Finite Group Databasebeta

← #13125880

Subgroups — #13125880

Order 1664.

420 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 117 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#540C211yesmaximal, characteristic, complemented
2#11719230C211yesmaximal, characteristic, complemented
3#11718735C211yesmaximal, characteristic, complemented
4#11718734C211yesmaximal, characteristic, complemented
5#11718729C211yesmaximal, characteristic, complemented
6#11718728C211yesmaximal, characteristic, complemented
7#11718698C212yesmaximal, complemented
8#11718697C212yesmaximal, complemented
9#11718677C212yesmaximal, complemented
10#11718676C212yesmaximal, complemented
11#11718661C211yesmaximal, characteristic, complemented
12C2×#6127C2211yescharacteristic
13C22×D52C2211yescharacteristic
14C13×#127C2211yescharacteristic, complemented
15C13×#125C2211yescharacteristic, complemented
16C13×#123—22no—
17C13×#121—22no—
18C13×#121C2212yes—
19C4×D4×C13C2212yescomplemented
20C13×#117C2211yescharacteristic
21C2×#6105C2212yescomplemented
22C2×#6104C2212yes—
23C2×#6104C2212yes—
24C2×#6104C2212yescomplemented
25#88149—22no—
26#88136—22no—
27#88129C2211yescharacteristic
28#88129C2211yescharacteristic
29#88128C2211yescharacteristic
30#88128C2211yescharacteristic
31C22⋊#1055C2212yes—
32#88050C2212yescomplemented
33#88049C2212yes—
34#88049C2212yes—
35#88049C2212yescomplemented
36C4⋊#1055C2212yescomplemented
37#88043C2211yescharacteristic, complemented
38C4×#1055C2211yescharacteristic, complemented
39C23×D13—21no—
40C2×D4×C13—22no—
41C2×D4×C13—22no—
42C2×D4×C13C2312yes—
43C22×C4×C13—22no—
44C22×C4×C13C2311yescharacteristic
45C2×C22⋊D13—21no—
46#6127—42no—
47C2×D52—21no—
48C2×D52—22no—
49C2×D52—22no—
50C2×D52—42no—
51C2×D52C2311yescharacteristic
52C2×D52C2311yescharacteristic
53C2×D52C2311yescharacteristic
54C2×C4×D13—21no—
55C2×Dic26C2311yescharacteristic
56C13×C4⋊C4—22no—
57C13×C4⋊C4D412yes—
58C13×C4⋊C4C2312yes—
59C13×C22⋊C4—22no—
60C13×C22⋊C4—22no—
61C13×C22⋊C4D412yes—
62C42×C13C2311yescharacteristic
63C42×C13C2311yescharacteristic
64#6105—42no—
65#6104—42no—
66#6104—42no—
67#6104—42no—
68#6103—22no—
69#6103—22no—
70C2×#1055C2312yes—
71C2×#1055C2312yes—
72#3220—131nomaximal, Sylow
73C23×C13—22no—
74C23×C13C2×D411yescharacteristic
75C22×D13—21no—
76C22×D13—21no—
77C22×D13—21no—
78C22×D13—42no—
79C22×D13—82no—
80D4×C13—22no—
81D4×C13—22no—
82D4×C13—82no—
83D4×C13—82no—
84C2×C4×C13—22no—
85C2×C4×C13—22no—
86C2×C4×C13—82no—
87C2×C4×C13C2×D412yes—
88C2×C4×C13C2×D412yes—
89C2×C4×C13C2×D411yescharacteristic
90C2×C4×C13C2411yescharacteristic
91C22⋊D13—42no—
92C2×Dic13—21no—
93D52—22no—
94D52—22no—
95D52—22no—
96D52—42no—
97D52—82no—
98D52—82no—
99C4×D13—42no—
100Dic26—22no—
101#1055—22no—
102#1055—22no—
103#540D1311yescharacteristic, complemented
104#535—131no—
105#496—131no—
106#493—131no—
107#490—131no—
108#488—131no—
109#463—132no—
110#459—132no—
111#449—132no—
112#447—132no—
113#433—131no—
114C22×C13—21no—
115C22×C13—22no—
116C22×C13—42no—
117C22×C13—42no—
118C22×C13—42no—
119C22×C13C22×D411yescharacteristic
120C2×D13—41no—
121C2×D13—41no—
122C2×D13—41no—
123C2×D13—42no—
124C2×D13—42no—
125C2×D13—42no—
126C2×D13—84no—
127C4×C13—21no—
128C4×C13—22no—
129C4×C13—22no—
130C4×C13—42no—
131C4×C13H(5,𝔽2)12yes—
132Dic13—41no—
133C2×#41—131no—
134C22×D4—131no—
135C2×SD16—132no—
136C2×D8—132no—
137C2×D8—132no—
138C2×D8—132no—
139#127—131no—
140#127—131no—
141#127C2×D1311yescharacteristic, complemented
142#125C2×D1311yescharacteristic, complemented
143#124—131no—
144#124—131no—
145#123—22no—
146#121—22no—
147#121—262no—
148#121C2×D1312yes—
149#120—262no—
150C4×D4C2×D1312yescomplemented
151#117C2×D1311yescharacteristic
152C4⋊C8—132no—
153#103—132no—
154#102—132no—
155#102—132no—
156#102—132no—
157C22⋊C8—132no—
158#97—131no—
159C4×C8—131no—
160C2×C13—41no—
161C2×C13—82no—
162C2×C13#53511yescharacteristic
163C2×C13#57612yes—
164D13—81no—
165D13—81no—
166D13—81no—
167C24—261no—
168#41—522no—
169C2×Q8—131no—
170C2×D4—22no—
171C2×D4—22no—
172C2×D4—131no—
173C2×D4—131no—
174C2×D4—131no—
175C2×D4—261no—
176C2×D4—261no—
177C2×D4—262no—
178C2×D4—262no—
179C2×D4—522no—
180C2×D4C22×D1312yes—
181C22×C4—22no—
182C22×C4—261no—
183C22×C4C22×D1311yescharacteristic
184SD16—522no—
185D8—522no—
186D8—522no—
187D8—522no—
188C2×C8—132no—
189C2×C8—132no—
190C4⋊C4—22no—
191C4⋊C4C22⋊D1312yes—
192C4⋊C4C22×D1312yes—
193C22⋊C4—22no—
194C22⋊C4—22no—
195C22⋊C4—262no—
196C22⋊C4—262no—
197C22⋊C4C22⋊D1312yes—
198C42C22×D1311yescharacteristic
199C42C22×D1311yescharacteristic
200C13#322011yescharacteristic, complemented, Sylow
201C23—22no—
202C23—261no—
203C23—261no—
204C23—261no—
205C23—522no—
206C23—1042no—
207C23C2×C22⋊D1311yescharacteristic
208Q8—262no—
209D4—22no—
210D4—22no—
211D4—82no—
212D4—82no—
213D4—262no—
214D4—262no—
215D4—262no—
216D4—522no—
217D4—522no—
218D4—1042no—
219D4—1042no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—82no—
223C2×C4—261no—
224C2×C4—522no—
225C2×C4C2×C22⋊D1312yes—
226C2×C4C2×C22⋊D1312yes—
227C2×C4C2×C22⋊D1311yescharacteristic
228C2×C4C23×D1311yescharacteristic
229C8—262no—
230C8—262no—
231C22—21no—
232C22—22no—
233C22—42no—
234C22—42no—
235C22—42no—
236C22—521no—
237C22—521no—
238C22—521no—
239C22—522no—
240C22—522no—
241C22—522no—
242C22—1044no—
243C22C22×C22⋊D1311yescharacteristic
244C4—21no—
245C4—22no—
246C4—22no—
247C4—42no—
248C4—521no—
249C4#8825612yes—
250C2—41no—
251C2—82no—
252C2—1041no—
253C2—1041no—
254C2—1041no—
255C2#1171953511yescharacteristic
256C2#1171954012yes—
subgroupG/H
centerC22C22×C22⋊D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#540C2
socleC22×C13C22×D4
hypercenter#540D13
hypocenterC13#3220
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ #117 ◁ #540

Complements

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

NH ≅ G/Ntype
1. C13×#540C2semidirect
2. #11719230C2semidirect
3. #11718735C2semidirect
4. #11718734C2semidirect
5. #11718729C2semidirect
6. #11718728C2semidirect
7. #11718698C2semidirect
8. #11718697C2semidirect
9. #11718677C2semidirect
10. #11718676C2semidirect
11. #11718661C2semidirect
14. C13×#127C22semidirect
15. C13×#125C22semidirect
19. C4×D4×C13C22semidirect
21. C2×#6105C22semidirect
24. C2×#6104C22semidirect
32. #88050C22semidirect
35. #88049C22semidirect
36. C4⋊#1055C22semidirect
37. #88043C22semidirect
38. C4×#1055C22semidirect
103. #540D13semidirect
141. #127C2×D13semidirect
142. #125C2×D13semidirect
150. C4×D4C2×D13semidirect
200. C13#3220semidirect

Maximal subgroups

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

subgroupindex
C13×#5402
#117192302
#117187352
#117187342
#117187292
#117187282
#117186982
#117186972
#117186772
#117186762
#117186612
#322013