Finite Group Databasebeta

← C13×#12863 #15699202

Subgroups — C13×#12863 #15699202

Order 3328.

614 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 614 conjugacy classes of subgroups — too many to draw. Only its 118 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×#2311C211yesmaximal, characteristic
2C13×#1785C212yesmaximal
3C13×#1394C214yesmaximal, complemented
4C22×C13×#41C2211yescharacteristic
5C2×C13×#117C411yescharacteristic
6C22×C13×C4⋊C4C411yescharacteristic
7C2×C13×#101C2214yes—
8C2×C13×#100—22no—
9C13×#407—22no—
10C13×#391C2212yes—
11C13×#390C412yes—
12C13×#386—22no—
13C13×#380—22no—
14C2×C13×#41—24no—
15C2×C13×#41—42no—
16C2×C13×#41—42no—
17C22×Q8×C13C2311yescharacteristic
18C22×D4×C13C2×C411yescharacteristic
19C22×D4×C13D412yes—
20C23×C4×C13—21no—
21C23×C4×C13C2×C411yescharacteristic
22C23×C4×C13D412yes—
23C2×C13×M16—24no—
24C13×#117—42no—
25C2×C13×C4⋊C4—21no—
26C2×C13×C4⋊C4—21no—
27C2×C13×C4⋊C4—42no—
28C2×C13×C4⋊C4C2×C412yes—
29C2×C13×C22⋊C4—21no—
30C2×C13×C22⋊C4—24no—
31C2×C42×C13C2×C412yes—
32C13×#101—28no—
33C13×#100—44no—
34C13×C22⋊C8—44no—
35C13×#95—24no—
36#12863C1311yesmaximal, characteristic, direct product factor, Sylow
37C24×C13C22⋊C412yes—
38C24×C13C22⋊C411yescharacteristic
39C13×#41—416no—
40C2×Q8×C13—41no—
41C2×Q8×C13—41no—
42C2×Q8×C13#4114yes—
43C2×D4×C13—24no—
44C2×D4×C13—22no—
45C2×D4×C13—24no—
46C2×D4×C13—41no—
47C2×D4×C13—41no—
48C2×D4×C13—42no—
49C22×C4×C13—22no—
50C22×C4×C13—22no—
51C22×C4×C13—22no—
52C22×C4×C13—24no—
53C22×C4×C13—24no—
54C22×C4×C13—22no—
55C22×C4×C13—22no—
56C22×C4×C13—42no—
57C22×C4×C13—42no—
58C22×C4×C13—82no—
59C22×C4×C13C22⋊C411yescharacteristic
60C22×C4×C13C22×C411yescharacteristic
61C22×C4×C13C2×D412yes—
62C13×M16—44no—
63C13×M16—44no—
64C2×C8×C13—44no—
65C13×C4⋊C4—42no—
66C13×C4⋊C4—42no—
67C13×C4⋊C4—42no—
68C13×C22⋊C4—42no—
69C13×C22⋊C4—84no—
70C42×C13—42no—
71#2311C2×C1311yescharacteristic
72#1785C2×C1312yes—
73#1394C2×C1314yescomplemented
74C23×C13—21no—
75C23×C13—21no—
76C23×C13—22no—
77C23×C13—22no—
78C23×C13—22no—
79C23×C13—41no—
80C23×C13—41no—
81C23×C13—42no—
82C23×C13—42no—
83C23×C13#9912yes—
84C23×C13C2×C22⋊C411yescharacteristic
85Q8×C13—44no—
86D4×C13—48no—
87D4×C13—44no—
88C2×C4×C13—28no—
89C2×C4×C13—21no—
90C2×C4×C13—21no—
91C2×C4×C13—21no—
92C2×C4×C13—22no—
93C2×C4×C13—21no—
94C2×C4×C13—22no—
95C2×C4×C13—48no—
96C2×C4×C13—42no—
97C2×C4×C13—44no—
98C2×C4×C13—42no—
99C2×C4×C13—42no—
100C2×C4×C13—42no—
101C2×C4×C13—84no—
102C2×C4×C13#9912yes—
103C2×C4×C13#11712yes—
104C2×C4×C13#12314yes—
105C8×C13—84no—
106C22×#41C22×C1311yescharacteristic
107C2×#117C4×C1311yescharacteristic
108C22×C4⋊C4C4×C1311yescharacteristic
109C2×#101C22×C1314yes—
110C2×#100—22no—
111#407—22no—
112#391C22×C1312yes—
113#390C4×C1312yes—
114#386—22no—
115#380—22no—
116C22×C13—21no—
117C22×C13—21no—
118C22×C13—22no—
119C22×C13—42no—
120C22×C13—42no—
121C22×C13—44no—
122C22×C13—41no—
123C22×C13—41no—
124C22×C13—42no—
125C22×C13—42no—
126C22×C13—42no—
127C22×C13—82no—
128C22×C13#38111yescharacteristic
129C22×C13C2×#9911yescharacteristic
130C22×C13C2×#9911yescharacteristic
131C4×C13—24no—
132C4×C13—22no—
133C4×C13—22no—
134C4×C13—82no—
135C4×C13—82no—
136C2×#41—24no—
137C2×#41—42no—
138C2×#41—42no—
139C22×Q8C23×C1311yescharacteristic
140C22×D4C2×C4×C1311yescharacteristic
141C22×D4D4×C1312yes—
142C23×C4—21no—
143C23×C4C2×C4×C1311yescharacteristic
144C23×C4D4×C1312yes—
145C2×M16—24no—
146#117—42no—
147C2×C4⋊C4—21no—
148C2×C4⋊C4—21no—
149C2×C4⋊C4—42no—
150C2×C4⋊C4C2×C4×C1312yes—
151C2×C22⋊C4—21no—
152C2×C22⋊C4—24no—
153C2×C42C2×C4×C1312yes—
154#101—28no—
155#100—44no—
156C22⋊C8—44no—
157#95—24no—
158C2×C13—21no—
159C2×C13—21no—
160C2×C13—42no—
161C2×C13—82no—
162C2×C13#181911yescharacteristic
163C2×C13#213411yescharacteristic
164C2×C13#213511yescharacteristic
165C24C13×C22⋊C412yes—
166C24C13×C22⋊C411yescharacteristic
167#41—416no—
168C2×Q8—41no—
169C2×Q8—41no—
170C2×Q8C13×#4114yes—
171C2×D4—24no—
172C2×D4—22no—
173C2×D4—24no—
174C2×D4—41no—
175C2×D4—41no—
176C2×D4—42no—
177C22×C4—22no—
178C22×C4—22no—
179C22×C4—22no—
180C22×C4—24no—
181C22×C4—24no—
182C22×C4—22no—
183C22×C4—22no—
184C22×C4—42no—
185C22×C4—42no—
186C22×C4—82no—
187C22×C4C13×C22⋊C411yescharacteristic
188C22×C4C22×C4×C1311yescharacteristic
189C22×C4C2×D4×C1312yes—
190M16—44no—
191M16—44no—
192C2×C8—44no—
193C4⋊C4—42no—
194C4⋊C4—42no—
195C4⋊C4—42no—
196C22⋊C4—42no—
197C22⋊C4—84no—
198C42—42no—
199C13#1286311yescharacteristic, direct product factor, Sylow
200C23—21no—
201C23—21no—
202C23—22no—
203C23—22no—
204C23—22no—
205C23—41no—
206C23—41no—
207C23—42no—
208C23—42no—
209C23C13×#9912yes—
210C23C2×C13×C22⋊C411yescharacteristic
211Q8—44no—
212D4—48no—
213D4—44no—
214C2×C4—28no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—48no—
222C2×C4—42no—
223C2×C4—44no—
224C2×C4—42no—
225C2×C4—42no—
226C2×C4—42no—
227C2×C4—84no—
228C2×C4C13×#9912yes—
229C2×C4C13×#11712yes—
230C2×C4C13×#12314yes—
231C8—84no—
232C22—21no—
233C22—21no—
234C22—22no—
235C22—42no—
236C22—42no—
237C22—44no—
238C22—41no—
239C22—41no—
240C22—42no—
241C22—42no—
242C22—42no—
243C22—82no—
244C22C13×#38111yescharacteristic
245C22C2×C13×#9911yescharacteristic
246C22C2×C13×#9911yescharacteristic
247C4—24no—
248C4—22no—
249C4—22no—
250C4—82no—
251C4—82no—
252C2—21no—
253C2—21no—
254C2—42no—
255C2—82no—
256C2C13×#181911yescharacteristic
257C2C13×#213411yescharacteristic
258C2C13×#213511yescharacteristic
subgroupG/H
center, socleC22×C13C2×#99
commutatorC22×C4C22×C4×C13
Frattini, cosocleC22×Q8C23×C13
prime radicalC22×C13×#41C22
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C22×C4×C13 ◁ C22×C13×#41 ◁ G

Complements

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

NH ≅ G/Ntype
3. C13×#1394C2semidirect
36. #12863C13direct (N × H)
73. #1394C2×C13semidirect
199. C13#12863direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#23112
C13×#17852
C13×#13942
#1286313