Finite Group Databasebeta

← C13×#11516 #15697855

Subgroups — C13×#11516 #15697855

Order 3328.

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

normal subgroups only

This group has 418 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×#2317C211yesmaximal, characteristic
2C13×#1464C212yesmaximal
3C13×#1325C214yesmaximal, complemented
4C2×C13×#117C411yescharacteristic
5C2×C13×#117C2211yescharacteristic
6C22×C13×C4⋊C4C411yescharacteristic
7C13×#432—22no—
8C13×#389—22no—
9C13×#385—22no—
10C13×#384C2212yes—
11C13×#382C412yes—
12C13×#324C2214yes—
13C13×#323—22no—
14C23×C4×C13—21no—
15C23×C4×C13C2×C411yescharacteristic
16C13×#117—24no—
17C13×#117—42no—
18C2×C13×C4⋊C4—21no—
19C2×C13×C4⋊C4—21no—
20C2×C13×C4⋊C4—24no—
21C2×C13×C4⋊C4—42no—
22C2×C13×C4⋊C4C2×C412yes—
23C2×C13×C4⋊C4C2×C411yescharacteristic
24C2×C13×C4⋊C4C2311yescharacteristic
25C2×C13×C22⋊C4—21no—
26C2×C13×C22⋊C4D412yes—
27C2×C42×C13C2×C412yes—
28C2×C42×C13D412yes—
29C13×C4⋊C8—42no—
30C13×C22⋊C8—24no—
31C13×#97—42no—
32C13×#95—24no—
33#11516C1311yesmaximal, characteristic, direct product factor, Sylow
34C24×C13C22⋊C411yescharacteristic
35C22×C4×C13—22no—
36C22×C4×C13—22no—
37C22×C4×C13—22no—
38C22×C4×C13—22no—
39C22×C4×C13—22no—
40C22×C4×C13—42no—
41C22×C4×C13—82no—
42C22×C4×C13C22⋊C412yes—
43C22×C4×C13C22⋊C411yescharacteristic
44C22×C4×C13C22×C411yescharacteristic
45C22×C4×C13C2×D412yes—
46C2×C8×C13—44no—
47C13×C4⋊C4—24no—
48C13×C4⋊C4—41no—
49C13×C4⋊C4—41no—
50C13×C4⋊C4—42no—
51C13×C4⋊C4—42no—
52C13×C4⋊C4—84no—
53C13×C22⋊C4—24no—
54C13×C22⋊C4—42no—
55C42×C13—22no—
56C42×C13—22no—
57C42×C13—22no—
58C42×C13M1614yes—
59#2317C2×C1311yescharacteristic
60#1464C2×C1312yes—
61#1325C2×C1314yescomplemented
62C23×C13—21no—
63C23×C13—21no—
64C23×C13—41no—
65C23×C13—41no—
66C23×C13#10112yes—
67C23×C13C2×C22⋊C411yescharacteristic
68C2×C4×C13—28no—
69C2×C4×C13—21no—
70C2×C4×C13—21no—
71C2×C4×C13—21no—
72C2×C4×C13—21no—
73C2×C4×C13—24no—
74C2×C4×C13—22no—
75C2×C4×C13—22no—
76C2×C4×C13—42no—
77C2×C4×C13—42no—
78C2×C4×C13—42no—
79C2×C4×C13—42no—
80C2×C4×C13—44no—
81C2×C4×C13—42no—
82C2×C4×C13—84no—
83C2×C4×C13#9912yes—
84C2×C4×C13C2×M1612yes—
85C8×C13—84no—
86C2×#117C4×C1311yescharacteristic
87C2×#117C22×C1311yescharacteristic
88C22×C4⋊C4C4×C1311yescharacteristic
89#432—22no—
90#389—22no—
91#385—22no—
92#384C22×C1312yes—
93#382C4×C1312yes—
94#324C22×C1314yes—
95#323—22no—
96C22×C13—21no—
97C22×C13—21no—
98C22×C13—22no—
99C22×C13—42no—
100C22×C13—42no—
101C22×C13—41no—
102C22×C13—41no—
103C22×C13#40711yescharacteristic
104C22×C13C2×#9911yescharacteristic
105C22×C13C2×#10111yescharacteristic
106C4×C13—22no—
107C4×C13—22no—
108C4×C13—44no—
109C4×C13—42no—
110C4×C13—42no—
111C4×C13—82no—
112C23×C4—21no—
113C23×C4C2×C4×C1311yescharacteristic
114#117—24no—
115#117—42no—
116C2×C4⋊C4—21no—
117C2×C4⋊C4—21no—
118C2×C4⋊C4—24no—
119C2×C4⋊C4—42no—
120C2×C4⋊C4C2×C4×C1312yes—
121C2×C4⋊C4C2×C4×C1311yescharacteristic
122C2×C4⋊C4C23×C1311yescharacteristic
123C2×C22⋊C4—21no—
124C2×C22⋊C4D4×C1312yes—
125C2×C42C2×C4×C1312yes—
126C2×C42D4×C1312yes—
127C4⋊C8—42no—
128C22⋊C8—24no—
129#97—42no—
130#95—24no—
131C2×C13—21no—
132C2×C13—21no—
133C2×C13—42no—
134C2×C13#146311yescharacteristic
135C2×C13#212811yescharacteristic
136C2×C13#213511yescharacteristic
137C24C13×C22⋊C411yescharacteristic
138C22×C4—22no—
139C22×C4—22no—
140C22×C4—22no—
141C22×C4—22no—
142C22×C4—22no—
143C22×C4—42no—
144C22×C4—82no—
145C22×C4C13×C22⋊C411yescharacteristic
146C22×C4C13×C22⋊C412yes—
147C22×C4C22×C4×C1311yescharacteristic
148C22×C4C2×D4×C1312yes—
149C2×C8—44no—
150C4⋊C4—24no—
151C4⋊C4—41no—
152C4⋊C4—41no—
153C4⋊C4—42no—
154C4⋊C4—42no—
155C4⋊C4—84no—
156C22⋊C4—24no—
157C22⋊C4—42no—
158C42—22no—
159C42—22no—
160C42—22no—
161C42C13×M1614yes—
162C13#1151611yescharacteristic, direct product factor, Sylow
163C23—21no—
164C23—21no—
165C23—41no—
166C23—41no—
167C23C13×#10112yes—
168C23C2×C13×C22⋊C411yescharacteristic
169C2×C4—28no—
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—21no—
173C2×C4—21no—
174C2×C4—24no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—42no—
178C2×C4—42no—
179C2×C4—42no—
180C2×C4—42no—
181C2×C4—44no—
182C2×C4—42no—
183C2×C4—84no—
184C2×C4C13×#9912yes—
185C2×C4C2×C13×M1612yes—
186C8—84no—
187C22—21no—
188C22—21no—
189C22—22no—
190C22—42no—
191C22—42no—
192C22—41no—
193C22—41no—
194C22C13×#40711yescharacteristic
195C22C2×C13×#9911yescharacteristic
196C22C2×C13×#10111yescharacteristic
197C4—22no—
198C4—22no—
199C4—44no—
200C4—42no—
201C4—42no—
202C4—82no—
203C2—21no—
204C2—21no—
205C2—42no—
206C2C13×#146311yescharacteristic
207C2C13×#212811yescharacteristic
208C2C13×#213511yescharacteristic
subgroupG/H
center, socleC22×C13C2×#99
commutatorC22×C4C22×C4×C13
Frattini, cosocleC2×C4⋊C4C23×C13
prime radicalC24×C13C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C22×C4×C13 ◁ C2×C13×#117 ◁ G

Complements

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

NH ≅ G/Ntype
3. C13×#1325C2semidirect
33. #11516C13direct (N × H)
61. #1325C2×C13semidirect
162. C13#11516direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#23172
C13×#14642
C13×#13252
#1151613