Finite Group Databasebeta

← D13⋊#353 #13131102

Subgroups — D13⋊#353 #13131102

Order 1664.

368 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 54 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
1D13×#127C211yesmaximal, characteristic
2D13⋊#99C212yesmaximal, complemented
3#11718294C212yesmaximal, complemented
4#11718225C212yesmaximal, complemented
5C2×D4×D13—22no—
6C2×D4×D13C411yescharacteristic, complemented
7C2×D4×D13C2211yescharacteristic
8C2×C22⋊#261—22no—
9C13×#127C411yescharacteristic, complemented
10#88194—22no—
11#88194C411yescharacteristic, complemented
12#88194C2211yescharacteristic
13#88128C2211yescharacteristic
14C42×D13C411yescharacteristic, complemented
15#88119—22no—
16#88107C2214yescomplemented
17C23×D13—21no—
18C23×D13D412yes—
19C22×#261—42no—
20C2×D4×C13—22no—
21C2×D4×C13C2×C411yescharacteristic
22C2×D4×C13C2×C411yescharacteristic, complemented
23C2×C22⋊D13—22no—
24C2×C22⋊D13—22no—
25C2×C22⋊D13—21no—
26C2×C22⋊D13D412yes—
27D4×D13—41no—
28D4×D13—41no—
29D4×D13—41no—
30D4×D13—41no—
31D4×D13—48no—
32C2×D52—22no—
33C2×D52C2×C411yescharacteristic, complemented
34C2×D52C2311yescharacteristic
35C2×C4×D13—21no—
36C2×C4×D13C2×C411yescharacteristic
37C22⋊#261—24no—
38C22⋊#261—42no—
39C42×C13C2×C411yescharacteristic, complemented
40C4×Dic13—21no—
41C4×Dic13C2×C411yescharacteristic, complemented
42C2×#353—131nomaximal, Sylow
43C23×C13—21no—
44C23×C13C22⋊C412yes—
45C22×D13—22no—
46C22×D13—22no—
47C22×D13—21no—
48C22×D13—44no—
49C22×D13—44no—
50C22×D13—41no—
51C22×D13—41no—
52C22×D13C22⋊C411yescharacteristic
53C22×D13C2×D412yes—
54C2×#261—44no—
55C2×#261—84no—
56D4×C13—41no—
57D4×C13—44no—
58D4×C13—41no—
59C2×C4×C13—21no—
60C2×C4×C13C22×C411yescharacteristic
61C22⋊D13—42no—
62C22⋊D13—44no—
63C22⋊D13—44no—
64C22⋊D13—42no—
65C2×Dic13—21no—
66C2×Dic13C22⋊C411yescharacteristic
67D52—41no—
68D52—44no—
69D52—41no—
70C4×D13—24no—
71C4×D13—21no—
72C4×D13—21no—
73C2×#127—131no—
74C2×#99—132no—
75#353—132no—
76#353—132no—
77C22×C13—22no—
78C22×C13—42no—
79C22×C13—42no—
80C22×C13—41no—
81C22×C13C2×C22⋊C411yescharacteristic
82C2×D13—22no—
83C2×D13—22no—
84C2×D13—44no—
85C2×D13—42no—
86C2×D13—42no—
87C2×D13—41no—
88C2×D13—82no—
89C2×D13—82no—
90C2×D13—82no—
91C2×D13#9911yescharacteristic
92C2×D13#9911yescharacteristic
93#261—84no—
94C4×C13—22no—
95C4×C13—21no—
96Dic13—22no—
97Dic13—21no—
98C22×D4—131no—
99C22×D4—131no—
100C22×D4—262no—
101#127—131no—
102#127—131no—
103#127—131no—
104#127—262no—
105#127#26111yescharacteristic, complemented
106C2×C22⋊C4—262no—
107C2×C42—131no—
108#99—134no—
109#99—262no—
110C2×C13—21no—
111C2×C13—42no—
112C2×C13—81no—
113C2×C13C2×#9911yescharacteristic
114D13—21no—
115D13—42no—
116D13—81no—
117D13#35312yescomplemented
118C24—132no—
119C24—261no—
120C2×D4—22no—
121C2×D4—132no—
122C2×D4—131no—
123C2×D4—131no—
124C2×D4—262no—
125C2×D4—261no—
126C2×D4—262no—
127C2×D4—262no—
128C2×D4—521no—
129C2×D4—521no—
130C2×D4—521no—
131C2×D4—521no—
132C2×D4—528no—
133C2×D4C2×#26111yescharacteristic
134C2×D4C2×#26111yescharacteristic, complemented
135C22×C4—131no—
136C22×C4—261no—
137C22×C4—522no—
138C22⋊C4—264no—
139C22⋊C4—522no—
140C42—131no—
141C42—261no—
142C42C2×#26111yescharacteristic, complemented
143C13C2×#35311yescharacteristic, complemented, Sylow
144C23—21no—
145C23—131no—
146C23—132no—
147C23—262no—
148C23—262no—
149C23—261no—
150C23—521no—
151C23—521no—
152C23—524no—
153C23—524no—
154C23C22⋊#26112yes—
155D4—41no—
156D4—41no—
157D4—44no—
158D4—521no—
159D4—521no—
160D4—524no—
161D4—522no—
162D4—524no—
163D4—524no—
164D4—522no—
165C2×C4—21no—
166C2×C4—131no—
167C2×C4—261no—
168C2×C4—261no—
169C2×C4—264no—
170C2×C4—261no—
171C2×C4—524no—
172C2×C4—1044no—
173C2×C4C22×#26111yescharacteristic
174C22—22no—
175C22—42no—
176C22—42no—
177C22—41no—
178C22—131no—
179C22—131no—
180C22—262no—
181C22—262no—
182C22—522no—
183C22—522no—
184C22—524no—
185C22—521no—
186C22—1042no—
187C22—1042no—
188C22—1042no—
189C22C2×C22⋊#26111yescharacteristic
190C4—22no—
191C4—21no—
192C4—262no—
193C4—261no—
194C4—1044no—
195C2—21no—
196C2—42no—
197C2—81no—
198C2—132no—
199C2—261no—
200C2—522no—
201C2—1041no—
202C2D13⋊#9911yescharacteristic
subgroupG/H
centerC2D13⋊#99
commutatorC2×C4×C13C22×C4
FrattiniC2×C4C22×#261
FittingC13×#127C4
socleC2×C13C2×#99
prime radicalD13×#127C2
cosocleC2×D52C23
hypercenter#127#261
hypocenterC13C2×#353
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #127

Complements

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

NH ≅ G/Ntype
2. D13⋊#99C2semidirect
3. #11718294C2semidirect
4. #11718225C2semidirect
6. C2×D4×D13C4semidirect
9. C13×#127C4semidirect
11. #88194C4semidirect
14. C42×D13C4semidirect
16. #88107C22semidirect
22. C2×D4×C13C2×C4semidirect
33. C2×D52C2×C4semidirect
39. C42×C13C2×C4semidirect
41. C4×Dic13C2×C4semidirect
105. #127#261semidirect
117. D13#353semidirect
134. C2×D4C2×#261semidirect
142. C42C2×#261semidirect
143. C13C2×#353semidirect

Maximal subgroups

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

subgroupindex
D13×#1272
D13⋊#992
#117182942
#117182252
C2×#35313