Finite Group Databasebeta

← C13×#11510 #15697849

Subgroups — C13×#11510 #15697849

Order 3328.

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

normal subgroups only

This group has 510 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×#2310C211yesmaximal, characteristic
2C13×#1464C212yesmaximal
3C13×#1319C214yesmaximal, complemented
4C23×Q8×C13C411yescharacteristic
5C2×C13×#117C411yescharacteristic
6C2×C13×#117C2211yescharacteristic
7C13×#432—22no—
8C13×#391—22no—
9C13×#391C412yes—
10C13×#391C2212yes—
11C13×#381—22no—
12C13×#324C2214yes—
13C13×#323—22no—
14C22×Q8×C13—24no—
15C22×Q8×C13—21no—
16C22×Q8×C13—42no—
17C22×Q8×C13—42no—
18C22×Q8×C13C2×C412yes—
19C23×C4×C13—21no—
20C23×C4×C13C2×C411yescharacteristic
21C13×#117—42no—
22C13×#117—42no—
23C2×C13×C4⋊C4—21no—
24C2×C13×C4⋊C4C2×C411yescharacteristic
25C2×C13×C4⋊C4C2311yescharacteristic
26C2×C13×C22⋊C4—21no—
27C2×C13×C22⋊C4D412yes—
28C2×C42×C13C2×C412yes—
29C2×C42×C13D412yes—
30C13×C4⋊C8—42no—
31C13×C22⋊C8—24no—
32C13×#97—42no—
33C13×#95—24no—
34C13×#95—24no—
35#11510C1311yesmaximal, characteristic, direct product factor, Sylow
36C24×C13C22⋊C411yescharacteristic
37C2×Q8×C13—24no—
38C2×Q8×C13—22no—
39C2×Q8×C13—416no—
40C2×Q8×C13—42no—
41C2×Q8×C13—42no—
42C2×Q8×C13—42no—
43C2×Q8×C13—42no—
44C2×Q8×C13M1614yes—
45C22×C4×C13—22no—
46C22×C4×C13—22no—
47C22×C4×C13—22no—
48C22×C4×C13—24no—
49C22×C4×C13—22no—
50C22×C4×C13—22no—
51C22×C4×C13—42no—
52C22×C4×C13—42no—
53C22×C4×C13C22⋊C412yes—
54C22×C4×C13C22⋊C411yescharacteristic
55C22×C4×C13C22×C411yescharacteristic
56C22×C4×C13C2×D412yes—
57C2×C8×C13—44no—
58C13×C4⋊C4—41no—
59C13×C4⋊C4—41no—
60C13×C4⋊C4—42no—
61C13×C22⋊C4—42no—
62C13×C22⋊C4—42no—
63C42×C13—22no—
64C42×C13—22no—
65C42×C13—42no—
66#2310C2×C1311yescharacteristic
67#1464C2×C1312yes—
68#1319C2×C1314yescomplemented
69C23×C13—21no—
70C23×C13—21no—
71C23×C13—41no—
72C23×C13—41no—
73C23×C13#10012yes—
74C23×C13C2×C22⋊C411yescharacteristic
75Q8×C13—48no—
76Q8×C13—44no—
77Q8×C13—44no—
78C2×C4×C13—28no—
79C2×C4×C13—21no—
80C2×C4×C13—21no—
81C2×C4×C13—21no—
82C2×C4×C13—21no—
83C2×C4×C13—24no—
84C2×C4×C13—22no—
85C2×C4×C13—22no—
86C2×C4×C13—48no—
87C2×C4×C13—42no—
88C2×C4×C13—42no—
89C2×C4×C13—42no—
90C2×C4×C13—42no—
91C2×C4×C13—42no—
92C2×C4×C13—42no—
93C2×C4×C13—42no—
94C2×C4×C13#9912yes—
95C2×C4×C13C2×M1612yes—
96C8×C13—84no—
97C23×Q8C4×C1311yescharacteristic
98C2×#117C4×C1311yescharacteristic
99C2×#117C22×C1311yescharacteristic
100#432—22no—
101#391—22no—
102#391C4×C1312yes—
103#391C22×C1312yes—
104#381—22no—
105#324C22×C1314yes—
106#323—22no—
107C22×C13—21no—
108C22×C13—21no—
109C22×C13—22no—
110C22×C13—42no—
111C22×C13—42no—
112C22×C13—41no—
113C22×C13—41no—
114C22×C13#40711yescharacteristic
115C22×C13C2×#9911yescharacteristic
116C22×C13C2×#10011yescharacteristic
117C4×C13—22no—
118C4×C13—22no—
119C4×C13—42no—
120C4×C13—42no—
121C4×C13—44no—
122C4×C13—82no—
123C22×Q8—24no—
124C22×Q8—21no—
125C22×Q8—42no—
126C22×Q8—42no—
127C22×Q8C2×C4×C1312yes—
128C23×C4—21no—
129C23×C4C2×C4×C1311yescharacteristic
130#117—42no—
131#117—42no—
132C2×C4⋊C4—21no—
133C2×C4⋊C4C2×C4×C1311yescharacteristic
134C2×C4⋊C4C23×C1311yescharacteristic
135C2×C22⋊C4—21no—
136C2×C22⋊C4D4×C1312yes—
137C2×C42C2×C4×C1312yes—
138C2×C42D4×C1312yes—
139C4⋊C8—42no—
140C22⋊C8—24no—
141#97—42no—
142#95—24no—
143#95—24no—
144C2×C13—21no—
145C2×C13—21no—
146C2×C13—42no—
147C2×C13#146211yescharacteristic
148C2×C13#212911yescharacteristic
149C2×C13#213511yescharacteristic
150C24C13×C22⋊C411yescharacteristic
151C2×Q8—24no—
152C2×Q8—22no—
153C2×Q8—416no—
154C2×Q8—42no—
155C2×Q8—42no—
156C2×Q8—42no—
157C2×Q8—42no—
158C2×Q8C13×M1614yes—
159C22×C4—22no—
160C22×C4—22no—
161C22×C4—22no—
162C22×C4—24no—
163C22×C4—22no—
164C22×C4—22no—
165C22×C4—42no—
166C22×C4—42no—
167C22×C4C13×C22⋊C411yescharacteristic
168C22×C4C13×C22⋊C412yes—
169C22×C4C22×C4×C1311yescharacteristic
170C22×C4C2×D4×C1312yes—
171C2×C8—44no—
172C4⋊C4—41no—
173C4⋊C4—41no—
174C4⋊C4—42no—
175C22⋊C4—42no—
176C22⋊C4—42no—
177C42—22no—
178C42—22no—
179C42—42no—
180C13#1151011yescharacteristic, direct product factor, Sylow
181C23—21no—
182C23—21no—
183C23—41no—
184C23—41no—
185C23C13×#10012yes—
186C23C2×C13×C22⋊C411yescharacteristic
187Q8—44no—
188Q8—48no—
189Q8—44no—
190C2×C4—28no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—21no—
195C2×C4—24no—
196C2×C4—22no—
197C2×C4—22no—
198C2×C4—48no—
199C2×C4—42no—
200C2×C4—42no—
201C2×C4—42no—
202C2×C4—42no—
203C2×C4—42no—
204C2×C4—42no—
205C2×C4—42no—
206C2×C4C13×#9912yes—
207C2×C4C2×C13×M1612yes—
208C8—84no—
209C22—21no—
210C22—21no—
211C22—22no—
212C22—42no—
213C22—42no—
214C22—41no—
215C22—41no—
216C22C13×#40711yescharacteristic
217C22C2×C13×#9911yescharacteristic
218C22C2×C13×#10011yescharacteristic
219C4—22no—
220C4—22no—
221C4—42no—
222C4—42no—
223C4—44no—
224C4—82no—
225C2—21no—
226C2—21no—
227C2—42no—
228C2C13×#146211yescharacteristic
229C2C13×#212911yescharacteristic
230C2C13×#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×#1319C2semidirect
35. #11510C13direct (N × H)
68. #1319C2×C13semidirect
180. C13#11510direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#23102
C13×#14642
C13×#13192
#1151013