Finite Group Databasebeta

← C13×#8750 #15695089

Subgroups — C13×#8750 #15695089

Order 3328.

538 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 538 conjugacy classes of subgroups — too many to draw. Only its 110 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×#2312C211yesmaximal, characteristic
2C13×#1819C212yesmaximal
3C13×#1304C214yesmaximal
4C22×C13×C22⋊C4C2211yescharacteristic
5C13×#388—24no—
6C13×#380C412yescomplemented
7C13×#379C2214yes—
8C13×#379C2212yes—
9C4×C13×C22⋊C4C412yescomplemented
10C13×#342—24no—
11C25×C13C2311yescharacteristic
12C23×C4×C13C2×C411yescharacteristic
13C23×C4×C13C2×C411yescharacteristic
14C2×C13×C4⋊C4—22no—
15C2×C13×C22⋊C4—24no—
16C2×C13×C22⋊C4—24no—
17C2×C13×C22⋊C4—22no—
18C2×C13×C22⋊C4—22no—
19C2×C13×C22⋊C4—24no—
20C2×C13×C22⋊C4—24no—
21C2×C13×C22⋊C4C2×C414yes—
22C2×C13×C22⋊C4D414yes—
23C2×C42×C13—22no—
24C13×#95—22no—
25C13×#95—22no—
26#8750C1311yesmaximal, characteristic, direct product factor, Sylow
27C24×C13—42no—
28C24×C13—81no—
29C24×C13—81no—
30C24×C13C22×C411yescharacteristic
31C24×C13C2×D412yes—
32C24×C13#4114yes—
33C22×C4×C13—22no—
34C22×C4×C13—22no—
35C22×C4×C13—24no—
36C22×C4×C13—44no—
37C22×C4×C13—81no—
38C22×C4×C13—81no—
39C22×C4×C13C22⋊C412yes—
40C22×C4×C13C22⋊C412yes—
41C13×C4⋊C4—82no—
42C13×C22⋊C4—28no—
43C13×C22⋊C4—44no—
44C13×C22⋊C4—48no—
45C13×C22⋊C4—82no—
46C13×C22⋊C4—82no—
47C13×C22⋊C4—84no—
48C13×C22⋊C4—84no—
49C42×C13—82no—
50#2312C2×C1311yescharacteristic
51#1819C2×C1312yes—
52#1304C2×C1314yes—
53C23×C13—22no—
54C23×C13—24no—
55C23×C13—41no—
56C23×C13—41no—
57C23×C13—42no—
58C23×C13—42no—
59C23×C13—44no—
60C23×C13—44no—
61C23×C13—44no—
62C23×C13—88no—
63C23×C13C2×C22⋊C411yescharacteristic
64C23×C13#11712yes—
65C23×C13#12314yes—
66C2×C4×C13—22no—
67C2×C4×C13—22no—
68C2×C4×C13—42no—
69C2×C4×C13—42no—
70C2×C4×C13—44no—
71C2×C4×C13—44no—
72C2×C4×C13—44no—
73C2×C4×C13—82no—
74C2×C4×C13—82no—
75C2×C4×C13—84no—
76C2×C4×C13—84no—
77C2×C4×C13—84no—
78C22×C22⋊C4C22×C1311yescharacteristic
79#388—24no—
80#380C4×C1312yescomplemented
81#379C22×C1314yes—
82#379C22×C1312yes—
83C4×C22⋊C4C4×C1312yescomplemented
84#342—24no—
85C22×C13—21no—
86C22×C13—21no—
87C22×C13—24no—
88C22×C13—22no—
89C22×C13—22no—
90C22×C13—22no—
91C22×C13—24no—
92C22×C13—24no—
93C22×C13—44no—
94C22×C13—84no—
95C22×C13—88no—
96C22×C13#38111yescharacteristic
97C22×C13#41012yes—
98C4×C13—42no—
99C4×C13—42no—
100C4×C13—84no—
101C4×C13—164no—
102C25C23×C1311yescharacteristic
103C23×C4C2×C4×C1311yescharacteristic
104C23×C4C2×C4×C1311yescharacteristic
105C2×C4⋊C4—22no—
106C2×C22⋊C4—24no—
107C2×C22⋊C4—24no—
108C2×C22⋊C4—22no—
109C2×C22⋊C4—22no—
110C2×C22⋊C4—24no—
111C2×C22⋊C4—24no—
112C2×C22⋊C4C2×C4×C1314yes—
113C2×C22⋊C4D4×C1314yes—
114C2×C42—22no—
115#95—22no—
116#95—22no—
117C2×C13—22no—
118C2×C13—44no—
119C2×C13—42no—
120C2×C13#182011yescharacteristic
121C2×C13#182811yescharacteristic
122C2×C13#182811yescharacteristic
123C24—42no—
124C24—81no—
125C24—81no—
126C24C22×C4×C1311yescharacteristic
127C24C2×D4×C1312yes—
128C24C13×#4114yes—
129C22×C4—22no—
130C22×C4—22no—
131C22×C4—24no—
132C22×C4—44no—
133C22×C4—81no—
134C22×C4—81no—
135C22×C4C13×C22⋊C412yes—
136C22×C4C13×C22⋊C412yes—
137C4⋊C4—82no—
138C22⋊C4—28no—
139C22⋊C4—44no—
140C22⋊C4—48no—
141C22⋊C4—82no—
142C22⋊C4—82no—
143C22⋊C4—84no—
144C22⋊C4—84no—
145C42—82no—
146C13#875011yescharacteristic, direct product factor, Sylow
147C23—22no—
148C23—24no—
149C23—41no—
150C23—41no—
151C23—42no—
152C23—42no—
153C23—44no—
154C23—44no—
155C23—44no—
156C23—88no—
157C23C2×C13×C22⋊C411yescharacteristic
158C23C13×#11712yes—
159C23C13×#12314yes—
160C2×C4—22no—
161C2×C4—22no—
162C2×C4—42no—
163C2×C4—42no—
164C2×C4—44no—
165C2×C4—44no—
166C2×C4—44no—
167C2×C4—82no—
168C2×C4—82no—
169C2×C4—84no—
170C2×C4—84no—
171C2×C4—84no—
172C22—21no—
173C22—21no—
174C22—24no—
175C22—22no—
176C22—22no—
177C22—22no—
178C22—24no—
179C22—24no—
180C22—44no—
181C22—84no—
182C22—88no—
183C22C13×#38111yescharacteristic
184C22C13×#41012yes—
185C4—42no—
186C4—42no—
187C4—84no—
188C4—164no—
189C2—22no—
190C2—44no—
191C2—42no—
192C2C13×#182011yescharacteristic
193C2C13×#182811yescharacteristic
194C2C13×#182811yescharacteristic
subgroupG/H
center, socleC22×C13#381
commutatorC24C22×C4×C13
Frattini, cosocleC25C23×C13
prime radicalC25×C13C23
LCSG ▷ C24 ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ C25×C13 ◁ G

Complements

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

NH ≅ G/Ntype
6. C13×#380C4semidirect
9. C4×C13×C22⋊C4C4semidirect
26. #8750C13direct (N × H)
80. #380C4×C13semidirect
83. C4×C22⋊C4C4×C13semidirect
146. C13#8750direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#23122
C13×#18192
C13×#13042
#875013