Finite Group Databasebeta

← C13×#11522 #15697861

Subgroups — C13×#11522 #15697861

Order 3328.

284 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 98 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×#2921C211yesmaximal, characteristic
2C13×#2165C212yesmaximal, complemented
3C13×#1327C212yesmaximal, complemented
4C13×#1320C212yesmaximal
5C2×C13×#117C411yescharacteristic
6C13×#433—22no—
7C13×#433—22no—
8C13×#423C411yescharacteristic
9C13×#423C2211yescharacteristic
10C13×#407C411yescharacteristic
11C13×#407C2211yescharacteristic
12C4×C13×M16C411yescharacteristic
13C4×C13×M16C2211yescharacteristic
14C13×#364—22no—
15C13×#349C2214yes—
16C13×#347—22no—
17C23×C4×C13C2×C411yescharacteristic
18C2×C13×M16C2×C411yescharacteristic
19C2×C13×M16C2×C411yescharacteristic
20C2×C13×M16C2×C411yescharacteristic
21C2×C13×M16C2311yescharacteristic
22C13×#117—21no—
23C13×#117—21no—
24C13×#117—22no—
25C2×C13×C4⋊C4—21no—
26C2×C13×C22⋊C4—21no—
27C2×C42×C13C2×C411yescharacteristic
28C2×C42×C13C2×C411yescharacteristic
29C13×M32—24no—
30C13×C4⋊C8—22no—
31C13×C4⋊C8—22no—
32C13×C22⋊C8—22no—
33C13×C22⋊C8—22no—
34C13×#97—21no—
35C13×#97D412yes—
36C4×C8×C13—21no—
37C4×C8×C13D412yes—
38#11522C1311yesmaximal, characteristic, direct product factor, Sylow
39C24×C13M1611yescharacteristic
40C22×C4×C13—21no—
41C22×C4×C13—21no—
42C22×C4×C13—21no—
43C22×C4×C13—21no—
44C22×C4×C13—41no—
45C22×C4×C13—41no—
46C22×C4×C13M1611yescharacteristic
47C22×C4×C13C22×C411yescharacteristic
48C13×M16—41no—
49C13×M16—41no—
50C13×M16—41no—
51C13×M16—41no—
52C2×C8×C13—21no—
53C2×C8×C13—21no—
54C2×C8×C13C22⋊C412yes—
55C2×C8×C13C2×D412yes—
56C13×C4⋊C4—22no—
57C13×C4⋊C4—22no—
58C13×C22⋊C4—22no—
59C13×C22⋊C4—22no—
60C42×C13—21no—
61C42×C13—21no—
62C42×C13C22⋊C411yescharacteristic
63C42×C13C22⋊C411yescharacteristic
64C42×C13M1612yes—
65C13×C16—44no—
66#2921C2×C1311yescharacteristic
67#2165C2×C1312yescomplemented
68#1327C2×C1312yescomplemented
69#1320C2×C1312yes—
70C23×C13—21no—
71C23×C13—41no—
72C23×C13—81no—
73C23×C13C2×M1611yescharacteristic
74C2×C4×C13—21no—
75C2×C4×C13—21no—
76C2×C4×C13—21no—
77C2×C4×C13—21no—
78C2×C4×C13—22no—
79C2×C4×C13—21no—
80C2×C4×C13—42no—
81C2×C4×C13—41no—
82C2×C4×C13—41no—
83C2×C4×C13—41no—
84C2×C4×C13—81no—
85C2×C4×C13—81no—
86C2×C4×C13C2×C22⋊C411yescharacteristic
87C2×C4×C13C2×M1611yescharacteristic
88C8×C13—22no—
89C8×C13—22no—
90C8×C13—41no—
91C8×C13—41no—
92C2×#117C4×C1311yescharacteristic
93#433—22no—
94#433—22no—
95#423C4×C1311yescharacteristic
96#423C22×C1311yescharacteristic
97#407C4×C1311yescharacteristic
98#407C22×C1311yescharacteristic
99C4×M16C4×C1311yescharacteristic
100C4×M16C22×C1311yescharacteristic
101#364—22no—
102#349C22×C1314yes—
103#347—22no—
104C22×C13—21no—
105C22×C13—41no—
106C22×C13—42no—
107C22×C13—41no—
108C22×C13—82no—
109C22×C13#40711yescharacteristic
110C4×C13—21no—
111C4×C13—41no—
112C4×C13—41no—
113C4×C13—42no—
114C4×C13—41no—
115C4×C13#41011yescharacteristic
116C4×C13#41311yescharacteristic
117C23×C4C2×C4×C1311yescharacteristic
118C2×M16C2×C4×C1311yescharacteristic
119C2×M16C2×C4×C1311yescharacteristic
120C2×M16C2×C4×C1311yescharacteristic
121C2×M16C23×C1311yescharacteristic
122#117—21no—
123#117—21no—
124#117—22no—
125C2×C4⋊C4—21no—
126C2×C22⋊C4—21no—
127C2×C42C2×C4×C1311yescharacteristic
128C2×C42C2×C4×C1311yescharacteristic
129M32—24no—
130C4⋊C8—22no—
131C4⋊C8—22no—
132C22⋊C8—22no—
133C22⋊C8—22no—
134#97—21no—
135#97D4×C1312yes—
136C4×C8—21no—
137C4×C8D4×C1312yes—
138C2×C13—21no—
139C2×C13—41no—
140C2×C13—81no—
141C2×C13#146411yescharacteristic
142C24C13×M1611yescharacteristic
143C22×C4—21no—
144C22×C4—21no—
145C22×C4—21no—
146C22×C4—21no—
147C22×C4—41no—
148C22×C4—41no—
149C22×C4C13×M1611yescharacteristic
150C22×C4C22×C4×C1311yescharacteristic
151M16—41no—
152M16—41no—
153M16—41no—
154M16—41no—
155C2×C8—21no—
156C2×C8—21no—
157C2×C8C13×C22⋊C412yes—
158C2×C8C2×D4×C1312yes—
159C4⋊C4—22no—
160C4⋊C4—22no—
161C22⋊C4—22no—
162C22⋊C4—22no—
163C42—21no—
164C42—21no—
165C42C13×C22⋊C411yescharacteristic
166C42C13×C22⋊C411yescharacteristic
167C42C13×M1612yes—
168C16—44no—
169C13#1152211yescharacteristic, direct product factor, Sylow
170C23—21no—
171C23—41no—
172C23—81no—
173C23C2×C13×M1611yescharacteristic
174C2×C4—21no—
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—22no—
179C2×C4—21no—
180C2×C4—42no—
181C2×C4—41no—
182C2×C4—41no—
183C2×C4—41no—
184C2×C4—81no—
185C2×C4—81no—
186C2×C4C2×C13×C22⋊C411yescharacteristic
187C2×C4C2×C13×M1611yescharacteristic
188C8—22no—
189C8—22no—
190C8—41no—
191C8—41no—
192C22—21no—
193C22—41no—
194C22—42no—
195C22—41no—
196C22—82no—
197C22C13×#40711yescharacteristic
198C4—21no—
199C4—41no—
200C4—41no—
201C4—42no—
202C4—41no—
203C4C13×#41011yescharacteristic
204C4C13×#41311yescharacteristic
205C2—21no—
206C2—41no—
207C2—81no—
208C2C13×#146411yescharacteristic
subgroupG/H
centerC4×C13#410
commutatorC22×C4C22×C4×C13
Frattini, cosocleC2×M16C23×C13
socleC2×C13#1464
prime radicalC24×C13M16
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C4×C13 ◁ C42×C13 ◁ C4×C13×M16 ◁ G

Complements

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

NH ≅ G/Ntype
2. C13×#2165C2semidirect
3. C13×#1327C2semidirect
38. #11522C13direct (N × H)
67. #2165C2×C13semidirect
68. #1327C2×C13semidirect
169. C13#11522direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#29212
C13×#21652
C13×#13272
C13×#13202
#1152213