Finite Group Databasebeta

← C13×#9425 #15695764

Subgroups — C13×#9425 #15695764

Order 3328.

534 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 534 conjugacy classes of subgroups — too many to draw. Only its 118 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×#3138C211yesmaximal, characteristic
2C13×#2380C211yesmaximal, characteristic
3C13×#1555C211yesmaximal, characteristic
4C13×#1515C212yesmaximal, complemented
5C13×#1288C212yesmaximal, complemented
6C13×#533C2211yescharacteristic
7C2×C13×#127C2211yescharacteristic
8C13×#490—22no—
9C13×#486C414yescomplemented
10C13×#432C2212yes—
11C13×#418—22no—
12C4×C13×M16C2211yescharacteristic
13C13×#386—22no—
14C13×#386—24no—
15C13×#383C2212yes—
16C13×#331—22no—
17C13×#328—24no—
18C22×D4×C13—22no—
19C22×D4×C13D412yes—
20C23×C4×C13—22no—
21C2×C13×M16—21no—
22C13×C4⋊Q8C2×C412yescomplemented
23C13×#127—22no—
24C13×#127C2×C412yes—
25C13×#127D412yes—
26C13×#125—21no—
27C13×C22⋊Q8—22no—
28C4×Q8×C13—22no—
29C13×#117—21no—
30C2×C13×C22⋊C4—24no—
31C2×C13×C22⋊C4—22no—
32C2×C42×C13C2311yescharacteristic
33C13×C4⋊C8—22no—
34C13×#102—28no—
35C13×C22⋊C8—22no—
36C13×#97—21no—
37C13×#97—22no—
38C4×C8×C13C2×C412yescomplemented
39C13×#95—22no—
40C13×#95—22no—
41C13×#95D414yes—
42#9425C1311yesmaximal, characteristic, direct product factor, Sylow
43C24×C13—22no—
44C2×Q8×C13—22no—
45C2×D4×C13—24no—
46C2×D4×C13—24no—
47C2×D4×C13—22no—
48C2×D4×C13—42no—
49C2×D4×C13—42no—
50C2×D4×C13—82no—
51C2×D4×C13—82no—
52C2×D4×C13C22⋊C414yes—
53C22×C4×C13—24no—
54C22×C4×C13—84no—
55C22×C4×C13—82no—
56C22×C4×C13C2×D411yescharacteristic
57C22×C4×C13C2×D412yes—
58C13×M16—42no—
59C2×C8×C13—22no—
60C2×C8×C13—42no—
61C13×C4⋊C4—22no—
62C13×C4⋊C4—22no—
63C13×C4⋊C4—42no—
64C13×C22⋊C4—41no—
65C13×C22⋊C4—84no—
66C13×C22⋊C4—82no—
67C42×C13—41no—
68C42×C13C22×C411yescharacteristic
69C42×C13C2×D411yescharacteristic
70C42×C13#4112yes—
71#3138C2×C1311yescharacteristic
72#2380C2×C1311yescharacteristic
73#1555C2×C1311yescharacteristic
74#1515C2×C1312yescomplemented
75#1288C2×C1312yescomplemented
76C23×C13—24no—
77C23×C13—44no—
78C23×C13—44no—
79C23×C13—42no—
80C23×C13—42no—
81C23×C13#12011yescharacteristic
82Q8×C13—82no—
83D4×C13—44no—
84D4×C13—82no—
85D4×C13—84no—
86D4×C13—84no—
87C2×C4×C13—22no—
88C2×C4×C13—42no—
89C2×C4×C13—48no—
90C2×C4×C13—42no—
91C2×C4×C13—44no—
92C2×C4×C13—88no—
93C2×C4×C13C2×C22⋊C411yescharacteristic
94C2×C4×C13C4×D412yes—
95C2×C4×C13#12112yes—
96C2×C4×C13#12311yescharacteristic
97C8×C13—42no—
98C8×C13—82no—
99#533C22×C1311yescharacteristic
100C2×#127C22×C1311yescharacteristic
101#490—22no—
102#486C4×C1314yescomplemented
103#432C22×C1312yes—
104#418—22no—
105C4×M16C22×C1311yescharacteristic
106#386—22no—
107#386—24no—
108#383C22×C1312yes—
109#331—22no—
110#328—24no—
111C22×C13—22no—
112C22×C13—44no—
113C22×C13—48no—
114C22×C13—82no—
115C22×C13—82no—
116C22×C13—84no—
117C22×C13#38611yescharacteristic
118C22×C13#45512yes—
119C4×C13—21no—
120C4×C13—21no—
121C4×C13—22no—
122C4×C13—22no—
123C4×C13—84no—
124C4×C13—82no—
125C22×D4—22no—
126C22×D4D4×C1312yes—
127C23×C4—22no—
128C2×M16—21no—
129C4⋊Q8C2×C4×C1312yescomplemented
130#127—22no—
131#127C2×C4×C1312yes—
132#127D4×C1312yes—
133#125—21no—
134C22⋊Q8—22no—
135C4×Q8—22no—
136#117—21no—
137C2×C22⋊C4—24no—
138C2×C22⋊C4—22no—
139C2×C42C23×C1311yescharacteristic
140C4⋊C8—22no—
141#102—28no—
142C22⋊C8—22no—
143#97—21no—
144#97—22no—
145C4×C8C2×C4×C1312yescomplemented
146#95—22no—
147#95—22no—
148#95D4×C1314yes—
149C2×C13—22no—
150C2×C13—84no—
151C2×C13#188511yescharacteristic
152C2×C13#190412yes—
153C24—22no—
154C2×Q8—22no—
155C2×D4—24no—
156C2×D4—24no—
157C2×D4—22no—
158C2×D4—42no—
159C2×D4—42no—
160C2×D4—82no—
161C2×D4—82no—
162C2×D4C13×C22⋊C414yes—
163C22×C4—24no—
164C22×C4—84no—
165C22×C4—82no—
166C22×C4C2×D4×C1311yescharacteristic
167C22×C4C2×D4×C1312yes—
168M16—42no—
169C2×C8—22no—
170C2×C8—42no—
171C4⋊C4—22no—
172C4⋊C4—22no—
173C4⋊C4—42no—
174C22⋊C4—41no—
175C22⋊C4—84no—
176C22⋊C4—82no—
177C42—41no—
178C42C22×C4×C1311yescharacteristic
179C42C2×D4×C1311yescharacteristic
180C42C13×#4112yes—
181C13#942511yescharacteristic, direct product factor, Sylow
182C23—24no—
183C23—44no—
184C23—44no—
185C23—42no—
186C23—42no—
187C23C13×#12011yescharacteristic
188Q8—82no—
189D4—44no—
190D4—82no—
191D4—84no—
192D4—84no—
193C2×C4—22no—
194C2×C4—42no—
195C2×C4—48no—
196C2×C4—42no—
197C2×C4—44no—
198C2×C4—88no—
199C2×C4C2×C13×C22⋊C411yescharacteristic
200C2×C4C4×D4×C1312yes—
201C2×C4C13×#12112yes—
202C2×C4C13×#12311yescharacteristic
203C8—42no—
204C8—82no—
205C22—22no—
206C22—44no—
207C22—48no—
208C22—82no—
209C22—82no—
210C22—84no—
211C22C13×#38611yescharacteristic
212C22C13×#45512yes—
213C4—21no—
214C4—21no—
215C4—22no—
216C4—22no—
217C4—84no—
218C4—82no—
219C2—22no—
220C2—84no—
221C2C13×#188511yescharacteristic
222C2C13×#190412yes—
subgroupG/H
center, socleC22×C13#386
commutatorC42C22×C4×C13
Frattini, cosocleC2×C42C23×C13
prime radicalC2×C13×#127C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G

Complements

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

NH ≅ G/Ntype
4. C13×#1515C2semidirect
5. C13×#1288C2semidirect
9. C13×#486C4semidirect
22. C13×C4⋊Q8C2×C4semidirect
38. C4×C8×C13C2×C4semidirect
42. #9425C13direct (N × H)
74. #1515C2×C13semidirect
75. #1288C2×C13semidirect
102. #486C4×C13semidirect
129. C4⋊Q8C2×C4×C13semidirect
145. C4×C8C2×C4×C13semidirect
181. C13#9425direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#31382
C13×#23802
C13×#15552
C13×#15152
C13×#12882
#942513