Finite Group Databasebeta

← #13128915

Subgroups — #13128915

Order 1664.

1104 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#520C211yesmaximal, characteristic, complemented
2#11719539C211yesmaximal, characteristic, complemented
3#11719536C211yesmaximal, characteristic, complemented
4#11719281C211yesmaximal, characteristic, complemented
5#11719279C211yesmaximal, characteristic, complemented
6C4×Q8×D13C211yesmaximal, characteristic, complemented
7Q8×Dic26C211yesmaximal, characteristic, complemented
8#11719266C213yesmaximal, complemented
9#11719264C213yesmaximal, complemented
10#11719256C213yesmaximal, complemented
11#11719253C213yesmaximal, complemented
12#11719239C213yesmaximal, complemented
13#11719233C213yesmaximal, complemented
14#11719216C213yesmaximal, complemented
15#11719212C213yesmaximal, complemented
16C2×C13×#41C2211yescharacteristic
17C2×#6131C2211yescharacteristic
18C2×Q8×D13C2211yescharacteristic
19C2×#6127C2216yes—
20C4×Q8×C13C2211yescharacteristic
21C4×Q8×C13C2211yescharacteristic
22C4×D4×C13C2213yes—
23C4×D4×C13C2213yes—
24C13×#117C2213yes—
25C2×C13×C4⋊C4C2213yes—
26Q8×Dic13C2211yescharacteristic
27Q8×Dic13C2211yescharacteristic
28#88194C2213yes—
29#88192C2213yes—
30#88192C2213yes—
31#88190C2213yes—
32#88184C2213yes—
33#88183C2216yes—
34C4×C22⋊D13C2213yes—
35C4×C22⋊D13C2213yes—
36C4×C22⋊D13C2216yes—
37#88178C2213yes—
38#88178C2216yes—
39#88152C2213yes—
40#88151C2213yes—
41#88150C2216yes—
42#88150C2211yescharacteristic
43#88149C2213yes—
44#88148C2213yes—
45#88147C2213yes—
46C4⋊C4×D13C2213yes—
47C4⋊C4×D13C2213yes—
48#88143C2213yes—
49#88142C2213yes—
50#88142C2213yes—
51#88141C2213yes—
52#88139C2213yes—
53#88139C2216yes—
54#88138C2213yes—
55#88137C2213yes—
56#88137C2216yes—
57#88133C2213yes—
58#88129C2213yes—
59C4×D52C2213yes—
60C4×D52C2213yes—
61#88126C2213yes—
62C42×D13C2213yes—
63#88123C2213yes—
64C4×Dic26C2213yes—
65C4×Dic26C2213yes—
66C13×#41—24no—
67C2×Q8×C13C2311yescharacteristic
68C2×D4×C13C2313yes—
69C22×C4×C13C2313yes—
70C22×C4×C13C2316yes—
71C2×C22⋊D13C2313yes—
72C2×C22⋊D13C2313yes—
73C2×C22⋊D13C2316yes—
74#6131—24no—
75Q8×D13—24no—
76#6127—412no—
77C2×D52C2313yes—
78C2×D52C2313yes—
79C2×C4×D13C2311yescharacteristic
80C2×C4×D13C2313yes—
81C2×C4×D13C2313yes—
82C2×C4×D13C2313yes—
83C2×C4×D13C2316yes—
84C2×Dic26C2311yescharacteristic
85C2×Dic26C2313yes—
86C2×Dic26C2316yes—
87C13×C4⋊C4C2313yes—
88C13×C4⋊C4C2313yes—
89C13×C4⋊C4C2313yes—
90C13×C4⋊C4C2311yescharacteristic
91C13×C22⋊C4C2313yes—
92C13×C22⋊C4C2313yes—
93C42×C13C2313yes—
94C42×C13C2313yes—
95C22⋊Dic13C2313yes—
96C22⋊Dic13C2313yes—
97C22⋊Dic13C2316yes—
98#6103C2313yes—
99#6103C2313yes—
100#6103C2311yescharacteristic
101#6103C2313yes—
102#6103C2316yes—
103#6103C2311yescharacteristic
104#6103C2313yes—
105C4⋊Dic13C2313yes—
106C4⋊Dic13C2313yes—
107C4⋊Dic13C2313yes—
108C4⋊Dic13C2313yes—
109#6101C2313yes—
110#6101C2316yes—
111#6101C2313yes—
112#6101C2311yescharacteristic
113#6101C2313yes—
114#6101C2311yescharacteristic
115#6101C2313yes—
116C4×Dic13C2313yes—
117C4×Dic13C2313yes—
118C4×Dic13C2313yes—
119C4×Dic13C2313yes—
120#3522—131nomaximal, Sylow
121C23×C13C2413yes—
122C22×D13C2413yes—
123C22×D13C2411yescharacteristic
124Q8×C13#4114yescomplemented
125D4×C13—26no—
126C2×C4×C13—26no—
127C2×C4×C13—46no—
128C2×C4×C13C2411yescharacteristic
129C2×C4×C13C2413yes—
130C2×C4×C13C2411yescharacteristic
131C2×C4×C13C2413yes—
132C2×C4×C13C2411yescharacteristic
133C2×C4×C13C2413yes—
134C22⋊D13—26no—
135C22⋊D13—26no—
136C22⋊D13—46no—
137C2×Dic13C2411yescharacteristic
138C2×Dic13C2413yes—
139C2×Dic13C2413yes—
140C2×Dic13C2413yes—
141C2×Dic13C2411yescharacteristic
142C2×Dic13C2411yescharacteristic
143D52—26no—
144D52—26no—
145C4×D13—26no—
146C4×D13—26no—
147C4×D13—26no—
148C4×D13—22no—
149C4×D13—46no—
150Dic26—26no—
151Dic26—22no—
152Dic26—46no—
153#559—133no—
154Q82—131no—
155#554—133no—
156#550—131no—
157#548—131no—
158#548—131no—
159#547—133no—
160#547—133no—
161#542—133no—
162#542—133no—
163#532—133no—
164#529—133no—
165#520—131no—
166#520D1311yescharacteristic, complemented
167C2×C4×Q8—131no—
168C22×C13—23no—
169C22×C13—23no—
170C22×C13—23no—
171C22×C13C2511yescharacteristic
172C2×D13—21no—
173C2×D13—21no—
174C2×D13—23no—
175C2×D13—23no—
176C2×D13—23no—
177C2×D13H(5,𝔽2)12yes—
178C4×C13—21no—
179C4×C13—23no—
180C4×C13—23no—
181C4×C13—21no—
182C4×C13—21no—
183C4×C13C2×#4116yes—
184Dic13—23no—
185Dic13—21no—
186Dic13—23no—
187Dic13—23no—
188Dic13—21no—
189Dic132−1+412yes—
190C2×#41—131no—
191C2×#41—136no—
192C2×#41C2×D1311yescharacteristic
193C22×Q8—131no—
194C4⋊Q8—133no—
195C4⋊Q8—133no—
196C4⋊Q8—133no—
197#127—133no—
198#126—133no—
199#126—133no—
200#125—133no—
201#124—133no—
202#124—133no—
203#124—136no—
204#124—133no—
205#123—136no—
206#123—133no—
207#123—133no—
208#123—136no—
209C22⋊Q8—136no—
210C22⋊Q8—133no—
211C22⋊Q8—131no—
212C22⋊Q8—136no—
213C22⋊Q8—133no—
214#121—133no—
215#121—133no—
216#121—133no—
217#121—133no—
218#121—133no—
219C4×Q8—131no—
220C4×Q8—131no—
221C4×Q8—133no—
222C4×Q8—133no—
223C4×Q8—133no—
224C4×Q8C2×D1311yescharacteristic
225C4×Q8C2×D1311yescharacteristic
226C4×D4—133no—
227C4×D4—133no—
228C4×D4—136no—
229C4×D4—133no—
230C4×D4—133no—
231C4×D4—133no—
232C4×D4C2×D1313yes—
233C4×D4C2×D1313yes—
234#117—133no—
235#117C2×D1313yes—
236C2×C4⋊C4—133no—
237C2×C4⋊C4—133no—
238C2×C4⋊C4C2×D1313yes—
239C2×C42—133no—
240C2×C13—43no—
241C2×C13C22×#4111yescharacteristic
242C2×C13C2×H(5,𝔽2)11yescharacteristic
243C2×C13C2×2−1+411yescharacteristic
244D13—22no—
245D13—43no—
246#41—24no—
247#41—264no—
248#41—5212no—
249C2×Q8—131no—
250C2×Q8—133no—
251C2×Q8—136no—
252C2×Q8—264no—
253C2×Q8C22×D1311yescharacteristic
254C2×D4—133no—
255C2×D4—133no—
256C2×D4—136no—
257C2×D4—133no—
258C2×D4—133no—
259C2×D4C22×D1313yes—
260C22×C4—131no—
261C22×C4—133no—
262C22×C4—133no—
263C22×C4—133no—
264C22×C4—136no—
265C22×C4C22×D1313yes—
266C22×C4C22×D1316yes—
267C4⋊C4—133no—
268C4⋊C4—133no—
269C4⋊C4—133no—
270C4⋊C4—136no—
271C4⋊C4—131no—
272C4⋊C4—131no—
273C4⋊C4—133no—
274C4⋊C4—133no—
275C4⋊C4—133no—
276C4⋊C4—133no—
277C4⋊C4—133no—
278C4⋊C4C22×D1313yes—
279C4⋊C4C22×D1313yes—
280C4⋊C4C22×D1313yes—
281C4⋊C4C22×D1311yescharacteristic
282C22⋊C4—133no—
283C22⋊C4—136no—
284C22⋊C4—133no—
285C22⋊C4—133no—
286C22⋊C4—133no—
287C22⋊C4—131no—
288C22⋊C4—131no—
289C22⋊C4—133no—
290C22⋊C4—136no—
291C22⋊C4—133no—
292C22⋊C4C22×D1313yes—
293C22⋊C4C22×D1313yes—
294C42—133no—
295C42—133no—
296C42—133no—
297C42—133no—
298C42C22×D1313yes—
299C42C22×D1313yes—
300C13#352211yescharacteristic, complemented, Sylow
301C23—131no—
302C23—133no—
303C23C23×D1313yes—
304Q8—262no—
305Q8—266no—
306Q8—526no—
307Q8#612714yescomplemented
308D4—26no—
309D4—266no—
310D4—266no—
311D4—266no—
312D4—266no—
313D4—526no—
314C2×C4—26no—
315C2×C4—46no—
316C2×C4—131no—
317C2×C4—131no—
318C2×C4—133no—
319C2×C4—133no—
320C2×C4—133no—
321C2×C4—131no—
322C2×C4—262no—
323C2×C4—266no—
324C2×C4—266no—
325C2×C4—266no—
326C2×C4—526no—
327C2×C4C23×D1311yescharacteristic
328C2×C4C23×D1313yes—
329C2×C4C23×D1311yescharacteristic
330C2×C4C23×D1313yes—
331C2×C4C23×D1311yescharacteristic
332C2×C4C23×D1313yes—
333C22—23no—
334C22—23no—
335C22—23no—
336C22—132no—
337C22—261no—
338C22—261no—
339C22—263no—
340C22—263no—
341C22—263no—
342C22C24×D1311yescharacteristic
343C4—21no—
344C4—23no—
345C4—23no—
346C4—21no—
347C4—21no—
348C4—132no—
349C4—261no—
350C4—263no—
351C4—263no—
352C4—263no—
353C4—261no—
354C4C2×#612716yes—
355C2—43no—
356C2—262no—
357C2—523no—
358C2C22×#612711yescharacteristic
359C2D13×H(5,𝔽2)11yescharacteristic
360C2D13×2−1+411yescharacteristic
subgroupG/H
center, FrattiniC22C24×D13
commutator, socle, cosocleC22×C13C25
FittingC13×#520C2
hypercenter#520D13
hypocenterC13#3522
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ #520

Complements

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

NH ≅ G/Ntype
1. C13×#520C2semidirect
2. #11719539C2semidirect
3. #11719536C2semidirect
4. #11719281C2semidirect
5. #11719279C2semidirect
6. C4×Q8×D13C2semidirect
7. Q8×Dic26C2semidirect
8. #11719266C2semidirect
9. #11719264C2semidirect
10. #11719256C2semidirect
11. #11719253C2semidirect
12. #11719239C2semidirect
13. #11719233C2semidirect
14. #11719216C2semidirect
15. #11719212C2semidirect
124. Q8×C13#41semidirect
166. #520D13semidirect
300. C13#3522semidirect
307. Q8#6127semidirect

Maximal subgroups

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

subgroupindex
C13×#5202
#117195392
#117195362
#117192812
#117192792
C4×Q8×D132
Q8×Dic262
#117192662
#117192642
#117192562
#117192532
#117192392
#117192332
#117192162
#117192122
#352213