Finite Group Databasebeta

← C13×#7674 #15694013

Subgroups — C13×#7674 #15694013

Order 3328.

550 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#2854C211yesmaximal, characteristic
2C13×#1749C211yesmaximal, characteristic, complemented
3C4×C13×C22⋊C8C211yesmaximal, characteristic, complemented
4C13×#1271C212yesmaximal, complemented
5C13×#1270C212yesmaximal, complemented
6C2×C13×#123—21no—
7C2×C13×#121C411yescharacteristic
8C22×C42×C13C2211yescharacteristic
9C2×C13×C22⋊C8—21no—
10C2×C13×C22⋊C8—21no—
11C2×C13×#97—21no—
12C2×C4×C8×C13—21no—
13C13×#390C411yescharacteristic
14C13×#390C2211yescharacteristic
15C13×#389C411yescharacteristic
16C13×#389C2211yescharacteristic
17C13×#388—21no—
18C13×#388—21no—
19C13×#386—21no—
20C13×#380C411yescharacteristic
21C13×#336C2212yes—
22C13×#336C2212yes—
23C22×D4×C13—21no—
24C22×D4×C13C2×C411yescharacteristic
25C23×C4×C13C2×C411yescharacteristic
26C23×C4×C13D411yescharacteristic
27C23×C4×C13D411yescharacteristic
28C22×C8×C13—22no—
29C22×C8×C13—22no—
30C13×#123—44no—
31C13×#121—42no—
32C2×C13×C4⋊C4—21no—
33C2×C13×C4⋊C4—21no—
34C2×C13×C4⋊C4C2×C411yescharacteristic
35C2×C13×C4⋊C4C2×C411yescharacteristic
36C2×C13×C4⋊C4C2×C411yescharacteristic
37C2×C13×C22⋊C4—21no—
38C2×C13×C22⋊C4—21no—
39C2×C13×C22⋊C4—21no—
40C2×C13×C22⋊C4—21no—
41C2×C13×C22⋊C4—21no—
42C2×C13×C22⋊C4—21no—
43C2×C42×C13—42no—
44C2×C42×C13C2×C411yescharacteristic
45C2×C42×C13D411yescharacteristic
46C2×C42×C13D411yescharacteristic
47C2×C42×C13C2311yescharacteristic
48C13×C22⋊C8—24no—
49C13×C22⋊C8—24no—
50C13×#97—42no—
51C4×C8×C13—42no—
52C13×#95—21no—
53C13×#95—21no—
54C13×#95—21no—
55#7674C1311yesmaximal, characteristic, direct product factor, Sylow
56C24×C13—21no—
57C24×C13C22⋊C411yescharacteristic
58C2×D4×C13—22no—
59C2×D4×C13—41no—
60C2×D4×C13—41no—
61C2×D4×C13—42no—
62C2×D4×C13—42no—
63C2×D4×C13—42no—
64C22×C4×C13—22no—
65C22×C4×C13—22no—
66C22×C4×C13—22no—
67C22×C4×C13—22no—
68C22×C4×C13—22no—
69C22×C4×C13—22no—
70C22×C4×C13—21no—
71C22×C4×C13—21no—
72C22×C4×C13—21no—
73C22×C4×C13—41no—
74C22×C4×C13—41no—
75C22×C4×C13—41no—
76C22×C4×C13C22⋊C411yescharacteristic
77C22×C4×C13C22⋊C411yescharacteristic
78C22×C4×C13C22⋊C411yescharacteristic
79C22×C4×C13C22×C411yescharacteristic
80C22×C4×C13C2×D411yescharacteristic
81C22×C4×C13C2×D411yescharacteristic
82C2×C8×C13—24no—
83C2×C8×C13—24no—
84C2×C8×C13—42no—
85C2×C8×C13—42no—
86C2×C8×C13—42no—
87C2×C8×C13—42no—
88C13×C4⋊C4—22no—
89C13×C4⋊C4—41no—
90C13×C4⋊C4—41no—
91C13×C4⋊C4—42no—
92C13×C4⋊C4—42no—
93C13×C22⋊C4—42no—
94C13×C22⋊C4—42no—
95C13×C22⋊C4—42no—
96C13×C22⋊C4—42no—
97C13×C22⋊C4—42no—
98C13×C22⋊C4—42no—
99C42×C13—22no—
100C42×C13—22no—
101C42×C13—41no—
102C42×C13—41no—
103#2854C2×C1311yescharacteristic
104#1749C2×C1311yescharacteristic, complemented
105C4×C22⋊C8C2×C1311yescharacteristic, complemented
106#1271C2×C1312yescomplemented
107#1270C2×C1312yescomplemented
108C23×C13—21no—
109C23×C13—21no—
110C23×C13—21no—
111C23×C13—21no—
112C23×C13—21no—
113C23×C13—21no—
114C23×C13—41no—
115C23×C13—41no—
116C23×C13—41no—
117C23×C13—41no—
118C23×C13—41no—
119C23×C13—41no—
120C23×C13—41no—
121C23×C13#10412yes—
122C23×C13C2×C22⋊C411yescharacteristic
123D4×C13—82no—
124D4×C13—84no—
125C2×C4×C13—21no—
126C2×C4×C13—21no—
127C2×C4×C13—21no—
128C2×C4×C13—21no—
129C2×C4×C13—21no—
130C2×C4×C13—21no—
131C2×C4×C13—21no—
132C2×C4×C13—21no—
133C2×C4×C13—21no—
134C2×C4×C13—21no—
135C2×C4×C13—21no—
136C2×C4×C13—21no—
137C2×C4×C13—21no—
138C2×C4×C13—44no—
139C2×C4×C13—44no—
140C2×C4×C13—44no—
141C2×C4×C13—41no—
142C2×C4×C13—41no—
143C2×C4×C13—41no—
144C2×C4×C13—41no—
145C2×C4×C13—41no—
146C2×C4×C13—41no—
147C2×C4×C13—41no—
148C2×C4×C13—41no—
149C2×C4×C13—41no—
150C2×C4×C13#9912yes—
151C2×C4×C13#10412yes—
152C2×C4×C13#13112yes—
153C2×C4×C13#13512yes—
154C2×C4×C13AGL(1,ℤ/8)12yes—
155C8×C13—44no—
156C8×C13—44no—
157C2×#123—21no—
158C2×#121C4×C1311yescharacteristic
159C22×C42C22×C1311yescharacteristic
160C2×C22⋊C8—21no—
161C2×C22⋊C8—21no—
162C2×#97—21no—
163C2×C4×C8—21no—
164#390C4×C1311yescharacteristic
165#390C22×C1311yescharacteristic
166#389C4×C1311yescharacteristic
167#389C22×C1311yescharacteristic
168#388—21no—
169#388—21no—
170#386—21no—
171#380C4×C1311yescharacteristic
172#336C22×C1312yes—
173#336C22×C1312yes—
174C22×C13—22no—
175C22×C13—22no—
176C22×C13—22no—
177C22×C13—41no—
178C22×C13—41no—
179C22×C13—41no—
180C22×C13—41no—
181C22×C13—81no—
182C22×C13—81no—
183C22×C13—81no—
184C22×C13—81no—
185C22×C13—81no—
186C22×C13—81no—
187C22×C13—81no—
188C22×C13#40811yescharacteristic
189C22×C13C2×#9911yescharacteristic
190C22×C13#41311yescharacteristic
191C22×C13#41611yescharacteristic
192C22×C13#41811yescharacteristic
193C22×C13C2×#10411yescharacteristic
194C22×C13C2×#10411yescharacteristic
195C4×C13—22no—
196C4×C13—22no—
197C4×C13—22no—
198C4×C13—22no—
199C4×C13—22no—
200C4×C13—41no—
201C4×C13—81no—
202C4×C13—81no—
203C4×C13—81no—
204C22×D4—21no—
205C22×D4C2×C4×C1311yescharacteristic
206C23×C4C2×C4×C1311yescharacteristic
207C23×C4D4×C1311yescharacteristic
208C23×C4D4×C1311yescharacteristic
209C22×C8—22no—
210C22×C8—22no—
211#123—44no—
212#121—42no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4C2×C4×C1311yescharacteristic
216C2×C4⋊C4C2×C4×C1311yescharacteristic
217C2×C4⋊C4C2×C4×C1311yescharacteristic
218C2×C22⋊C4—21no—
219C2×C22⋊C4—21no—
220C2×C22⋊C4—21no—
221C2×C22⋊C4—21no—
222C2×C22⋊C4—21no—
223C2×C22⋊C4—21no—
224C2×C42—42no—
225C2×C42C2×C4×C1311yescharacteristic
226C2×C42D4×C1311yescharacteristic
227C2×C42D4×C1311yescharacteristic
228C2×C42C23×C1311yescharacteristic
229C22⋊C8—24no—
230C22⋊C8—24no—
231#97—42no—
232C4×C8—42no—
233#95—21no—
234#95—21no—
235#95—21no—
236C2×C13—42no—
237C2×C13—161no—
238C2×C13#146811yescharacteristic
239C2×C13#148411yescharacteristic
240C2×C13#149411yescharacteristic
241C2×C13#150111yescharacteristic
242C2×C13#150711yescharacteristic
243C2×C13#152411yescharacteristic
244C2×C13#155311yescharacteristic
245C24—21no—
246C24C13×C22⋊C411yescharacteristic
247C2×D4—22no—
248C2×D4—41no—
249C2×D4—41no—
250C2×D4—42no—
251C2×D4—42no—
252C2×D4—42no—
253C22×C4—22no—
254C22×C4—22no—
255C22×C4—22no—
256C22×C4—22no—
257C22×C4—22no—
258C22×C4—22no—
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—41no—
263C22×C4—41no—
264C22×C4—41no—
265C22×C4C13×C22⋊C411yescharacteristic
266C22×C4C13×C22⋊C411yescharacteristic
267C22×C4C13×C22⋊C411yescharacteristic
268C22×C4C22×C4×C1311yescharacteristic
269C22×C4C2×D4×C1311yescharacteristic
270C22×C4C2×D4×C1311yescharacteristic
271C2×C8—24no—
272C2×C8—24no—
273C2×C8—42no—
274C2×C8—42no—
275C2×C8—42no—
276C2×C8—42no—
277C4⋊C4—22no—
278C4⋊C4—41no—
279C4⋊C4—41no—
280C4⋊C4—42no—
281C4⋊C4—42no—
282C22⋊C4—42no—
283C22⋊C4—42no—
284C22⋊C4—42no—
285C22⋊C4—42no—
286C22⋊C4—42no—
287C22⋊C4—42no—
288C42—22no—
289C42—22no—
290C42—41no—
291C42—41no—
292C13#767411yescharacteristic, direct product factor, Sylow
293C23—21no—
294C23—21no—
295C23—21no—
296C23—21no—
297C23—21no—
298C23—21no—
299C23—41no—
300C23—41no—
301C23—41no—
302C23—41no—
303C23—41no—
304C23—41no—
305C23—41no—
306C23C13×#10412yes—
307C23C2×C13×C22⋊C411yescharacteristic
308D4—82no—
309D4—84no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—44no—
324C2×C4—44no—
325C2×C4—44no—
326C2×C4—41no—
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×C4C13×#9912yes—
336C2×C4C13×#10412yes—
337C2×C4C13×#13112yes—
338C2×C4C13×#13512yes—
339C2×C4C13×AGL(1,ℤ/8)12yes—
340C8—44no—
341C8—44no—
342C22—22no—
343C22—22no—
344C22—22no—
345C22—41no—
346C22—41no—
347C22—41no—
348C22—41no—
349C22—81no—
350C22—81no—
351C22—81no—
352C22—81no—
353C22—81no—
354C22—81no—
355C22—81no—
356C22C13×#40811yescharacteristic
357C22C2×C13×#9911yescharacteristic
358C22C13×#41311yescharacteristic
359C22C13×#41611yescharacteristic
360C22C13×#41811yescharacteristic
361C22C2×C13×#10411yescharacteristic
362C22C2×C13×#10411yescharacteristic
363C4—22no—
364C4—22no—
365C4—22no—
366C4—22no—
367C4—22no—
368C4—41no—
369C4—81no—
370C4—81no—
371C4—81no—
372C2—42no—
373C2—161no—
374C2C13×#146811yescharacteristic
375C2C13×#148411yescharacteristic
376C2C13×#149411yescharacteristic
377C2C13×#150111yescharacteristic
378C2C13×#150711yescharacteristic
379C2C13×#152411yescharacteristic
380C2C13×#155311yescharacteristic
subgroupG/H
center, socleC23×C13C2×C22⋊C4
commutatorC22×C4C22×C4×C13
Frattini, cosocleC2×C42C23×C13
prime radicalC2×C13×#121C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C13 ◁ C22×C42×C13 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C13×#1749C2semidirect
3. C4×C13×C22⋊C8C2semidirect
4. C13×#1271C2semidirect
5. C13×#1270C2semidirect
55. #7674C13direct (N × H)
104. #1749C2×C13semidirect
105. C4×C22⋊C8C2×C13semidirect
106. #1271C2×C13semidirect
107. #1270C2×C13semidirect
292. C13#7674direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#28542
C13×#17492
C4×C13×C22⋊C82
C13×#12712
C13×#12702
#767413