Finite Group Databasebeta

← D13⋊#355 #13131122

Subgroups — D13⋊#355 #13131122

Order 1664.

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

normal subgroups only

This group has 260 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×#124C211yesmaximal, characteristic
2D13⋊#101C212yesmaximal, complemented
3#11718295C212yesmaximal, complemented
4#11718228C212yesmaximal, complemented
5C2×Q8×D13C2211yescharacteristic
6C2×D4×D13C411yescharacteristic
7D13⋊M16—22no—
8C13×#124C411yescharacteristic
9#88201C411yescharacteristic
10#88190C2211yescharacteristic
11#88139—22no—
12C22⋊C4×D13—22no—
13#88129C2211yescharacteristic
14C42×D13C411yescharacteristic
15#88113—22no—
16#88113C2214yescomplemented
17C23×D13—21no—
18C2×Q8×C13C2×C411yescharacteristic
19C2×D4×C13C2×C411yescharacteristic
20C2×C22⋊D13—21no—
21Q8×D13—41no—
22Q8×D13—41no—
23D4×D13—41no—
24D4×D13—41no—
25C2×D52C2×C411yescharacteristic
26C2×C4×D13—21no—
27C2×C4×D13C2×C411yescharacteristic
28C2×C4×D13D412yes—
29C2×Dic26D412yes—
30C2×Dic26C2311yescharacteristic
31#6122—24no—
32#6118—42no—
33D13⋊C8—42no—
34C13×C22⋊C4—22no—
35C42×C13C2×C411yescharacteristic
36C22⋊Dic13—22no—
37#6103—22no—
38#6103—22no—
39C4×Dic13—21no—
40C4×Dic13C2×C411yescharacteristic
41C2×#355—131nomaximal, Sylow
42C23×C13—21no—
43C22×D13—21no—
44C22×D13—44no—
45C22×D13—41no—
46C22×D13—41no—
47C22×D13C22⋊C411yescharacteristic
48Q8×C13—41no—
49D4×C13—41no—
50C2×C4×C13—21no—
51C2×C4×C13C22⋊C412yes—
52C2×C4×C13C22×C411yescharacteristic
53C22⋊D13—42no—
54C2×Dic13—21no—
55C2×Dic13C22⋊C411yescharacteristic
56C2×Dic13C2×D412yes—
57D52—41no—
58C4×D13—22no—
59C4×D13—22no—
60C4×D13—21no—
61C4×D13—21no—
62C4×D13—42no—
63Dic26—42no—
64Dic26—41no—
65#1057—44no—
66C2×#124—131no—
67C2×#101—132no—
68#355—132no—
69#355—132no—
70C22×C13—42no—
71C22×C13—41no—
72C22×C13C2×C22⋊C411yescharacteristic
73C2×D13—22no—
74C2×D13—42no—
75C2×D13—41no—
76C2×D13—82no—
77C2×D13—82no—
78C2×D13#9911yescharacteristic
79C2×D13#9911yescharacteristic
80C4×C13—21no—
81C4×C13—22no—
82C4×C13—41no—
83Dic13—22no—
84Dic13—21no—
85Dic13—41no—
86C22×Q8—131no—
87C22×D4—131no—
88C2×M16—262no—
89#124—131no—
90#124—131no—
91#124—131no—
92#124—262no—
93#124#26111yescharacteristic
94C2×C22⋊C4—262no—
95C2×C42—131no—
96#101—134no—
97#101—262no—
98C2×C13—21no—
99C2×C13—81no—
100C2×C13C2×#9911yescharacteristic
101D13—21no—
102D13—81no—
103D13#35512yescomplemented
104C24—261no—
105C2×Q8—132no—
106C2×Q8—131no—
107C2×Q8—521no—
108C2×Q8—521no—
109C2×Q8C2×#26111yescharacteristic
110C2×D4—131no—
111C2×D4—261no—
112C2×D4—521no—
113C2×D4—521no—
114C2×D4C2×#26111yescharacteristic
115C22×C4—132no—
116C22×C4—131no—
117C22×C4—261no—
118M16—264no—
119M16—522no—
120C2×C8—522no—
121C22⋊C4—22no—
122C22⋊C4—262no—
123C22⋊C4—262no—
124C22⋊C4—262no—
125C42—131no—
126C42—261no—
127C42C2×#26111yescharacteristic
128C13C2×#35511yescharacteristic, complemented, Sylow
129C23—21no—
130C23—131no—
131C23—261no—
132C23—521no—
133C23—521no—
134C23—524no—
135Q8—41no—
136Q8—522no—
137Q8—521no—
138D4—41no—
139D4—521no—
140D4—522no—
141C2×C4—21no—
142C2×C4—131no—
143C2×C4—132no—
144C2×C4—262no—
145C2×C4—262no—
146C2×C4—261no—
147C2×C4—261no—
148C2×C4—261no—
149C2×C4—522no—
150C2×C4C22⋊#26112yes—
151C2×C4C22×#26111yescharacteristic
152C8—524no—
153C22—42no—
154C22—41no—
155C22—131no—
156C22—131no—
157C22—262no—
158C22—522no—
159C22—521no—
160C22—1042no—
161C22—1042no—
162C22C2×C22⋊#26111yescharacteristic
163C4—22no—
164C4—21no—
165C4—41no—
166C4—262no—
167C4—261no—
168C4—521no—
169C2—21no—
170C2—81no—
171C2—132no—
172C2—261no—
173C2—1041no—
174C2D13⋊#9911yescharacteristic
subgroupG/H
centerC2D13⋊#99
commutatorC2×C4×C13C22×C4
FrattiniC2×C4C22×#261
FittingC13×#124C4
socleC2×C13C2×#99
prime radicalC2×D4×D13C4
cosocleC2×Dic26C23
hypercenter#124#261
hypocenterC13C2×#355
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #124

Complements

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

NH ≅ G/Ntype
2. D13⋊#101C2semidirect
3. #11718295C2semidirect
4. #11718228C2semidirect
16. #88113C22semidirect
103. D13#355semidirect
128. C13C2×#355semidirect

Maximal subgroups

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

subgroupindex
D13×#1242
D13⋊#1012
#117182952
#117182282
C2×#35513