34C13×C4⋊Q8D412yes—
35C13×#127C2×C411yescharacteristic
36C13×#124—21no—
37C13×#121—21no—
38C13×#121—21no—
39C4×D4×C13—21no—
40C4×D4×C13—21no—
41C2×C13×C4⋊C4—21no—
42C2×C13×C4⋊C4—21no—
43C2×C13×C4⋊C4—22no—
44C2×C13×C4⋊C4D412yes—
45C2×C42×C13—22no—
46C2×C42×C13D411yescharacteristic
47C2×C42×C13D411yescharacteristic
48C2×C42×C13C2311yescharacteristic
49C13×#106—24no—
50C13×C4⋊C8—21no—
51C13×C4⋊C8—21no—
52C13×C4⋊C8—21no—
53C13×C4⋊C8—21no—
54C13×#104—42no—
55C13×#104—42no—
56C13×#102—24no—
57C13×C22⋊C8—21no—
58C13×C22⋊C8—21no—
59C4×C8×C13—21no—
60C4×C8×C13C2×C412yes—
61C13×#95—22no—
62C13×#95—22no—
63C13×#95—21no—
64C13×#95—21no—
65C13×#95—21no—
66C13×#95D412yes—
67#9302C1311yesmaximal, characteristic, direct product factor, Sylow
68C13×#41—41no—
69C13×#41—41no—
70C13×#41—41no—
71C13×#41—41no—
72C2×Q8×C13—22no—
73C2×Q8×C13—22no—
74C2×Q8×C13—21no—
75C2×Q8×C13—82no—
76C2×D4×C13—21no—
77C2×D4×C13—21no—
78C2×D4×C13—21no—
79C2×D4×C13—41no—
80C22×C4×C13—21no—
81C22×C4×C13—22no—
82C22×C4×C13—21no—
83C22×C4×C13—22no—
84C22×C4×C13—41no—
85C22×C4×C13C2×D411yescharacteristic
86C22×C4×C13C2×D411yescharacteristic
87C22×C4×C13C2×D411yescharacteristic
88C13×M16—41no—
89C13×M16—41no—
90C2×C8×C13—22no—
91C2×C8×C13—41no—
92C2×C8×C13—41no—
93C13×C4⋊C4—22no—
94C13×C4⋊C4—22no—
95C13×C4⋊C4—22no—
96C13×C4⋊C4—21no—
97C13×C4⋊C4—21no—
98C13×C4⋊C4—41no—
99C13×C4⋊C4—41no—
100C13×C4⋊C4—82no—
101C13×C4⋊C4C22⋊C414yes—
102C13×C22⋊C4—41no—
103C13×C22⋊C4—41no—
104C42×C13—21no—
105C42×C13—21no—
106C42×C13—21no—
107C42×C13—82no—
108C42×C13SD1612yes—
109C42×C13C22×C411yescharacteristic
110C42×C13C2×D411yescharacteristic
111C42×C13#4111yescharacteristic
112C42×C13#4111yescharacteristic
113#3227C2×C1311yescharacteristic
114#2331C2×C1311yescharacteristic, complemented
115#1963C2×C1311yescharacteristic
116#1549C2×C1311yescharacteristic, complemented
117#1517C2×C1311yescharacteristic
118#1286C2×C1311yescharacteristic, complemented
119#1274C2×C1311yescharacteristic, complemented
120C23×C13—41no—
121C23×C13#12011yescharacteristic
122Q8×C13—41no—
123Q8×C13—41no—
124Q8×C13—82no—
125Q8×C13—82no—
126D4×C13—42no—
127D4×C13—41no—
128D4×C13—41no—
129D4×C13—81no—
130D4×C13—81no—
131D4×C13—81no—
132C2×C4×C13—24no—
133C2×C4×C13—22no—
134C2×C4×C13—41no—
135C2×C4×C13—41no—
136C2×C4×C13—41no—
137C2×C4×C13—42no—
138C2×C4×C13—42no—
139C2×C4×C13—41no—
140C2×C4×C13—42no—
141C2×C4×C13—41no—
142C2×C4×C13—41no—
143C2×C4×C13—42no—
144C2×C4×C13—41no—
145C2×C4×C13—41no—
146C2×C4×C13—42no—
147C2×C4×C13—81no—
148C2×C4×C13—81no—
149C2×C4×C13C2×C22⋊C411yescharacteristic
150C2×C4×C13C4×D411yescharacteristic
151C2×C4×C13C4×D411yescharacteristic
152C2×C4×C13#12111yescharacteristic
153C2×C4×C13#12111yescharacteristic
154C2×C4×C13#12311yescharacteristic
155C2×C4×C13C2×SD1611yescharacteristic
156C2×C4×C13#13511yescharacteristic
157C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
158C2×C4×C13#13711yescharacteristic
159C8×C13—42no—
160C8×C13—81no—
161C8×C13—81no—
162#532C22×C1311yescharacteristic
163C2×C4⋊Q8C22×C1311yescharacteristic
164#498C4×C1312yescomplemented
165#486C4×C1312yescomplemented
166#481—22no—
167#476—22no—
168#431C22×C1311yescharacteristic
169#431C22×C1311yescharacteristic
170#423C22×C1311yescharacteristic
171C2×#104—21no—
172C2×#104—21no—
173#391—22no—
174#389—21no—
175#387—22no—
176#382C22×C1311yescharacteristic
177C4×C4⋊C4—21no—
178#376C22×C1311yescharacteristic
179#332—22no—
180#327—22no—
181C22×C13—21no—
182C22×C13—21no—
183C22×C13—81no—
184C22×C13—81no—
185C22×C13—81no—
186C22×C13#38611yescharacteristic
187C22×C13#44811yescharacteristic
188C22×C13#44911yescharacteristic
189C4×C13—21no—
190C4×C13—21no—
191C4×C13—21no—
192C4×C13—21no—
193C4×C13—42no—
194C4×C13—44no—
195C4×C13—82no—
196C4×C13—81no—
197C4×C13—81no—
198C4×C13C4×SD1611yescharacteristic
199C4×C13#44011yescharacteristic
200C4×C13#46011yescharacteristic
201C4×C13#46411yescharacteristic
202C2×#41—21no—
203C22×Q8—21no—
204C2×M16—21no—
205C4⋊Q8—21no—
206C4⋊Q8—21no—
207C4⋊Q8C2×C4×C1311yescharacteristic
208C4⋊Q8C2×C4×C1312yes—
209C4⋊Q8D4×C1312yes—
210#127C2×C4×C1311yescharacteristic
211#124—21no—
212#121—21no—
213#121—21no—
214C4×D4—21no—
215C4×D4—21no—
216C2×C4⋊C4—21no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4—22no—
219C2×C4⋊C4D4×C1312yes—
220C2×C42—22no—
221C2×C42D4×C1311yescharacteristic
222C2×C42D4×C1311yescharacteristic
223C2×C42C23×C1311yescharacteristic
224#106—24no—
225C4⋊C8—21no—
226C4⋊C8—21no—
227C4⋊C8—21no—
228C4⋊C8—21no—
229#104—42no—
230#104—42no—
231#102—24no—
232C22⋊C8—21no—
233C22⋊C8—21no—
234C4×C8—21no—
235C4×C8C2×C4×C1312yes—
236#95—22no—
237#95—22no—
238#95—21no—
239#95—21no—
240#95—21no—
241#95D4×C1312yes—
242C2×C13—21no—
243C2×C13—21no—
244C2×C13—161no—
245C2×C13#188011yescharacteristic
246C2×C13#190411yescharacteristic
247C2×C13#191211yescharacteristic
248#41—41no—
249#41—41no—
250#41—41no—
251#41—41no—
252C2×Q8—22no—
253C2×Q8—22no—
254C2×Q8—21no—
255C2×Q8—82no—
256C2×D4—21no—
257C2×D4—21no—
258C2×D4—21no—
259C2×D4—41no—
260C22×C4—21no—
261C22×C4—22no—
262C22×C4—21no—
263C22×C4—22no—
264C22×C4—41no—
265C22×C4C2×D4×C1311yescharacteristic
266C22×C4C2×D4×C1311yescharacteristic
267C22×C4C2×D4×C1311yescharacteristic
268M16—41no—
269M16—41no—
270C2×C8—22no—
271C2×C8—41no—
272C2×C8—41no—
273C4⋊C4—22no—
274C4⋊C4—22no—
275C4⋊C4—22no—
276C4⋊C4—21no—
277C4⋊C4—21no—
278C4⋊C4—41no—
279C4⋊C4—41no—
280C4⋊C4—82no—
281C4⋊C4C13×C22⋊C414yes—
282C22⋊C4—41no—
283C22⋊C4—41no—
284C42—21no—
285C42—21no—
286C42—21no—
287C42—82no—
288C42C13×SD1612yes—
289C42C22×C4×C1311yescharacteristic
290C42C2×D4×C1311yescharacteristic
291C42C13×#4111yescharacteristic
292C42C13×#4111yescharacteristic
293C13#930211yescharacteristic, direct product factor, Sylow
294C23—41no—
295C23C13×#12011yescharacteristic
296Q8—41no—
297Q8—41no—
298Q8—82no—
299Q8—82no—
300D4—42no—
301D4—41no—
302D4—41no—
303D4—81no—
304D4—81no—
305D4—81no—
306C2×C4—24no—
307C2×C4—22no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—41no—
314C2×C4—42no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—42no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—42no—
321C2×C4—81no—
322C2×C4—81no—
323C2×C4C2×C13×C22⋊C411yescharacteristic
324C2×C4C4×D4×C1311yescharacteristic
325C2×C4C4×D4×C1311yescharacteristic
326C2×C4C13×#12111yescharacteristic
327C2×C4C13×#12111yescharacteristic
328C2×C4C13×#12311yescharacteristic
329C2×C4C2×C13×SD1611yescharacteristic
330C2×C4C13×#13511yescharacteristic
331C2×C4C13×AGL(1,ℤ/8)11yescharacteristic
332C2×C4C13×#13711yescharacteristic
333C8—42no—
334C8—81no—
335C8—81no—
336C22—21no—
337C22—21no—
338C22—81no—
339C22—81no—
340C22—81no—
341C22C13×#38611yescharacteristic
342C22C13×#44811yescharacteristic
343C22C13×#44911yescharacteristic
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—42no—
349C4—44no—
350C4—82no—
351C4—81no—
352C4—81no—
353C4C4×C13×SD1611yescharacteristic
354C4C13×#44011yescharacteristic
355C4C13×#46011yescharacteristic
356C4C13×#46411yescharacteristic
357C2—21no—
358C2—21no—
359C2—161no—
360C2C13×#188011yescharacteristic
361C2C13×#190411yescharacteristic
362C2C13×#191211yescharacteristic
subgroupG/H
center, socleC22×C13#386
commutatorC42C22×C4×C13
Frattini, cosocleC2×C42C23×C13
prime radicalC13×#532C22
LCSG ▷ 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×#2331C2semidirect
4. C13×#1549C2semidirect
6. C13×#1286C2semidirect
7. C13×#1274C2semidirect
10. C13×#498C4semidirect
11. C13×#486C4semidirect
67. #9302C13direct (N × H)
114. #2331C2×C13semidirect
116. #1549C2×C13semidirect
118. #1286C2×C13semidirect
119. #1274C2×C13semidirect
164. #498C4×C13semidirect
165. #486C4×C13semidirect
293. C13#9302direct (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×#23312
C13×#19632
C13×#15492
C13×#15172
C13×#12862
C13×#12742
#930213