Finite Group Databasebeta

← #13122019

Subgroups — #13122019

Order 1664.

448 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#398C211yesmaximal, characteristic, complemented
2#11718653C211yesmaximal, characteristic, complemented
3#11718652C211yesmaximal, characteristic
4#11718651C211yesmaximal, characteristic, complemented
5#11718651C211yesmaximal, characteristic, complemented
6#11718650C211yesmaximal, characteristic, complemented
7#11718650C211yesmaximal, characteristic, complemented
8#11718648C211yesmaximal, characteristic, complemented
9#11718643C211yesmaximal, characteristic, complemented
10#11718335C211yesmaximal, characteristic, complemented
11#11718326C211yesmaximal, characteristic
12#11718326C211yesmaximal, characteristic
13#11718325C211yesmaximal, characteristic, complemented
14C13⋊#401C211yesmaximal, characteristic, complemented
15#11718314C211yesmaximal, characteristic, complemented
16C22×D52C2211yescharacteristic
17C22×C4×D13C2211yescharacteristic
18C22×C4×D13C2211yescharacteristic
19C2×C13×C4⋊C4C2211yescharacteristic
20C2×C13×C4⋊C4C2211yescharacteristic
21C2×C13×C4⋊C4C2211yescharacteristic
22C2×C13×C4⋊C4C2211yescharacteristic
23C2×#6103C2211yescharacteristic
24C2×#6103C2211yescharacteristic
25C2×#6103C2211yescharacteristic
26C2×#6103C2211yescharacteristic
27C2×#6103C2211yescharacteristic
28C2×#6103C2211yescharacteristic
29C2×#6103C2211yescharacteristic
30C2×#6103C2211yescharacteristic
31C2×#6103C2211yescharacteristic
32C2×#6103C2211yescharacteristic
33C2×C4⋊Dic13C2211yescharacteristic
34C2×#6101C2211yescharacteristic
35C2×#6101C2211yescharacteristic
36C2×C4×Dic13C2211yescharacteristic
37C13×#95C2211yescharacteristic
38C13×#95C2211yescharacteristic
39C13×#95C2211yescharacteristic
40#88071C2211yescharacteristic
41#88071C2211yescharacteristic
42#88071C2211yescharacteristic
43#88071C2211yescharacteristic
44#88071C2211yescharacteristic
45#88071C2211yescharacteristic
46#88071C2211yescharacteristic
47#88071C2211yescharacteristic
48#88071C2211yescharacteristic
49#88071C2211yescharacteristic
50#88071C2211yescharacteristic
51C23×D13C2311yescharacteristic
52C23×D13C2311yescharacteristic
53C22×C4×C13C2311yescharacteristic
54C22×C4×C13C2311yescharacteristic
55C22×C4×C13C2311yescharacteristic
56C22×C4×C13C2311yescharacteristic
57C22×C4×C13C2311yescharacteristic
58C22×C4×C13C2311yescharacteristic
59C22×C4×C13C2311yescharacteristic
60C22×Dic13C2311yescharacteristic
61C22×Dic13C2311yescharacteristic
62C22×Dic13C2311yescharacteristic
63C22×Dic13C2311yescharacteristic
64C22×Dic13C2311yescharacteristic
65C22×Dic13C2311yescharacteristic
66C2×D52—22no—
67C2×D52—22no—
68C2×D52—41no—
69C2×C4×D13—22no—
70C2×C4×D13—22no—
71C2×C4×D13—41no—
72C2×C4×D13—41no—
73C2×C4×D13—41no—
74C2×C4×D13—41no—
75C13×C4⋊C4—41no—
76C13×C4⋊C4—41no—
77C13×C4⋊C4—41no—
78C13×C4⋊C4—41no—
79#6103—22no—
80#6103—22no—
81#6103—22no—
82#6103—22no—
83#6103—41no—
84#6103—41no—
85#6103—41no—
86#6103—41no—
87#6103—41no—
88#6103—41no—
89C4⋊Dic13—22no—
90#6101—41no—
91#6101—41no—
92C4×Dic13—41no—
93#2746—131nomaximal, Sylow
94C23×C13C2411yescharacteristic
95C22×D13—21no—
96C22×D13—21no—
97C22×D13—21no—
98C22×D13—21no—
99C22×D13—21no—
100C22×D13—21no—
101C22×D13—21no—
102C22×D13—21no—
103C22×D13—21no—
104C22×D13—21no—
105C22×D13—21no—
106C22×D13—21no—
107C22×D13#4112yes—
108C22×D13#4112yes—
109C2×C4×C13—21no—
110C2×C4×C13—21no—
111C2×C4×C13—21no—
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13—21no—
124C2×C4×C13—21no—
125C2×C4×C13—21no—
126C2×C4×C13—21no—
127C2×C4×C13—21no—
128C2×C4×C13—21no—
129C2×C4×C13#4112yes—
130C2×Dic13—21no—
131C2×Dic13—21no—
132C2×Dic13—21no—
133C2×Dic13—21no—
134C2×Dic13—21no—
135C2×Dic13—21no—
136C2×Dic13—21no—
137C2×Dic13—21no—
138C2×Dic13—21no—
139C2×Dic13—21no—
140C2×Dic13—21no—
141C2×Dic13—21no—
142C2×Dic13—21no—
143C2×Dic13—21no—
144C2×Dic13—21no—
145C2×Dic13—21no—
146C2×Dic13—21no—
147C2×Dic13—21no—
148D52—44no—
149C4×D13—44no—
150C4×D13—44no—
151#401—131no—
152#400—131no—
153#399—131no—
154#398D1311yescharacteristic, complemented
155#397—131no—
156#394—131no—
157#388—131no—
158#388—131no—
159#387—131no—
160#386—131no—
161#386—131no—
162#385—131no—
163#385—131no—
164#381—131no—
165#380—131no—
166C22×C13C2×#4111yescharacteristic
167C22×C13C2×#4111yescharacteristic
168C22×C13C2×#4111yescharacteristic
169C22×C13H(5,𝔽2)11yescharacteristic
170C22×C13H(5,𝔽2)11yescharacteristic
171C22×C13H(5,𝔽2)11yescharacteristic
172C22×C132−1+411yescharacteristic
173C2×D13—22no—
174C2×D13—22no—
175C2×D13—22no—
176C2×D13—22no—
177C2×D13—22no—
178C2×D13—22no—
179C2×D13—41no—
180C2×D13—41no—
181C2×D13—41no—
182C2×D13—41no—
183C2×D13—41no—
184C2×D13—41no—
185C2×D13—41no—
186C2×D13—41no—
187C4×C13—22no—
188C4×C13—41no—
189C4×C13—41no—
190C4×C13—41no—
191C4×C13—41no—
192C4×C13—41no—
193C4×C13—41no—
194Dic13—41no—
195Dic13—41no—
196Dic13—41no—
197Dic13—41no—
198Dic13—41no—
199Dic13—41no—
200C22×D4—131no—
201C23×C4—131no—
202C23×C4—131no—
203C2×C4⋊C4—131no—
204C2×C4⋊C4—131no—
205C2×C4⋊C4—131no—
206C2×C4⋊C4C2×D1311yescharacteristic
207C2×C4⋊C4C2×D1311yescharacteristic
208C2×C4⋊C4C2×D1311yescharacteristic
209C2×C4⋊C4C2×D1311yescharacteristic
210C2×C22⋊C4—131no—
211C2×C22⋊C4—131no—
212C2×C22⋊C4—131no—
213C2×C22⋊C4—131no—
214C2×C22⋊C4—131no—
215C2×C22⋊C4—131no—
216C2×C22⋊C4—131no—
217C2×C22⋊C4—131no—
218C2×C22⋊C4—131no—
219C2×C22⋊C4—131no—
220C2×C42—131no—
221#95—131no—
222#95—131no—
223#95—131no—
224#95—131no—
225#95—131no—
226#95—131no—
227#95—131no—
228#95—131no—
229#95—131no—
230#95—131no—
231#95—131no—
232#95C2×D1311yescharacteristic
233#95C2×D1311yescharacteristic
234#95C2×D1311yescharacteristic
235C2×C13#53911yescharacteristic
236C2×C13#53911yescharacteristic
237C2×C13#54211yescharacteristic
238C2×C13#55111yescharacteristic
239C2×C13#55111yescharacteristic
240C2×C13#55311yescharacteristic
241C2×C13#56011yescharacteristic
242D13—42no—
243D13—42no—
244C24—131no—
245C24—131no—
246C2×D4—262no—
247C2×D4—262no—
248C2×D4—521no—
249C22×C4—131no—
250C22×C4—131no—
251C22×C4—131no—
252C22×C4—131no—
253C22×C4—131no—
254C22×C4—131no—
255C22×C4—262no—
256C22×C4—262no—
257C22×C4—521no—
258C22×C4—521no—
259C22×C4—521no—
260C22×C4—521no—
261C22×C4C22×D1311yescharacteristic
262C22×C4C22×D1311yescharacteristic
263C22×C4C22×D1311yescharacteristic
264C22×C4C22×D1311yescharacteristic
265C22×C4C22×D1311yescharacteristic
266C22×C4C22×D1311yescharacteristic
267C22×C4C22×D1311yescharacteristic
268C4⋊C4—41no—
269C4⋊C4—41no—
270C4⋊C4—41no—
271C4⋊C4—41no—
272C4⋊C4—262no—
273C4⋊C4—521no—
274C4⋊C4—521no—
275C22⋊C4—262no—
276C22⋊C4—262no—
277C22⋊C4—262no—
278C22⋊C4—262no—
279C22⋊C4—521no—
280C22⋊C4—521no—
281C22⋊C4—521no—
282C22⋊C4—521no—
283C22⋊C4—521no—
284C22⋊C4—521no—
285C42—521no—
286C13#274611yescharacteristic, complemented, Sylow
287C23—132no—
288C23—132no—
289C23—261no—
290C23—261no—
291C23—261no—
292C23—261no—
293C23—261no—
294C23—261no—
295C23—261no—
296C23—261no—
297C23—261no—
298C23—261no—
299C23—261no—
300C23—261no—
301C23C23×D1311yescharacteristic
302D4—524no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
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—261no—
324C2×C4—261no—
325C2×C4—261no—
326C2×C4—261no—
327C2×C4—261no—
328C2×C4—261no—
329C2×C4—261no—
330C2×C4—261no—
331C2×C4—261no—
332C2×C4—261no—
333C2×C4—261no—
334C2×C4—261no—
335C2×C4—261no—
336C2×C4—261no—
337C2×C4—261no—
338C2×C4—261no—
339C2×C4—261no—
340C2×C4—261no—
341C2×C4—524no—
342C2×C4—524no—
343C2×C4#613112yes—
344C22—262no—
345C22—262no—
346C22—262no—
347C22—262no—
348C22—262no—
349C22—262no—
350C22—521no—
351C22—521no—
352C22—521no—
353C22—521no—
354C22—521no—
355C22—521no—
356C22—521no—
357C22—521no—
358C22#8825111yescharacteristic
359C22#8825111yescharacteristic
360C22C2×#613111yescharacteristic
361C22#8825411yescharacteristic
362C22#41×D1311yescharacteristic
363C22#41×D1311yescharacteristic
364C22#8825611yescharacteristic
365C4—22no—
366C4—41no—
367C4—41no—
368C4—41no—
369C4—41no—
370C4—41no—
371C4—41no—
372C4—521no—
373C4—521no—
374C4—521no—
375C4—521no—
376C4—521no—
377C4—521no—
378C2—522no—
379C2—522no—
380C2#1171932511yescharacteristic
381C2#1171934211yescharacteristic
382C2#1171934311yescharacteristic
383C2#1171936411yescharacteristic
384C2#1171939711yescharacteristic
385C2#1171940011yescharacteristic
386C2#1171943811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#398C2
prime radicalC22×D52C22
hypercenter#398D13
hypocenterC13#2746
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
1. C13×#398C2semidirect
2. #11718653C2semidirect
4. #11718651C2semidirect
5. #11718651C2semidirect
6. #11718650C2semidirect
7. #11718650C2semidirect
8. #11718648C2semidirect
9. #11718643C2semidirect
10. #11718335C2semidirect
13. #11718325C2semidirect
14. C13⋊#401C2semidirect
15. #11718314C2semidirect
154. #398D13semidirect
286. C13#2746semidirect

Maximal subgroups

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

subgroupindex
C13×#3982
#117186532
#117186522
#117186512
#117186502
#117186482
#117186432
#117183352
#117183262
#117183252
C13⋊#4012
#117183142
#274613