Finite Group Databasebeta

← C13×#10334 #15696673

Subgroups — C13×#10334 #15696673

Order 3328.

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

normal subgroups only

This group has 754 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
2C13×#2434C212yesmaximal
3C13×#1784C211yesmaximal, characteristic
4C13×#1508C212yesmaximal
5C13×#1297C211yesmaximal, characteristic
6C23×Q8×C13C2211yescharacteristic
7C2×C13×C4⋊Q8—22no—
8C2×C13×C22⋊Q8C2212yes—
9C13×#483—22no—
10C13×#470—22no—
11C13×#451—22no—
12C2×C13×#101—22no—
13C13×#407C2211yescharacteristic
14C13×#407C2211yescharacteristic
15C13×#395—24no—
16C13×#391—22no—
17C13×#385—24no—
18C4×C13×C22⋊C4C2212yes—
19C13×#328—24no—
20C22×Q8×C13—22no—
21C22×Q8×C13—21no—
22C22×Q8×C13—22no—
23C22×Q8×C13—21no—
24C22×Q8×C13—44no—
25C22×Q8×C13D412yes—
26C23×C4×C13D412yes—
27C23×C4×C13C2311yescharacteristic
28C2×C13×Q16—22no—
29C2×C13×M16—21no—
30C2×C13×M16D412yes—
31C13×C4⋊Q8—48no—
32C13×C22⋊Q8—22no—
33C13×C22⋊Q8—22no—
34C13×C22⋊Q8—22no—
35C13×C22⋊Q8—22no—
36C2×C13×C4⋊C4—28no—
37C2×C13×C4⋊C4—22no—
38C2×C13×C4⋊C4D412yes—
39C2×C13×C22⋊C4—22no—
40C2×C13×C22⋊C4—22no—
41C2×C42×C13—22no—
42C13×#106—22no—
43C13×#103—24no—
44C13×#101—44no—
45C13×C22⋊C8—22no—
46C13×C22⋊C8—22no—
47C13×#95—28no—
48C13×#95D414yes—
49#10334C1311yesmaximal, characteristic, direct product factor, Sylow
50C24×C13C2×D411yescharacteristic
51C2×Q8×C13—24no—
52C2×Q8×C13—28no—
53C2×Q8×C13—22no—
54C2×Q8×C13—22no—
55C2×Q8×C13—44no—
56C2×Q8×C13—42no—
57C2×Q8×C13—48no—
58C2×Q8×C13—44no—
59C2×Q8×C13—44no—
60C2×Q8×C13—41no—
61C2×Q8×C13—42no—
62C2×Q8×C13—41no—
63C22×C4×C13—24no—
64C22×C4×C13—24no—
65C22×C4×C13—22no—
66C22×C4×C13—22no—
67C22×C4×C13—22no—
68C22×C4×C13—44no—
69C22×C4×C13—42no—
70C22×C4×C13C2×D412yes—
71C22×C4×C13C2×D411yescharacteristic
72C22×C4×C13C2×D412yes—
73C22×C4×C13#4111yescharacteristic
74C13×Q16—82no—
75C13×M16—42no—
76C13×M16—42no—
77C2×C8×C13—22no—
78C2×C8×C13—41no—
79C13×C4⋊C4—22no—
80C13×C4⋊C4—22no—
81C13×C4⋊C4—416no—
82C13×C4⋊C4—42no—
83C13×C4⋊C4—42no—
84C13×C22⋊C4—28no—
85C13×C22⋊C4—42no—
86C13×C22⋊C4—42no—
87C42×C13—44no—
88#3195C2×C1311yescharacteristic
89#2434C2×C1312yes—
90#1784C2×C1311yescharacteristic
91#1508C2×C1312yes—
92#1297C2×C1311yescharacteristic
93C23×C13—24no—
94C23×C13—41no—
95C23×C13#12012yes—
96C23×C13#12111yescharacteristic
97Q8×C13—44no—
98Q8×C13—48no—
99Q8×C13—44no—
100Q8×C13—44no—
101Q8×C13—82no—
102C2×C4×C13—24no—
103C2×C4×C13—22no—
104C2×C4×C13—28no—
105C2×C4×C13—28no—
106C2×C4×C13—24no—
107C2×C4×C13—42no—
108C2×C4×C13—41no—
109C2×C4×C13—44no—
110C2×C4×C13—44no—
111C2×C4×C13—42no—
112C2×C4×C13—42no—
113C2×C4×C13—44no—
114C2×C4×C13—44no—
115C2×C4×C13—42no—
116C2×C4×C13—42no—
117C2×C4×C13—44no—
118C2×C4×C13#12011yescharacteristic
119C2×C4×C13#12112yes—
120C2×C4×C13#12711yescharacteristic
121C8×C13—42no—
122C8×C13—81no—
123C23×Q8C22×C1311yescharacteristic
124C2×C4⋊Q8—22no—
125C2×C22⋊Q8C22×C1312yes—
126#483—22no—
127#470—22no—
128#451—22no—
129C2×#101—22no—
130#407C22×C1311yescharacteristic
131#407C22×C1311yescharacteristic
132#395—24no—
133#391—22no—
134#385—24no—
135C4×C22⋊C4C22×C1312yes—
136#328—24no—
137C22×C13—22no—
138C22×C13—22no—
139C22×C13—22no—
140C22×C13—21no—
141C22×C13—44no—
142C22×C13#39211yescharacteristic
143C22×C13#45614yes—
144C4×C13—21no—
145C4×C13—22no—
146C4×C13—48no—
147C4×C13—44no—
148C4×C13—82no—
149C4×C13—82no—
150C4×C13B(4,𝔽2)12yes—
151C22×Q8—22no—
152C22×Q8—21no—
153C22×Q8—22no—
154C22×Q8—21no—
155C22×Q8—44no—
156C22×Q8D4×C1312yes—
157C23×C4D4×C1312yes—
158C23×C4C23×C1311yescharacteristic
159C2×Q16—22no—
160C2×M16—21no—
161C2×M16D4×C1312yes—
162C4⋊Q8—48no—
163C22⋊Q8—22no—
164C22⋊Q8—22no—
165C22⋊Q8—22no—
166C22⋊Q8—22no—
167C2×C4⋊C4—28no—
168C2×C4⋊C4—22no—
169C2×C4⋊C4D4×C1312yes—
170C2×C22⋊C4—22no—
171C2×C22⋊C4—22no—
172C2×C42—22no—
173#106—22no—
174#103—24no—
175#101—44no—
176C22⋊C8—22no—
177C22⋊C8—22no—
178#95—28no—
179#95D4×C1314yes—
180C2×C13—24no—
181C2×C13—41no—
182C2×C13#200512yes—
183C2×C13#202111yescharacteristic
184C24C2×D4×C1311yescharacteristic
185C2×Q8—24no—
186C2×Q8—28no—
187C2×Q8—22no—
188C2×Q8—22no—
189C2×Q8—44no—
190C2×Q8—42no—
191C2×Q8—48no—
192C2×Q8—44no—
193C2×Q8—44no—
194C2×Q8—41no—
195C2×Q8—42no—
196C2×Q8—41no—
197C22×C4—24no—
198C22×C4—24no—
199C22×C4—22no—
200C22×C4—22no—
201C22×C4—22no—
202C22×C4—44no—
203C22×C4—42no—
204C22×C4C2×D4×C1312yes—
205C22×C4C2×D4×C1311yescharacteristic
206C22×C4C2×D4×C1312yes—
207C22×C4C13×#4111yescharacteristic
208Q16—82no—
209M16—42no—
210M16—42no—
211C2×C8—22no—
212C2×C8—41no—
213C4⋊C4—22no—
214C4⋊C4—22no—
215C4⋊C4—416no—
216C4⋊C4—42no—
217C4⋊C4—42no—
218C22⋊C4—28no—
219C22⋊C4—42no—
220C22⋊C4—42no—
221C42—44no—
222C13#1033411yescharacteristic, direct product factor, Sylow
223C23—24no—
224C23—41no—
225C23C13×#12012yes—
226C23C13×#12111yescharacteristic
227Q8—44no—
228Q8—48no—
229Q8—44no—
230Q8—44no—
231Q8—82no—
232C2×C4—24no—
233C2×C4—22no—
234C2×C4—28no—
235C2×C4—28no—
236C2×C4—24no—
237C2×C4—42no—
238C2×C4—41no—
239C2×C4—44no—
240C2×C4—44no—
241C2×C4—42no—
242C2×C4—42no—
243C2×C4—44no—
244C2×C4—44no—
245C2×C4—42no—
246C2×C4—42no—
247C2×C4—44no—
248C2×C4C13×#12011yescharacteristic
249C2×C4C13×#12112yes—
250C2×C4C13×#12711yescharacteristic
251C8—42no—
252C8—81no—
253C22—22no—
254C22—22no—
255C22—22no—
256C22—21no—
257C22—44no—
258C22C13×#39211yescharacteristic
259C22C13×#45614yes—
260C4—21no—
261C4—22no—
262C4—48no—
263C4—44no—
264C4—82no—
265C4—82no—
266C4C13×B(4,𝔽2)12yes—
267C2—24no—
268C2—41no—
269C2C13×#200512yes—
270C2C13×#202111yescharacteristic
subgroupG/H
center, socleC22×C13#392
commutator, Frattini, cosocleC23×C4C23×C13
prime radicalC24×C13C2×D4
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
49. #10334C13direct (N × H)
222. C13#10334direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#31952
C13×#24342
C13×#17842
C13×#15082
C13×#12972
#1033413