Finite Group Databasebeta

← C13×#1613 #13110671

Subgroups — C13×#1613 #13110671

Order 1664.

288 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 68 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×#534C211yesmaximal, characteristic
2C13×#481C212yesmaximal, complemented
3C13×#399C211yesmaximal, characteristic, complemented
4C13×#327C212yesmaximal, complemented
5C13×#323C211yesmaximal, characteristic, complemented
6C22×D4×C13—21no—
7C13×#123—22no—
8C13×#121—21no—
9C13×#121C2212yes—
10C13×#120—22no—
11C2×C13×C4⋊C4—21no—
12C2×C13×C4⋊C4C2211yescharacteristic, complemented
13C2×C13×C22⋊C4—21no—
14C2×C13×C22⋊C4C2211yescharacteristic
15C13×#106—22no—
16C13×#102—22no—
17C13×C22⋊C8C2212yescomplemented
18C13×#95C2211yescharacteristic, complemented
19C24×C13—21no—
20C24×C13D411yescharacteristic
21C2×D4×C13—22no—
22C2×D4×C13—22no—
23C2×D4×C13—21no—
24C2×D4×C13—42no—
25C2×D4×C13—42no—
26C2×D4×C13D412yes—
27C22×C4×C13—21no—
28C22×C4×C13—21no—
29C22×C4×C13—21no—
30C22×C4×C13D411yescharacteristic
31C22×C4×C13C2311yescharacteristic
32C2×C8×C13—22no—
33C13×C4⋊C4—21no—
34C13×C4⋊C4—22no—
35C13×C4⋊C4—42no—
36C13×C4⋊C4D412yes—
37C13×C22⋊C4—22no—
38C13×C22⋊C4—22no—
39C13×C22⋊C4—22no—
40C13×C22⋊C4—42no—
41#1613C1311yesmaximal, characteristic, direct product factor, Sylow
42C23×C13—21no—
43C23×C13—21no—
44C23×C13—22no—
45C23×C13—41no—
46C23×C13—41no—
47C23×C13—42no—
48C23×C13—81no—
49C23×C13—81no—
50C23×C13SD1612yes—
51C23×C13C2×D411yescharacteristic
52D4×C13—42no—
53D4×C13—44no—
54D4×C13—42no—
55D4×C13—42no—
56D4×C13—81no—
57C2×C4×C13—22no—
58C2×C4×C13—21no—
59C2×C4×C13—22no—
60C2×C4×C13—41no—
61C2×C4×C13—41no—
62C2×C4×C13—42no—
63C2×C4×C13—41no—
64C2×C4×C13—41no—
65C2×C4×C13—41no—
66C2×C4×C13—41no—
67C2×C4×C13—41no—
68C2×C4×C13C2×D412yes—
69C8×C13—42no—
70#534C2×C1311yescharacteristic
71#481C2×C1312yescomplemented
72#399C2×C1311yescharacteristic, complemented
73#327C2×C1312yescomplemented
74#323C2×C1311yescharacteristic, complemented
75C22×C13—21no—
76C22×C13—21no—
77C22×C13—22no—
78C22×C13—42no—
79C22×C13—41no—
80C22×C13—41no—
81C22×C13—42no—
82C22×C13—42no—
83C22×C13—42no—
84C22×C13—81no—
85C22×C13—84no—
86C22×C13#12011yescharacteristic
87C22×C13C2×SD1611yescharacteristic
88C22×C13AGL(1,ℤ/8)11yescharacteristic
89C4×C13—22no—
90C4×C13—42no—
91C4×C13—42no—
92C4×C13—41no—
93C4×C13—81no—
94C22×D4—21no—
95#123—22no—
96#121—21no—
97#121C22×C1312yes—
98#120—22no—
99C2×C4⋊C4—21no—
100C2×C4⋊C4C22×C1311yescharacteristic, complemented
101C2×C22⋊C4—21no—
102C2×C22⋊C4C22×C1311yescharacteristic
103#106—22no—
104#102—22no—
105C22⋊C8C22×C1312yescomplemented
106#95C22×C1311yescharacteristic, complemented
107C2×C13—21no—
108C2×C13—21no—
109C2×C13—42no—
110C2×C13—82no—
111C2×C13#45011yescharacteristic
112C2×C13#45311yescharacteristic
113C2×C13#45811yescharacteristic
114C24—21no—
115C24D4×C1311yescharacteristic
116C2×D4—22no—
117C2×D4—22no—
118C2×D4—21no—
119C2×D4—42no—
120C2×D4—42no—
121C2×D4D4×C1312yes—
122C22×C4—21no—
123C22×C4—21no—
124C22×C4—21no—
125C22×C4D4×C1311yescharacteristic
126C22×C4C23×C1311yescharacteristic
127C2×C8—22no—
128C4⋊C4—21no—
129C4⋊C4—22no—
130C4⋊C4—42no—
131C4⋊C4D4×C1312yes—
132C22⋊C4—22no—
133C22⋊C4—22no—
134C22⋊C4—22no—
135C22⋊C4—42no—
136C13#161311yescharacteristic, direct product factor, Sylow
137C23—21no—
138C23—21no—
139C23—22no—
140C23—41no—
141C23—41no—
142C23—42no—
143C23—81no—
144C23—81no—
145C23C13×SD1612yes—
146C23C2×D4×C1311yescharacteristic
147D4—42no—
148D4—44no—
149D4—42no—
150D4—42no—
151D4—81no—
152C2×C4—22no—
153C2×C4—21no—
154C2×C4—22no—
155C2×C4—41no—
156C2×C4—42no—
157C2×C4—41no—
158C2×C4—41no—
159C2×C4—41no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—41no—
163C2×C4C2×D4×C1312yes—
164C8—42no—
165C22—21no—
166C22—21no—
167C22—22no—
168C22—42no—
169C22—41no—
170C22—41no—
171C22—42no—
172C22—42no—
173C22—42no—
174C22—81no—
175C22—84no—
176C22C13×#12011yescharacteristic
177C22C2×C13×SD1611yescharacteristic
178C22C13×AGL(1,ℤ/8)11yescharacteristic
179C4—22no—
180C4—42no—
181C4—42no—
182C4—41no—
183C4—81no—
184C2—21no—
185C2—21no—
186C2—42no—
187C2—82no—
188C2C13×#45011yescharacteristic
189C2C13×#45311yescharacteristic
190C2C13×#45811yescharacteristic
subgroupG/H
center, socleC22×C13#120
commutator, Frattini, cosocleC22×C4C23×C13
prime radicalC13×#534C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ C22×C4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C13×#481C2semidirect
3. C13×#399C2semidirect
4. C13×#327C2semidirect
5. C13×#323C2semidirect
12. C2×C13×C4⋊C4C22semidirect
17. C13×C22⋊C8C22semidirect
18. C13×#95C22semidirect
41. #1613C13direct (N × H)
71. #481C2×C13semidirect
72. #399C2×C13semidirect
73. #327C2×C13semidirect
74. #323C2×C13semidirect
100. C2×C4⋊C4C22×C13semidirect
105. C22⋊C8C22×C13semidirect
106. #95C22×C13semidirect
136. C13#1613direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#5342
C13×#4812
C13×#3992
C13×#3272
C13×#3232
#161313