Finite Group Databasebeta

← C13×#11518 #15697857

Subgroups — C13×#11518 #15697857

Order 3328.

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

normal subgroups only

This group has 446 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×#2296C211yesmaximal, characteristic
2C13×#1464C212yesmaximal
3C13×#1326C214yesmaximal
4C2×C13×#117C411yescharacteristic
5C2×C13×#117C2211yescharacteristic
6C22×C42×C13C411yescharacteristic
7C13×#432—22no—
8C13×#389—22no—
9C13×#385C412yes—
10C13×#385C2212yes—
11C4×C13×C4⋊C4—22no—
12C13×#324—22no—
13C13×#323C2214yes—
14C23×C4×C13C2×C411yescharacteristic
15C23×C4×C13C2×C412yes—
16C13×#117—24no—
17C13×#117—42no—
18C2×C13×C4⋊C4—21no—
19C2×C13×C4⋊C4—22no—
20C2×C13×C4⋊C4—22no—
21C2×C13×C4⋊C4D412yes—
22C2×C13×C22⋊C4C2×C412yes—
23C2×C13×C22⋊C4C2×C411yescharacteristic
24C2×C13×C22⋊C4C2311yescharacteristic
25C2×C42×C13—21no—
26C2×C42×C13—21no—
27C2×C42×C13—21no—
28C2×C42×C13—42no—
29C2×C42×C13D412yes—
30C13×C4⋊C8—42no—
31C13×C22⋊C8—24no—
32C13×#97—42no—
33C13×#95—22no—
34C13×#95—22no—
35#11518C1311yesmaximal, characteristic, direct product factor, Sylow
36C24×C13C22×C411yescharacteristic
37C22×C4×C13—22no—
38C22×C4×C13—22no—
39C22×C4×C13—22no—
40C22×C4×C13—22no—
41C22×C4×C13—22no—
42C22×C4×C13—44no—
43C22×C4×C13—42no—
44C22×C4×C13C22⋊C411yescharacteristic
45C22×C4×C13C22⋊C412yes—
46C22×C4×C13C22⋊C411yescharacteristic
47C22×C4×C13C2×D412yes—
48C2×C8×C13—44no—
49C13×C4⋊C4—24no—
50C13×C4⋊C4—42no—
51C13×C4⋊C4—44no—
52C13×C4⋊C4—44no—
53C13×C22⋊C4—22no—
54C13×C22⋊C4—41no—
55C13×C22⋊C4—41no—
56C13×C22⋊C4M1614yes—
57C42×C13—24no—
58C42×C13—22no—
59C42×C13—22no—
60C42×C13—42no—
61C42×C13—42no—
62#2296C2×C1311yescharacteristic
63#1464C2×C1312yes—
64#1326C2×C1314yes—
65C23×C13—21no—
66C23×C13—21no—
67C23×C13—42no—
68C23×C13C2×C22⋊C411yescharacteristic
69C23×C13C2×M1612yes—
70C2×C4×C13—28no—
71C2×C4×C13—21no—
72C2×C4×C13—21no—
73C2×C4×C13—21no—
74C2×C4×C13—21no—
75C2×C4×C13—24no—
76C2×C4×C13—24no—
77C2×C4×C13—22no—
78C2×C4×C13—22no—
79C2×C4×C13—42no—
80C2×C4×C13—42no—
81C2×C4×C13—42no—
82C2×C4×C13—44no—
83C2×C4×C13—42no—
84C2×C4×C13—42no—
85C2×C4×C13—42no—
86C2×C4×C13—44no—
87C2×C4×C13#9912yes—
88C2×C4×C13#10112yes—
89C8×C13—84no—
90C2×#117C4×C1311yescharacteristic
91C2×#117C22×C1311yescharacteristic
92C22×C42C4×C1311yescharacteristic
93#432—22no—
94#389—22no—
95#385C4×C1312yes—
96#385C22×C1312yes—
97C4×C4⋊C4—22no—
98#324—22no—
99#323C22×C1314yes—
100C22×C13—22no—
101C22×C13—22no—
102C22×C13—42no—
103C22×C13—42no—
104C22×C13—42no—
105C22×C13#40711yescharacteristic
106C22×C13C2×#9911yescharacteristic
107C22×C13C2×#10111yescharacteristic
108C4×C13—22no—
109C4×C13—22no—
110C4×C13—44no—
111C4×C13—42no—
112C4×C13—42no—
113C4×C13—44no—
114C23×C4C2×C4×C1311yescharacteristic
115C23×C4C2×C4×C1312yes—
116#117—24no—
117#117—42no—
118C2×C4⋊C4—21no—
119C2×C4⋊C4—22no—
120C2×C4⋊C4—22no—
121C2×C4⋊C4D4×C1312yes—
122C2×C22⋊C4C2×C4×C1312yes—
123C2×C22⋊C4C2×C4×C1311yescharacteristic
124C2×C22⋊C4C23×C1311yescharacteristic
125C2×C42—21no—
126C2×C42—21no—
127C2×C42—21no—
128C2×C42—42no—
129C2×C42D4×C1312yes—
130C4⋊C8—42no—
131C22⋊C8—24no—
132#97—42no—
133#95—22no—
134#95—22no—
135C2×C13—21no—
136C2×C13—21no—
137C2×C13—42no—
138C2×C13#146311yescharacteristic
139C2×C13#212012yes—
140C24C22×C4×C1311yescharacteristic
141C22×C4—22no—
142C22×C4—22no—
143C22×C4—22no—
144C22×C4—22no—
145C22×C4—22no—
146C22×C4—44no—
147C22×C4—42no—
148C22×C4C13×C22⋊C411yescharacteristic
149C22×C4C13×C22⋊C411yescharacteristic
150C22×C4C13×C22⋊C412yes—
151C22×C4C2×D4×C1312yes—
152C2×C8—44no—
153C4⋊C4—24no—
154C4⋊C4—42no—
155C4⋊C4—44no—
156C4⋊C4—44no—
157C22⋊C4—22no—
158C22⋊C4—41no—
159C22⋊C4—41no—
160C22⋊C4C13×M1614yes—
161C42—24no—
162C42—22no—
163C42—22no—
164C42—42no—
165C42—42no—
166C13#1151811yescharacteristic, direct product factor, Sylow
167C23—21no—
168C23—21no—
169C23—42no—
170C23C2×C13×C22⋊C411yescharacteristic
171C23C2×C13×M1612yes—
172C2×C4—28no—
173C2×C4—21no—
174C2×C4—21no—
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—24no—
178C2×C4—24no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—42no—
182C2×C4—42no—
183C2×C4—42no—
184C2×C4—44no—
185C2×C4—42no—
186C2×C4—42no—
187C2×C4—42no—
188C2×C4—44no—
189C2×C4C13×#9912yes—
190C2×C4C13×#10112yes—
191C8—84no—
192C22—22no—
193C22—22no—
194C22—42no—
195C22—42no—
196C22—42no—
197C22C13×#40711yescharacteristic
198C22C2×C13×#9911yescharacteristic
199C22C2×C13×#10111yescharacteristic
200C4—22no—
201C4—22no—
202C4—44no—
203C4—42no—
204C4—42no—
205C4—44no—
206C2—21no—
207C2—21no—
208C2—42no—
209C2C13×#146311yescharacteristic
210C2C13×#212012yes—
subgroupG/H
center, socleC22×C13C2×#99
commutatorC24C22×C4×C13
Frattini, cosocleC2×C22⋊C4C23×C13
prime radicalC24×C13C22×C4
LCSG ▷ C24 ▷ 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
35. #11518C13direct (N × H)
166. C13#11518direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#22962
C13×#14642
C13×#13262
#1151813