Finite Group Databasebeta

← C13×#12857 #15699196

Subgroups — C13×#12857 #15699196

Order 3328.

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

normal subgroups only

This group has 670 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×#2297C211yesmaximal, characteristic
2C13×#1782C212yesmaximal
3C13×#1393C214yesmaximal, complemented
4C22×C13×#41C2211yescharacteristic
5C2×C13×#117C411yescharacteristic, complemented
6C22×C42×C13C411yescharacteristic, complemented
7C2×C13×#99—22no—
8C2×C13×#99C2214yes—
9C13×#391C412yescomplemented
10C13×#390C2212yes—
11C13×#386—22no—
12C13×#381—22no—
13C4×C13×C22⋊C4—22no—
14C2×C13×#41—24no—
15C2×C13×#41—42no—
16C2×C13×#41—42no—
17C22×Q8×C13C2×C411yescharacteristic
18C22×D4×C13D412yes—
19C22×D4×C13C2311yescharacteristic
20C23×C4×C13—21no—
21C23×C4×C13C2×C411yescharacteristic
22C23×C4×C13D412yes—
23C13×#117—42no—
24C2×C13×C4⋊C4C2×C412yes—
25C2×C13×C22⋊C4—21no—
26C2×C13×C22⋊C4—24no—
27C2×C13×C22⋊C4—24no—
28C2×C42×C13—21no—
29C2×C42×C13—21no—
30C2×C42×C13—42no—
31C2×C42×C13C2×C412yes—
32C13×#99—28no—
33C13×#99—44no—
34C13×#95—24no—
35C13×#95—44no—
36#12857C1311yesmaximal, characteristic, direct product factor, Sylow
37C24×C13C22⋊C411yescharacteristic
38C24×C13C2×D412yes—
39C13×#41—416no—
40C2×Q8×C13—22no—
41C2×Q8×C13—41no—
42C2×Q8×C13—41no—
43C2×D4×C13—24no—
44C2×D4×C13—24no—
45C2×D4×C13—42no—
46C2×D4×C13—41no—
47C2×D4×C13—41no—
48C2×D4×C13#4114yes—
49C22×C4×C13—22no—
50C22×C4×C13—22no—
51C22×C4×C13—22no—
52C22×C4×C13—22no—
53C22×C4×C13—24no—
54C22×C4×C13—24no—
55C22×C4×C13—22no—
56C22×C4×C13—42no—
57C22×C4×C13—44no—
58C22×C4×C13—42no—
59C22×C4×C13—44no—
60C22×C4×C13C22⋊C412yes—
61C22×C4×C13C22⋊C411yescharacteristic
62C22×C4×C13C22×C411yescharacteristic
63C13×C4⋊C4—42no—
64C13×C22⋊C4—48no—
65C13×C22⋊C4—42no—
66C13×C22⋊C4—44no—
67C13×C22⋊C4—44no—
68C42×C13—42no—
69C42×C13—42no—
70C42×C13—42no—
71#2297C2×C1311yescharacteristic
72#1782C2×C1312yes—
73#1393C2×C1314yescomplemented
74C23×C13—21no—
75C23×C13—21no—
76C23×C13—22no—
77C23×C13—22no—
78C23×C13—42no—
79C23×C13—44no—
80C23×C13#9912yes—
81C23×C13C2×C22⋊C411yescharacteristic
82C23×C13#12314yes—
83Q8×C13—44no—
84D4×C13—44no—
85D4×C13—48no—
86C2×C4×C13—28no—
87C2×C4×C13—21no—
88C2×C4×C13—21no—
89C2×C4×C13—21no—
90C2×C4×C13—21no—
91C2×C4×C13—24no—
92C2×C4×C13—22no—
93C2×C4×C13—22no—
94C2×C4×C13—22no—
95C2×C4×C13—48no—
96C2×C4×C13—42no—
97C2×C4×C13—48no—
98C2×C4×C13—42no—
99C2×C4×C13—44no—
100C2×C4×C13—42no—
101C2×C4×C13—84no—
102C2×C4×C13—88no—
103C2×C4×C13#9912yes—
104C2×C4×C13#11712yes—
105C22×#41C22×C1311yescharacteristic
106C2×#117C4×C1311yescharacteristic, complemented
107C22×C42C4×C1311yescharacteristic, complemented
108C2×#99—22no—
109C2×#99C22×C1314yes—
110#391C4×C1312yescomplemented
111#390C22×C1312yes—
112#386—22no—
113#381—22no—
114C4×C22⋊C4—22no—
115C22×C13—22no—
116C22×C13—22no—
117C22×C13—24no—
118C22×C13—42no—
119C22×C13—44no—
120C22×C13—42no—
121C22×C13—44no—
122C22×C13—42no—
123C22×C13—82no—
124C22×C13#38111yescharacteristic
125C22×C13C2×#9911yescharacteristic
126C22×C13C2×#9911yescharacteristic
127C4×C13—22no—
128C4×C13—22no—
129C4×C13—44no—
130C4×C13—42no—
131C4×C13—82no—
132C4×C13—164no—
133C2×#41—24no—
134C2×#41—42no—
135C2×#41—42no—
136C22×Q8C2×C4×C1311yescharacteristic
137C22×D4D4×C1312yes—
138C22×D4C23×C1311yescharacteristic
139C23×C4—21no—
140C23×C4C2×C4×C1311yescharacteristic
141C23×C4D4×C1312yes—
142#117—42no—
143C2×C4⋊C4C2×C4×C1312yes—
144C2×C22⋊C4—21no—
145C2×C22⋊C4—24no—
146C2×C22⋊C4—24no—
147C2×C42—21no—
148C2×C42—21no—
149C2×C42—42no—
150C2×C42C2×C4×C1312yes—
151#99—28no—
152#99—44no—
153#95—24no—
154#95—44no—
155C2×C13—21no—
156C2×C13—21no—
157C2×C13—44no—
158C2×C13—42no—
159C2×C13#181911yescharacteristic
160C2×C13#212612yes—
161C24C13×C22⋊C411yescharacteristic
162C24C2×D4×C1312yes—
163#41—416no—
164C2×Q8—22no—
165C2×Q8—41no—
166C2×Q8—41no—
167C2×D4—24no—
168C2×D4—24no—
169C2×D4—42no—
170C2×D4—41no—
171C2×D4—41no—
172C2×D4C13×#4114yes—
173C22×C4—22no—
174C22×C4—22no—
175C22×C4—22no—
176C22×C4—22no—
177C22×C4—24no—
178C22×C4—24no—
179C22×C4—22no—
180C22×C4—42no—
181C22×C4—44no—
182C22×C4—42no—
183C22×C4—44no—
184C22×C4C13×C22⋊C412yes—
185C22×C4C13×C22⋊C411yescharacteristic
186C22×C4C22×C4×C1311yescharacteristic
187C4⋊C4—42no—
188C22⋊C4—48no—
189C22⋊C4—42no—
190C22⋊C4—44no—
191C22⋊C4—44no—
192C42—42no—
193C42—42no—
194C42—42no—
195C13#1285711yescharacteristic, direct product factor, Sylow
196C23—21no—
197C23—21no—
198C23—22no—
199C23—22no—
200C23—42no—
201C23—44no—
202C23C13×#9912yes—
203C23C2×C13×C22⋊C411yescharacteristic
204C23C13×#12314yes—
205Q8—44no—
206D4—44no—
207D4—48no—
208C2×C4—28no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—24no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—48no—
218C2×C4—42no—
219C2×C4—48no—
220C2×C4—42no—
221C2×C4—44no—
222C2×C4—42no—
223C2×C4—84no—
224C2×C4—88no—
225C2×C4C13×#9912yes—
226C2×C4C13×#11712yes—
227C22—22no—
228C22—22no—
229C22—24no—
230C22—42no—
231C22—44no—
232C22—42no—
233C22—44no—
234C22—42no—
235C22—82no—
236C22C13×#38111yescharacteristic
237C22C2×C13×#9911yescharacteristic
238C22C2×C13×#9911yescharacteristic
239C4—22no—
240C4—22no—
241C4—44no—
242C4—42no—
243C4—82no—
244C4—164no—
245C2—21no—
246C2—21no—
247C2—44no—
248C2—42no—
249C2C13×#181911yescharacteristic
250C2C13×#212612yes—
subgroupG/H
center, socleC22×C13C2×#99
commutatorC22×C4C22×C4×C13
Frattini, cosocleC22×D4C23×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×#1393C2semidirect
5. C2×C13×#117C4semidirect
6. C22×C42×C13C4semidirect
9. C13×#391C4semidirect
36. #12857C13direct (N × H)
73. #1393C2×C13semidirect
106. C2×#117C4×C13semidirect
107. C22×C42C4×C13semidirect
110. #391C4×C13semidirect
195. C13#12857direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#22972
C13×#17822
C13×#13932
#1285713