Finite Group Databasebeta

← C13×#8540 #15694879

Subgroups — C13×#8540 #15694879

Order 3328.

718 conjugacy classes of subgroups; only the 142 normal subgroups are shown.

normal subgroups only

This group has 718 conjugacy classes of subgroups — too many to draw. Only its 142 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×#3491C211yesmaximal, characteristic
2C13×#1822C211yesmaximal, characteristic, complemented
3C13×#1818C211yesmaximal, characteristic, complemented
4C13×#1468C214yesmaximal, complemented
5C13×#552—24no—
6C13×#551—24no—
7C13×#543C411yescharacteristic
8C13×#539—22no—
9C13×#534C411yescharacteristic
10C13×#529—22no—
11C2×C13×#123C2212yes—
12C13×#518C412yes—
13C2×C13×#117C2211yescharacteristic
14C13×#407C2212yes—
15C2×C13×C22⋊C8C2212yes—
16C13×#343—22no—
17C13×#336—22no—
18C13×#324—24no—
19C13×#323—24no—
20C22×D4×C13C2×C412yes—
21C23×C4×C13C2311yescharacteristic
22C2×C13×M16—22no—
23C22×C8×C13—22no—
24C13×#126—24no—
25C13×#126—24no—
26C13×#125—22no—
27C13×#125—24no—
28C13×#124—22no—
29C13×#123—24no—
30C13×#123—22no—
31C13×#123—22no—
32C13×#123—22no—
33C13×#123—24no—
34C13×C22⋊Q8—24no—
35C13×C22⋊Q8—22no—
36C13×C22⋊Q8—24no—
37C13×#121—22no—
38C13×#120—22no—
39C4×Q8×C13—22no—
40C4×D4×C13—22no—
41C4×D4×C13—24no—
42C4×D4×C13—24no—
43C13×#117—24no—
44C13×#117—22no—
45C13×#117—24no—
46C2×C13×C4⋊C4D414yes—
47C2×C13×C4⋊C4D412yes—
48C2×C13×C22⋊C4—22no—
49C2×C13×C22⋊C4C2×C411yescharacteristic
50C2×C13×C22⋊C4C2×C411yescharacteristic
51C2×C13×C22⋊C4C2×C412yes—
52C2×C13×C22⋊C4D414yes—
53C2×C42×C13D412yes—
54C13×C22⋊C8—24no—
55C13×C22⋊C8—24no—
56#8540C1311yesmaximal, characteristic, direct product factor, Sylow
57C24×C13C22⋊C412yes—
58C24×C13C22×C411yescharacteristic
59C2×Q8×C13—22no—
60C2×D4×C13—22no—
61C2×D4×C13—22no—
62C2×D4×C13—22no—
63C2×D4×C13—44no—
64C22×C4×C13—24no—
65C22×C4×C13—42no—
66C22×C4×C13C22⋊C412yes—
67C22×C4×C13C22⋊C412yes—
68C22×C4×C13C22⋊C414yes—
69C22×C4×C13C22⋊C412yes—
70C22×C4×C13C2×D411yescharacteristic
71C22×C4×C13C2×D411yescharacteristic
72C22×C4×C13C2×D414yes—
73C13×M16—44no—
74C2×C8×C13—44no—
75C2×C8×C13—42no—
76C2×C8×C13—42no—
77C13×C4⋊C4—24no—
78C13×C4⋊C4—24no—
79C13×C4⋊C4—22no—
80C13×C4⋊C4—22no—
81C13×C4⋊C4—24no—
82C13×C4⋊C4—24no—
83C13×C4⋊C4—24no—
84C13×C22⋊C4—24no—
85C13×C22⋊C4—24no—
86C13×C22⋊C4—22no—
87C13×C22⋊C4—22no—
88C13×C22⋊C4—22no—
89C13×C22⋊C4—22no—
90C13×C22⋊C4—24no—
91C13×C22⋊C4—24no—
92C42×C13—24no—
93C42×C13—22no—
94C42×C13—22no—
95#3491C2×C1311yescharacteristic
96#1822C2×C1311yescharacteristic, complemented
97#1818C2×C1311yescharacteristic, complemented
98#1468C2×C1314yescomplemented
99C23×C13—22no—
100C23×C13—22no—
101C23×C13—42no—
102C23×C13—42no—
103C23×C13—44no—
104C23×C13C2×C22⋊C412yes—
105C23×C13C2×C22⋊C411yescharacteristic
106Q8×C13—82no—
107D4×C13—44no—
108D4×C13—44no—
109D4×C13—82no—
110C2×C4×C13—22no—
111C2×C4×C13—22no—
112C2×C4×C13—22no—
113C2×C4×C13—22no—
114C2×C4×C13—22no—
115C2×C4×C13—24no—
116C2×C4×C13—44no—
117C2×C4×C13—42no—
118C2×C4×C13—44no—
119C2×C4×C13—42no—
120C2×C4×C13—42no—
121C2×C4×C13—84no—
122C2×C4×C13#12012yes—
123C2×C4×C13#12012yes—
124C8×C13—82no—
125C8×C13—82no—
126#552—24no—
127#551—24no—
128#543C4×C1311yescharacteristic
129#539—22no—
130#534C4×C1311yescharacteristic
131#529—22no—
132C2×#123C22×C1312yes—
133#518C4×C1312yes—
134C2×#117C22×C1311yescharacteristic
135#407C22×C1312yes—
136C2×C22⋊C8C22×C1312yes—
137#343—22no—
138#336—22no—
139#324—24no—
140#323—24no—
141C22×C13—22no—
142C22×C13—22no—
143C22×C13—24no—
144C22×C13—42no—
145C22×C13—44no—
146C22×C13—82no—
147C22×C13—162no—
148C22×C13#37911yescharacteristic
149C22×C13#41012yes—
150C4×C13—22no—
151C4×C13—22no—
152C4×C13—42no—
153C4×C13—42no—
154C4×C13—44no—
155C4×C13—42no—
156C22×D4C2×C4×C1312yes—
157C23×C4C23×C1311yescharacteristic
158C2×M16—22no—
159C22×C8—22no—
160#126—24no—
161#126—24no—
162#125—22no—
163#125—24no—
164#124—22no—
165#123—24no—
166#123—22no—
167#123—22no—
168#123—22no—
169#123—24no—
170C22⋊Q8—24no—
171C22⋊Q8—22no—
172C22⋊Q8—24no—
173#121—22no—
174#120—22no—
175C4×Q8—22no—
176C4×D4—22no—
177C4×D4—24no—
178C4×D4—24no—
179#117—24no—
180#117—22no—
181#117—24no—
182C2×C4⋊C4D4×C1312yes—
183C2×C4⋊C4D4×C1314yes—
184C2×C22⋊C4—22no—
185C2×C22⋊C4C2×C4×C1311yescharacteristic
186C2×C22⋊C4C2×C4×C1311yescharacteristic
187C2×C22⋊C4C2×C4×C1312yes—
188C2×C22⋊C4D4×C1314yes—
189C2×C42D4×C1312yes—
190C22⋊C8—24no—
191C22⋊C8—24no—
192C2×C13—22no—
193C2×C13—42no—
194C2×C13—82no—
195C2×C13#178211yescharacteristic
196C2×C13#179112yes—
197C24C13×C22⋊C412yes—
198C24C22×C4×C1311yescharacteristic
199C2×Q8—22no—
200C2×D4—22no—
201C2×D4—22no—
202C2×D4—22no—
203C2×D4—44no—
204C22×C4—24no—
205C22×C4—42no—
206C22×C4C13×C22⋊C412yes—
207C22×C4C13×C22⋊C412yes—
208C22×C4C13×C22⋊C414yes—
209C22×C4C13×C22⋊C412yes—
210C22×C4C2×D4×C1311yescharacteristic
211C22×C4C2×D4×C1311yescharacteristic
212C22×C4C2×D4×C1314yes—
213M16—44no—
214C2×C8—44no—
215C2×C8—42no—
216C2×C8—42no—
217C4⋊C4—24no—
218C4⋊C4—24no—
219C4⋊C4—22no—
220C4⋊C4—22no—
221C4⋊C4—24no—
222C4⋊C4—24no—
223C4⋊C4—24no—
224C22⋊C4—24no—
225C22⋊C4—24no—
226C22⋊C4—22no—
227C22⋊C4—22no—
228C22⋊C4—22no—
229C22⋊C4—22no—
230C22⋊C4—24no—
231C22⋊C4—24no—
232C42—24no—
233C42—22no—
234C42—22no—
235C13#854011yescharacteristic, direct product factor, Sylow
236C23—22no—
237C23—22no—
238C23—42no—
239C23—42no—
240C23—44no—
241C23C2×C13×C22⋊C412yes—
242C23C2×C13×C22⋊C411yescharacteristic
243Q8—82no—
244D4—44no—
245D4—44no—
246D4—82no—
247C2×C4—22no—
248C2×C4—22no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—24no—
253C2×C4—44no—
254C2×C4—42no—
255C2×C4—42no—
256C2×C4—44no—
257C2×C4—42no—
258C2×C4—84no—
259C2×C4C13×#12012yes—
260C2×C4C13×#12012yes—
261C8—82no—
262C8—82no—
263C22—22no—
264C22—22no—
265C22—24no—
266C22—42no—
267C22—44no—
268C22—82no—
269C22—162no—
270C22C13×#37911yescharacteristic
271C22C13×#41012yes—
272C4—22no—
273C4—22no—
274C4—42no—
275C4—42no—
276C4—44no—
277C4—42no—
278C2—22no—
279C2—42no—
280C2—82no—
281C2C13×#178211yescharacteristic
282C2C13×#179112yes—
subgroupG/H
center, socleC22×C13#379
commutatorC24C22×C4×C13
Frattini, cosocleC23×C4C23×C13
prime radicalC13×#534C4
LCSG ▷ C24 ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ C23×C4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C13×#1822C2semidirect
3. C13×#1818C2semidirect
4. C13×#1468C2semidirect
56. #8540C13direct (N × H)
96. #1822C2×C13semidirect
97. #1818C2×C13semidirect
98. #1468C2×C13semidirect
235. C13#8540direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#34912
C13×#18222
C13×#18182
C13×#14682
#854013