Finite Group Databasebeta

← C13×#9722 #15696061

Subgroups — C13×#9722 #15696061

Order 3328.

460 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×#3167C211yesmaximal, characteristic
2C13×#1986C211yesmaximal, characteristic, complemented
3C13×#1980C211yesmaximal, characteristic
4C4×C13×#107C211yesmaximal, characteristic, complemented
5C13×#1503C211yesmaximal, characteristic, complemented
6C13×#1502C211yesmaximal, characteristic
7C13×#1451C211yesmaximal, characteristic, complemented
8C13×#533C2211yescharacteristic
9C13×#532C2211yescharacteristic
10C13×#498C411yescharacteristic, complemented
11C13×#492C411yescharacteristic, complemented
12C13×#487C411yescharacteristic, complemented
13C13×#486C411yescharacteristic, complemented
14C13×#465—21no—
15C13×#465—21no—
16C4×C13×SD16—21no—
17C4×C13×SD16—21no—
18C13×#431C2211yescharacteristic
19C2×C13×#107—21no—
20C2×C13×#104—22no—
21C4×C13×M16C2211yescharacteristic
22C2×C4×C8×C13C2211yescharacteristic
23C4×C13×C4⋊C4C2211yescharacteristic
24C4×C13×C4⋊C4C2211yescharacteristic
25C13×#340—21no—
26C13×#339—22no—
27C13×#328—22no—
28C13×#327—22no—
29C13×#322—21no—
30C13×#322—21no—
31C2×C13×#41—21no—
32C2×C13×SD16—21no—
33C2×C13×SD16—21no—
34C2×C13×M16D412yes—
35C22×C8×C13D411yescharacteristic
36C22×C8×C13D411yescharacteristic
37C13×C4⋊Q8C2×C411yescharacteristic
38C13×C4⋊Q8C2×C411yescharacteristic
39C13×C4⋊Q8C2×C411yescharacteristic
40C13×#127C2×C411yescharacteristic
41C13×#125—21no—
42C13×#124—21no—
43C13×C22⋊Q8—21no—
44C13×C22⋊Q8—21no—
45C13×#121—21no—
46C13×#121—21no—
47C4×Q8×C13—21no—
48C4×Q8×C13—21no—
49C4×D4×C13—21no—
50C4×D4×C13—21no—
51C13×#117—21no—
52C2×C13×C4⋊C4—21no—
53C2×C13×C4⋊C4—21no—
54C2×C42×C13—21no—
55C2×C42×C13—21no—
56C2×C42×C13C2311yescharacteristic
57C13×#107—24no—
58C13×#106—21no—
59C13×#106—21no—
60C13×C4⋊C8—21no—
61C13×#104—44no—
62C13×#103—21no—
63C13×#103—21no—
64C13×#102—21no—
65C13×#102—21no—
66C13×C22⋊C8D412yes—
67C13×#97—21no—
68C4×C8×C13—21no—
69C4×C8×C13—21no—
70C4×C8×C13C2×C411yescharacteristic
71C4×C8×C13C2×C411yescharacteristic
72C4×C8×C13D411yescharacteristic
73C4×C8×C13D411yescharacteristic
74C13×#95—21no—
75C13×#95—21no—
76#9722C1311yesmaximal, characteristic, direct product factor, Sylow
77C13×#41—42no—
78C13×#41—42no—
79C2×Q8×C13—21no—
80C2×Q8×C13—21no—
81C2×Q8×C13—21no—
82C2×D4×C13—21no—
83C2×D4×C13—21no—
84C2×D4×C13—21no—
85C2×D4×C13—41no—
86C22×C4×C13—41no—
87C22×C4×C13—41no—
88C22×C4×C13—41no—
89C22×C4×C13C2×D411yescharacteristic
90C22×C4×C13C2×D411yescharacteristic
91C22×C4×C13C2×D411yescharacteristic
92C13×SD16—42no—
93C13×SD16—42no—
94C13×M16—22no—
95C13×M16—22no—
96C2×C8×C13—22no—
97C2×C8×C13—22no—
98C2×C8×C13—22no—
99C2×C8×C13—41no—
100C2×C8×C13C22⋊C411yescharacteristic
101C2×C8×C13C22⋊C411yescharacteristic
102C2×C8×C13C22⋊C411yescharacteristic
103C2×C8×C13C22⋊C411yescharacteristic
104C13×C4⋊C4—22no—
105C13×C4⋊C4—22no—
106C13×C4⋊C4—21no—
107C13×C4⋊C4—21no—
108C13×C4⋊C4—21no—
109C13×C4⋊C4—21no—
110C13×C4⋊C4—21no—
111C13×C4⋊C4—21no—
112C13×C4⋊C4—41no—
113C13×C4⋊C4—41no—
114C13×C4⋊C4—41no—
115C13×C4⋊C4—41no—
116C13×C22⋊C4—41no—
117C13×C22⋊C4—41no—
118C13×C22⋊C4—41no—
119C42×C13—41no—
120C42×C13—42no—
121C42×C13—42no—
122C42×C13C22×C411yescharacteristic
123C42×C13C2×D411yescharacteristic
124C42×C13#4111yescharacteristic
125C42×C13#4111yescharacteristic
126#3167C2×C1311yescharacteristic
127#1986C2×C1311yescharacteristic, complemented
128#1980C2×C1311yescharacteristic
129C4×#107C2×C1311yescharacteristic, complemented
130#1503C2×C1311yescharacteristic, complemented
131#1502C2×C1311yescharacteristic
132#1451C2×C1311yescharacteristic, complemented
133C23×C13—41no—
134C23×C13#12711yescharacteristic
135Q8×C13—41no—
136Q8×C13—41no—
137Q8×C13—42no—
138Q8×C13—81no—
139D4×C13—41no—
140D4×C13—41no—
141D4×C13—42no—
142D4×C13—81no—
143D4×C13—81no—
144D4×C13—81no—
145C2×C4×C13—21no—
146C2×C4×C13—21no—
147C2×C4×C13—41no—
148C2×C4×C13—42no—
149C2×C4×C13—42no—
150C2×C4×C13—41no—
151C2×C4×C13—41no—
152C2×C4×C13—41no—
153C2×C4×C13—81no—
154C2×C4×C13—81no—
155C2×C4×C13—81no—
156C2×C4×C13—81no—
157C2×C4×C13—82no—
158C2×C4×C13C2×C22⋊C411yescharacteristic
159C2×C4×C13C4×D411yescharacteristic
160C2×C4×C13C4×D411yescharacteristic
161C2×C4×C13#12111yescharacteristic
162C2×C4×C13#12111yescharacteristic
163C2×C4×C13#12411yescharacteristic
164C2×C4×C13AGL(1,ℤ/8)12yes—
165C2×C4×C13#13712yes—
166C8×C13—21no—
167C8×C13—21no—
168C8×C13—21no—
169C8×C13—42no—
170C8×C13—42no—
171C8×C13#10412yescomplemented
172#533C22×C1311yescharacteristic
173#532C22×C1311yescharacteristic
174#498C4×C1311yescharacteristic, complemented
175#492C4×C1311yescharacteristic, complemented
176#487C4×C1311yescharacteristic, complemented
177#486C4×C1311yescharacteristic, complemented
178#465—21no—
179#465—21no—
180C4×SD16—21no—
181C4×SD16—21no—
182#431C22×C1311yescharacteristic
183C2×#107—21no—
184C2×#104—22no—
185C4×M16C22×C1311yescharacteristic
186C2×C4×C8C22×C1311yescharacteristic
187C4×C4⋊C4C22×C1311yescharacteristic
188C4×C4⋊C4C22×C1311yescharacteristic
189#340—21no—
190#339—22no—
191#328—22no—
192#327—22no—
193#322—21no—
194#322—21no—
195C22×C13—21no—
196C22×C13—21no—
197C22×C13—81no—
198C22×C13—81no—
199C22×C13—81no—
200C22×C13#39011yescharacteristic
201C22×C13#49611yescharacteristic
202C22×C13#49711yescharacteristic
203C4×C13—21no—
204C4×C13—21no—
205C4×C13—21no—
206C4×C13—82no—
207C4×C13—82no—
208C4×C13—81no—
209C4×C13—81no—
210C4×C13—81no—
211C4×C13C2×#10411yescharacteristic
212C4×C13#42111yescharacteristic
213C4×C13#44012yes—
214C4×C13#46812yes—
215C2×#41—21no—
216C2×SD16—21no—
217C2×SD16—21no—
218C2×M16D4×C1312yes—
219C22×C8D4×C1311yescharacteristic
220C22×C8D4×C1311yescharacteristic
221C4⋊Q8C2×C4×C1311yescharacteristic
222C4⋊Q8C2×C4×C1311yescharacteristic
223C4⋊Q8C2×C4×C1311yescharacteristic
224#127C2×C4×C1311yescharacteristic
225#125—21no—
226#124—21no—
227C22⋊Q8—21no—
228C22⋊Q8—21no—
229#121—21no—
230#121—21no—
231C4×Q8—21no—
232C4×Q8—21no—
233C4×D4—21no—
234C4×D4—21no—
235#117—21no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—21no—
238C2×C42—21no—
239C2×C42—21no—
240C2×C42C23×C1311yescharacteristic
241#107—24no—
242#106—21no—
243#106—21no—
244C4⋊C8—21no—
245#104—44no—
246#103—21no—
247#103—21no—
248#102—21no—
249#102—21no—
250C22⋊C8D4×C1312yes—
251#97—21no—
252C4×C8—21no—
253C4×C8—21no—
254C4×C8C2×C4×C1311yescharacteristic
255C4×C8C2×C4×C1311yescharacteristic
256C4×C8D4×C1311yescharacteristic
257C4×C8D4×C1311yescharacteristic
258#95—21no—
259#95—21no—
260C2×C13—21no—
261C2×C13—21no—
262C2×C13—161no—
263C2×C13#197311yescharacteristic
264C2×C13#197611yescharacteristic
265C2×C13#198011yescharacteristic
266#41—42no—
267#41—42no—
268C2×Q8—21no—
269C2×Q8—21no—
270C2×Q8—21no—
271C2×D4—21no—
272C2×D4—21no—
273C2×D4—21no—
274C2×D4—41no—
275C22×C4—41no—
276C22×C4—41no—
277C22×C4—41no—
278C22×C4C2×D4×C1311yescharacteristic
279C22×C4C2×D4×C1311yescharacteristic
280C22×C4C2×D4×C1311yescharacteristic
281SD16—42no—
282SD16—42no—
283M16—22no—
284M16—22no—
285C2×C8—22no—
286C2×C8—22no—
287C2×C8—22no—
288C2×C8—41no—
289C2×C8C13×C22⋊C411yescharacteristic
290C2×C8C13×C22⋊C411yescharacteristic
291C2×C8C13×C22⋊C411yescharacteristic
292C2×C8C13×C22⋊C411yescharacteristic
293C4⋊C4—22no—
294C4⋊C4—22no—
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—21no—
298C4⋊C4—21no—
299C4⋊C4—21no—
300C4⋊C4—21no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4—41no—
305C22⋊C4—41no—
306C22⋊C4—41no—
307C22⋊C4—41no—
308C42—41no—
309C42—42no—
310C42—42no—
311C42C22×C4×C1311yescharacteristic
312C42C2×D4×C1311yescharacteristic
313C42C13×#4111yescharacteristic
314C42C13×#4111yescharacteristic
315C13#972211yescharacteristic, direct product factor, Sylow
316C23—41no—
317C23C13×#12711yescharacteristic
318Q8—41no—
319Q8—41no—
320Q8—42no—
321Q8—81no—
322D4—41no—
323D4—41no—
324D4—42no—
325D4—81no—
326D4—81no—
327D4—81no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—41no—
331C2×C4—42no—
332C2×C4—42no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—81no—
337C2×C4—81no—
338C2×C4—81no—
339C2×C4—81no—
340C2×C4—82no—
341C2×C4C2×C13×C22⋊C411yescharacteristic
342C2×C4C4×D4×C1311yescharacteristic
343C2×C4C4×D4×C1311yescharacteristic
344C2×C4C13×#12111yescharacteristic
345C2×C4C13×#12111yescharacteristic
346C2×C4C13×#12411yescharacteristic
347C2×C4C13×AGL(1,ℤ/8)12yes—
348C2×C4C13×#13712yes—
349C8—21no—
350C8—21no—
351C8—21no—
352C8—42no—
353C8—42no—
354C8C13×#10412yescomplemented
355C22—21no—
356C22—21no—
357C22—81no—
358C22—81no—
359C22—81no—
360C22C13×#39011yescharacteristic
361C22C13×#49611yescharacteristic
362C22C13×#49711yescharacteristic
363C4—21no—
364C4—21no—
365C4—21no—
366C4—82no—
367C4—82no—
368C4—81no—
369C4—81no—
370C4—81no—
371C4C2×C13×#10411yescharacteristic
372C4C13×#42111yescharacteristic
373C4C13×#44012yes—
374C4C13×#46812yes—
375C2—21no—
376C2—21no—
377C2—161no—
378C2C13×#197311yescharacteristic
379C2C13×#197611yescharacteristic
380C2C13×#198011yescharacteristic
subgroupG/H
centerC2×C4×C13#121
commutatorC42C22×C4×C13
Frattini, cosocleC2×C42C23×C13
socleC22×C13#390
prime radicalC13×#532C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C13 ◁ C2×C42×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C13×#1986C2semidirect
4. C4×C13×#107C2semidirect
5. C13×#1503C2semidirect
7. C13×#1451C2semidirect
10. C13×#498C4semidirect
11. C13×#492C4semidirect
12. C13×#487C4semidirect
13. C13×#486C4semidirect
76. #9722C13direct (N × H)
127. #1986C2×C13semidirect
129. C4×#107C2×C13semidirect
130. #1503C2×C13semidirect
132. #1451C2×C13semidirect
171. C8×C13#104semidirect
174. #498C4×C13semidirect
175. #492C4×C13semidirect
176. #487C4×C13semidirect
177. #486C4×C13semidirect
315. C13#9722direct (N × H)
354. C8C13×#104semidirect

Maximal subgroups

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

subgroupindex
C13×#31672
C13×#19862
C13×#19802
C4×C13×#1072
C13×#15032
C13×#15022
C13×#14512
#972213