Finite Group Databasebeta

← C13×#3093 #13112151

Subgroups — C13×#3093 #13112151

Order 1664.

414 conjugacy classes of subgroups; only the 184 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 184 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×#525C211yesmaximal, characteristic
2C2×C13×#117C211yesmaximal, characteristic, complemented
3C13×#485C214yesmaximal, complemented
4C13×#482C214yesmaximal, complemented
5C13×#428C212yesmaximal, complemented
6C13×#417C212yesmaximal, complemented
7C13×#407C211yesmaximal, characteristic, complemented
8C2×C13×#41C2211yescharacteristic
9C23×C4×C13C2211yescharacteristic
10C2×C13×M16C2212yes—
11C13×#123—21no—
12C13×C22⋊Q8C2212yes—
13C13×#121C2212yes—
14C13×#120—21no—
15C4×D4×C13—22no—
16C13×#117—22no—
17C13×#117C2211yescharacteristic
18C13×#117C2214yes—
19C2×C13×C4⋊C4C2212yes—
20C2×C13×C22⋊C4—21no—
21C2×C42×C13—21no—
22C13×#107C2214yescomplemented
23C13×#106C2214yescomplemented
24C13×#103C2214yescomplemented
25C13×#102C2214yescomplemented
26C13×C22⋊C8C2214yes—
27C24×C13D411yescharacteristic
28C13×#41—24no—
29C2×Q8×C13C2311yescharacteristic
30C2×D4×C13—22no—
31C2×D4×C13—21no—
32C2×D4×C13C2311yescharacteristic
33C22×C4×C13—24no—
34C22×C4×C13—22no—
35C22×C4×C13—21no—
36C22×C4×C13D411yescharacteristic
37C22×C4×C13D412yes—
38C22×C4×C13C2312yes—
39C22×C4×C13C2311yescharacteristic
40C13×M16—24no—
41C2×C8×C13C2314yes—
42C13×C4⋊C4—22no—
43C13×C4⋊C4—22no—
44C13×C4⋊C4C2314yes—
45C13×C4⋊C4C2312yes—
46C13×C22⋊C4—24no—
47C13×C22⋊C4—21no—
48C13×C22⋊C4—22no—
49C13×C22⋊C4—22no—
50C42×C13—24no—
51C42×C13—21no—
52#3093C1311yesmaximal, characteristic, direct product factor, Sylow
53C23×C13—22no—
54C23×C13—21no—
55C23×C13—42no—
56C23×C13C2×D412yes—
57C23×C13C2×D411yescharacteristic
58Q8×C13—22no—
59D4×C13—22no—
60D4×C13—44no—
61D4×C13—42no—
62C2×C4×C13—22no—
63C2×C4×C13—24no—
64C2×C4×C13—24no—
65C2×C4×C13—24no—
66C2×C4×C13—22no—
67C2×C4×C13—21no—
68C2×C4×C13—44no—
69C2×C4×C13—42no—
70C2×C4×C13C2×D412yes—
71C2×C4×C13C2×D411yescharacteristic
72C2×C4×C13#4114yes—
73C2×C4×C13C2411yescharacteristic
74C8×C13—24no—
75#525C2×C1311yescharacteristic
76C2×#117C2×C1311yescharacteristic, complemented
77#485C2×C1314yescomplemented
78#482C2×C1314yescomplemented
79#428C2×C1312yescomplemented
80#417C2×C1312yescomplemented
81#407C2×C1311yescharacteristic, complemented
82C22×C13—22no—
83C22×C13—22no—
84C22×C13—22no—
85C22×C13—22no—
86C22×C13—44no—
87C22×C13—41no—
88C22×C13—42no—
89C22×C13#12312yes—
90C22×C13C22×D411yescharacteristic
91C4×C13—22no—
92C4×C13—41no—
93C4×C13—44no—
94C4×C13—42no—
95C4×C13#12312yes—
96C4×C13C2×#4112yes—
97C2×#41C22×C1311yescharacteristic
98C23×C4C22×C1311yescharacteristic
99C2×M16C22×C1312yes—
100#123—21no—
101C22⋊Q8C22×C1312yes—
102#121C22×C1312yes—
103#120—21no—
104C4×D4—22no—
105#117—22no—
106#117C22×C1314yes—
107#117C22×C1311yescharacteristic
108C2×C4⋊C4C22×C1312yes—
109C2×C22⋊C4—21no—
110C2×C42—21no—
111#107C22×C1314yescomplemented
112#106C22×C1314yescomplemented
113#103C22×C1314yescomplemented
114#102C22×C1314yescomplemented
115C22⋊C8C22×C1314yes—
116C2×C13—22no—
117C2×C13—42no—
118C2×C13—81no—
119C2×C13C2×#12311yescharacteristic
120C2×C13#57512yes—
121C24D4×C1311yescharacteristic
122#41—24no—
123C2×Q8C23×C1311yescharacteristic
124C2×D4—22no—
125C2×D4—21no—
126C2×D4C23×C1311yescharacteristic
127C22×C4—24no—
128C22×C4—22no—
129C22×C4—21no—
130C22×C4D4×C1311yescharacteristic
131C22×C4D4×C1312yes—
132C22×C4C23×C1312yes—
133C22×C4C23×C1311yescharacteristic
134M16—24no—
135C2×C8C23×C1314yes—
136C4⋊C4—22no—
137C4⋊C4—22no—
138C4⋊C4C23×C1314yes—
139C4⋊C4C23×C1312yes—
140C22⋊C4—24no—
141C22⋊C4—21no—
142C22⋊C4—22no—
143C22⋊C4—22no—
144C42—24no—
145C42—21no—
146C13#309311yescharacteristic, direct product factor, Sylow
147C23—22no—
148C23—21no—
149C23—42no—
150C23C2×D4×C1312yes—
151C23C2×D4×C1311yescharacteristic
152Q8—22no—
153D4—22no—
154D4—44no—
155D4—42no—
156C2×C4—22no—
157C2×C4—24no—
158C2×C4—24no—
159C2×C4—24no—
160C2×C4—22no—
161C2×C4—21no—
162C2×C4—44no—
163C2×C4—42no—
164C2×C4C2×D4×C1312yes—
165C2×C4C2×D4×C1311yescharacteristic
166C2×C4C13×#4114yes—
167C2×C4C24×C1311yescharacteristic
168C8—24no—
169C22—22no—
170C22—22no—
171C22—22no—
172C22—22no—
173C22—44no—
174C22—41no—
175C22—42no—
176C22C13×#12312yes—
177C22C22×D4×C1311yescharacteristic
178C4—22no—
179C4—41no—
180C4—44no—
181C4—42no—
182C4C13×#12312yes—
183C4C2×C13×#4112yes—
184C2—22no—
185C2—42no—
186C2—81no—
187C2C2×C13×#12311yescharacteristic
188C2C13×#57512yes—
subgroupG/H
center, socleC22×C13C22×D4
commutator, Frattini, cosocleC2×C4C24×C13
prime radicalC13×#525C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C23×C4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C13×#117C2semidirect
3. C13×#485C2semidirect
4. C13×#482C2semidirect
5. C13×#428C2semidirect
6. C13×#417C2semidirect
7. C13×#407C2semidirect
22. C13×#107C22semidirect
23. C13×#106C22semidirect
24. C13×#103C22semidirect
25. C13×#102C22semidirect
52. #3093C13direct (N × H)
76. C2×#117C2×C13semidirect
77. #485C2×C13semidirect
78. #482C2×C13semidirect
79. #428C2×C13semidirect
80. #417C2×C13semidirect
81. #407C2×C13semidirect
111. #107C22×C13semidirect
112. #106C22×C13semidirect
113. #103C22×C13semidirect
114. #102C22×C13semidirect
146. C13#3093direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#5252
C2×C13×#1172
C13×#4852
C13×#4822
C13×#4282
C13×#4172
C13×#4072
#309313