Finite Group Databasebeta

← C13×#9990 #15696329

Subgroups — C13×#9990 #15696329

Order 3328.

826 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 826 conjugacy classes of subgroups — too many to draw. Only its 106 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×#3195C211yesmaximal, characteristic, complemented
2C2×C13×#450C212yesmaximal
3C13×#1783C211yesmaximal, characteristic
4C13×#1472C212yesmaximal, complemented
5C13×#1298C211yesmaximal, characteristic, complemented
6C23×D4×C13C2211yescharacteristic
7C22×C13×SD16—22no—
8C2×C13×C22⋊Q8C2212yes—
9C13×#483—22no—
10C13×#470—22no—
11C13×#451—22no—
12C13×#450—24no—
13C13×#450—24no—
14C2×C13×#102—22no—
15C2×C13×#100—22no—
16C13×#407C2211yescharacteristic
17C13×#407C2211yescharacteristic
18C2×C13×C22⋊C8C2212yes—
19C13×#324—24no—
20C25×C13—21no—
21C22×Q8×C13D412yes—
22C22×D4×C13—22no—
23C22×D4×C13—21no—
24C22×D4×C13—22no—
25C22×D4×C13—44no—
26C22×D4×C13D412yes—
27C23×C4×C13C2311yescharacteristic
28C2×C13×Q16—22no—
29C2×C13×SD16—28no—
30C2×C13×SD16—48no—
31C2×C13×M16—21no—
32C2×C13×M16D412yes—
33C22×C8×C13—22no—
34C13×C22⋊Q8—22no—
35C13×C22⋊Q8—22no—
36C13×C22⋊Q8—22no—
37C13×C22⋊Q8—22no—
38C2×C13×C4⋊C4—22no—
39C2×C13×C4⋊C4D412yes—
40C2×C13×C22⋊C4—22no—
41C13×#106—22no—
42C13×#103—24no—
43C13×#102—28no—
44C13×#100—44no—
45C13×C22⋊C8—22no—
46C13×C22⋊C8—22no—
47C13×C22⋊C8—22no—
48C13×C22⋊C8D414yes—
49#9990C1311yesmaximal, characteristic, direct product factor, Sylow
50C24×C13—22no—
51C24×C13—44no—
52C24×C13—42no—
53C24×C13—84no—
54C24×C13#4111yescharacteristic
55C2×Q8×C13—22no—
56C2×Q8×C13—22no—
57C2×Q8×C13—44no—
58C2×D4×C13—28no—
59C2×D4×C13—24no—
60C2×D4×C13—24no—
61C2×D4×C13—44no—
62C2×D4×C13—42no—
63C2×D4×C13—44no—
64C2×D4×C13—48no—
65C2×D4×C13—41no—
66C2×D4×C13—41no—
67C22×C4×C13—22no—
68C22×C4×C13—22no—
69C22×C4×C13—42no—
70C22×C4×C13C2×D412yes—
71C22×C4×C13C2×D411yescharacteristic
72C22×C4×C13C2×D411yescharacteristic
73C22×C4×C13C2×D412yes—
74C13×Q16—82no—
75C13×SD16—416no—
76C13×M16—42no—
77C13×M16—42no—
78C2×C8×C13—22no—
79C2×C8×C13—24no—
80C2×C8×C13—44no—
81C2×C8×C13—41no—
82C13×C4⋊C4—22no—
83C13×C4⋊C4—22no—
84C13×C4⋊C4—42no—
85C13×C4⋊C4—42no—
86C13×C22⋊C4—42no—
87C13×C22⋊C4—42no—
88#3195C2×C1311yescharacteristic, complemented
89C2×#450C2×C1312yes—
90#1783C2×C1311yescharacteristic
91#1472C2×C1312yescomplemented
92#1298C2×C1311yescharacteristic, complemented
93C23×C13—24no—
94C23×C13—24no—
95C23×C13—41no—
96C23×C13—48no—
97C23×C13—42no—
98C23×C13—42no—
99C23×C13—84no—
100C23×C13—84no—
101C23×C13—816no—
102C23×C13—84no—
103C23×C13#12111yescharacteristic
104C23×C13#12112yes—
105Q8×C13—44no—
106Q8×C13—44no—
107D4×C13—28no—
108D4×C13—44no—
109D4×C13—44no—
110D4×C13—44no—
111C2×C4×C13—24no—
112C2×C4×C13—22no—
113C2×C4×C13—41no—
114C2×C4×C13—42no—
115C2×C4×C13—42no—
116C2×C4×C13—42no—
117C2×C4×C13—44no—
118C2×C4×C13—82no—
119C2×C4×C13#12012yes—
120C2×C4×C13#12011yescharacteristic
121C2×C4×C13#12711yescharacteristic
122C8×C13—44no—
123C8×C13—42no—
124C8×C13—81no—
125C23×D4C22×C1311yescharacteristic
126C22×SD16—22no—
127C2×C22⋊Q8C22×C1312yes—
128#483—22no—
129#470—22no—
130#451—22no—
131#450—24no—
132#450—24no—
133C2×#102—22no—
134C2×#100—22no—
135#407C22×C1311yescharacteristic
136#407C22×C1311yescharacteristic
137C2×C22⋊C8C22×C1312yes—
138#324—24no—
139C22×C13—22no—
140C22×C13—22no—
141C22×C13—22no—
142C22×C13—21no—
143C22×C13—44no—
144C22×C13—44no—
145C22×C13—816no—
146C22×C13—84no—
147C22×C13—84no—
148C22×C13—84no—
149C22×C13#39211yescharacteristic
150C22×C13#47114yes—
151C4×C13—22no—
152C4×C13—21no—
153C4×C13—82no—
154C4×C13—82no—
155C4×C13B(4,𝔽2)12yes—
156C25—21no—
157C22×Q8D4×C1312yes—
158C22×D4—22no—
159C22×D4—21no—
160C22×D4—22no—
161C22×D4—44no—
162C22×D4D4×C1312yes—
163C23×C4C23×C1311yescharacteristic
164C2×Q16—22no—
165C2×SD16—28no—
166C2×SD16—48no—
167C2×M16—21no—
168C2×M16D4×C1312yes—
169C22×C8—22no—
170C22⋊Q8—22no—
171C22⋊Q8—22no—
172C22⋊Q8—22no—
173C22⋊Q8—22no—
174C2×C4⋊C4—22no—
175C2×C4⋊C4D4×C1312yes—
176C2×C22⋊C4—22no—
177#106—22no—
178#103—24no—
179#102—28no—
180#100—44no—
181C22⋊C8—22no—
182C22⋊C8—22no—
183C22⋊C8—22no—
184C22⋊C8D4×C1314yes—
185C2×C13—24no—
186C2×C13—41no—
187C2×C13—84no—
188C2×C13#201912yes—
189C2×C13#202111yescharacteristic
190C24—22no—
191C24—44no—
192C24—42no—
193C24—84no—
194C24C13×#4111yescharacteristic
195C2×Q8—22no—
196C2×Q8—22no—
197C2×Q8—44no—
198C2×D4—28no—
199C2×D4—24no—
200C2×D4—24no—
201C2×D4—44no—
202C2×D4—42no—
203C2×D4—44no—
204C2×D4—48no—
205C2×D4—41no—
206C2×D4—41no—
207C22×C4—22no—
208C22×C4—22no—
209C22×C4—42no—
210C22×C4C2×D4×C1312yes—
211C22×C4C2×D4×C1311yescharacteristic
212C22×C4C2×D4×C1311yescharacteristic
213C22×C4C2×D4×C1312yes—
214Q16—82no—
215SD16—416no—
216M16—42no—
217M16—42no—
218C2×C8—22no—
219C2×C8—24no—
220C2×C8—44no—
221C2×C8—41no—
222C4⋊C4—22no—
223C4⋊C4—22no—
224C4⋊C4—42no—
225C4⋊C4—42no—
226C22⋊C4—42no—
227C22⋊C4—42no—
228C13#999011yescharacteristic, direct product factor, Sylow
229C23—24no—
230C23—24no—
231C23—41no—
232C23—48no—
233C23—42no—
234C23—42no—
235C23—84no—
236C23—84no—
237C23—816no—
238C23—84no—
239C23C13×#12111yescharacteristic
240C23C13×#12112yes—
241Q8—44no—
242Q8—44no—
243D4—28no—
244D4—44no—
245D4—44no—
246D4—44no—
247C2×C4—24no—
248C2×C4—22no—
249C2×C4—41no—
250C2×C4—42no—
251C2×C4—42no—
252C2×C4—42no—
253C2×C4—44no—
254C2×C4—82no—
255C2×C4C13×#12012yes—
256C2×C4C13×#12011yescharacteristic
257C2×C4C13×#12711yescharacteristic
258C8—44no—
259C8—42no—
260C8—81no—
261C22—22no—
262C22—22no—
263C22—22no—
264C22—21no—
265C22—44no—
266C22—44no—
267C22—816no—
268C22—84no—
269C22—84no—
270C22—84no—
271C22C13×#39211yescharacteristic
272C22C13×#47114yes—
273C4—22no—
274C4—21no—
275C4—82no—
276C4—82no—
277C4C13×B(4,𝔽2)12yes—
278C2—24no—
279C2—41no—
280C2—84no—
281C2C13×#201912yes—
282C2C13×#202111yescharacteristic
subgroupG/H
center, socleC22×C13#392
commutator, Frattini, cosocleC23×C4C23×C13
prime radicalC23×D4×C13C22
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ C23×C4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×#3195C2semidirect
4. C13×#1472C2semidirect
5. C13×#1298C2semidirect
49. #9990C13direct (N × H)
88. #3195C2×C13semidirect
91. #1472C2×C13semidirect
92. #1298C2×C13semidirect
228. C13#9990direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#31952
C2×C13×#4502
C13×#17832
C13×#14722
C13×#12982
#999013