Finite Group Databasebeta

← C13×#10333 #15696672

Subgroups — C13×#10333 #15696672

Order 3328.

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

normal subgroups only

This group has 914 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
2C13×#2435C212yesmaximal
3C13×#1783C211yesmaximal, characteristic
4C13×#1508C212yesmaximal, complemented
5C13×#1297C211yesmaximal, characteristic, complemented
6C23×D4×C13C2211yescharacteristic
7C2×C13×#124—22no—
8C2×C13×C22⋊Q8C2212yes—
9C13×#483—22no—
10C13×#470—22no—
11C13×#451—22no—
12C2×C13×#100—22no—
13C13×#407C2211yescharacteristic
14C13×#407C2211yescharacteristic
15C13×#394—24no—
16C13×#390—22no—
17C13×#379—24no—
18C4×C13×C22⋊C4C2212yes—
19C13×#328—24no—
20C25×C13D412yes—
21C22×Q8×C13D412yes—
22C22×D4×C13—22no—
23C22×D4×C13—21no—
24C22×D4×C13—22no—
25C22×D4×C13—21no—
26C22×D4×C13—44no—
27C23×C4×C13C2311yescharacteristic
28C2×C13×Q16—22no—
29C2×C13×M16—21no—
30C2×C13×M16D412yes—
31C13×#124—48no—
32C13×C22⋊Q8—22no—
33C13×C22⋊Q8—22no—
34C13×C22⋊Q8—22no—
35C13×C22⋊Q8—22no—
36C2×C13×C4⋊C4—22no—
37C2×C13×C4⋊C4D412yes—
38C2×C13×C22⋊C4—28no—
39C2×C13×C22⋊C4—22no—
40C2×C13×C22⋊C4—22no—
41C2×C13×C22⋊C4—28no—
42C2×C42×C13—22no—
43C13×#106—22no—
44C13×#103—24no—
45C13×#100—44no—
46C13×C22⋊C8—22no—
47C13×C22⋊C8—22no—
48C13×#95D414yes—
49#10333C1311yesmaximal, characteristic, direct product factor, Sylow
50C24×C13—24no—
51C24×C13—22no—
52C24×C13—44no—
53C24×C13—48no—
54C24×C13C2×D411yescharacteristic
55C2×Q8×C13—22no—
56C2×Q8×C13—22no—
57C2×Q8×C13—44no—
58C2×D4×C13—24no—
59C2×D4×C13—28no—
60C2×D4×C13—44no—
61C2×D4×C13—42no—
62C2×D4×C13—48no—
63C2×D4×C13—44no—
64C2×D4×C13—41no—
65C2×D4×C13—42no—
66C2×D4×C13—41no—
67C22×C4×C13—24no—
68C22×C4×C13—22no—
69C22×C4×C13—22no—
70C22×C4×C13—42no—
71C22×C4×C13C2×D412yes—
72C22×C4×C13C2×D411yescharacteristic
73C22×C4×C13C2×D412yes—
74C22×C4×C13#4111yescharacteristic
75C13×Q16—82no—
76C13×M16—42no—
77C13×M16—42no—
78C2×C8×C13—22no—
79C2×C8×C13—41no—
80C13×C4⋊C4—22no—
81C13×C4⋊C4—22no—
82C13×C4⋊C4—42no—
83C13×C4⋊C4—42no—
84C13×C22⋊C4—44no—
85C13×C22⋊C4—416no—
86C13×C22⋊C4—42no—
87C13×C22⋊C4—42no—
88C13×C22⋊C4—88no—
89C42×C13—44no—
90#3195C2×C1311yescharacteristic, complemented
91#2435C2×C1312yes—
92#1783C2×C1311yescharacteristic
93#1508C2×C1312yescomplemented
94#1297C2×C1311yescharacteristic, complemented
95C23×C13—24no—
96C23×C13—28no—
97C23×C13—24no—
98C23×C13—41no—
99C23×C13—44no—
100C23×C13—42no—
101C23×C13—48no—
102C23×C13—42no—
103C23×C13—48no—
104C23×C13—84no—
105C23×C13—816no—
106C23×C13#12012yes—
107C23×C13#12111yescharacteristic
108Q8×C13—44no—
109Q8×C13—82no—
110D4×C13—44no—
111D4×C13—48no—
112D4×C13—44no—
113C2×C4×C13—24no—
114C2×C4×C13—22no—
115C2×C4×C13—42no—
116C2×C4×C13—41no—
117C2×C4×C13—44no—
118C2×C4×C13—44no—
119C2×C4×C13—44no—
120C2×C4×C13—42no—
121C2×C4×C13—42no—
122C2×C4×C13—44no—
123C2×C4×C13—44no—
124C2×C4×C13#12011yescharacteristic
125C2×C4×C13#12112yes—
126C2×C4×C13#12711yescharacteristic
127C8×C13—42no—
128C8×C13—81no—
129C23×D4C22×C1311yescharacteristic
130C2×#124—22no—
131C2×C22⋊Q8C22×C1312yes—
132#483—22no—
133#470—22no—
134#451—22no—
135C2×#100—22no—
136#407C22×C1311yescharacteristic
137#407C22×C1311yescharacteristic
138#394—24no—
139#390—22no—
140#379—24no—
141C4×C22⋊C4C22×C1312yes—
142#328—24no—
143C22×C13—22no—
144C22×C13—22no—
145C22×C13—22no—
146C22×C13—21no—
147C22×C13—44no—
148C22×C13—416no—
149C22×C13—44no—
150C22×C13—88no—
151C22×C13—84no—
152C22×C13—84no—
153C22×C13—84no—
154C22×C13#39211yescharacteristic
155C22×C13#45514yes—
156C4×C13—21no—
157C4×C13—22no—
158C4×C13—84no—
159C4×C13—82no—
160C4×C13—82no—
161C4×C13B(4,𝔽2)12yes—
162C25D4×C1312yes—
163C22×Q8D4×C1312yes—
164C22×D4—22no—
165C22×D4—21no—
166C22×D4—22no—
167C22×D4—21no—
168C22×D4—44no—
169C23×C4C23×C1311yescharacteristic
170C2×Q16—22no—
171C2×M16—21no—
172C2×M16D4×C1312yes—
173#124—48no—
174C22⋊Q8—22no—
175C22⋊Q8—22no—
176C22⋊Q8—22no—
177C22⋊Q8—22no—
178C2×C4⋊C4—22no—
179C2×C4⋊C4D4×C1312yes—
180C2×C22⋊C4—28no—
181C2×C22⋊C4—22no—
182C2×C22⋊C4—22no—
183C2×C22⋊C4—28no—
184C2×C42—22no—
185#106—22no—
186#103—24no—
187#100—44no—
188C22⋊C8—22no—
189C22⋊C8—22no—
190#95D4×C1314yes—
191C2×C13—24no—
192C2×C13—41no—
193C2×C13—84no—
194C2×C13#200412yes—
195C2×C13#202111yescharacteristic
196C24—24no—
197C24—22no—
198C24—44no—
199C24—48no—
200C24C2×D4×C1311yescharacteristic
201C2×Q8—22no—
202C2×Q8—22no—
203C2×Q8—44no—
204C2×D4—24no—
205C2×D4—28no—
206C2×D4—44no—
207C2×D4—42no—
208C2×D4—48no—
209C2×D4—44no—
210C2×D4—41no—
211C2×D4—42no—
212C2×D4—41no—
213C22×C4—24no—
214C22×C4—22no—
215C22×C4—22no—
216C22×C4—42no—
217C22×C4C2×D4×C1312yes—
218C22×C4C2×D4×C1311yescharacteristic
219C22×C4C2×D4×C1312yes—
220C22×C4C13×#4111yescharacteristic
221Q16—82no—
222M16—42no—
223M16—42no—
224C2×C8—22no—
225C2×C8—41no—
226C4⋊C4—22no—
227C4⋊C4—22no—
228C4⋊C4—42no—
229C4⋊C4—42no—
230C22⋊C4—416no—
231C22⋊C4—44no—
232C22⋊C4—42no—
233C22⋊C4—42no—
234C22⋊C4—88no—
235C42—44no—
236C13#1033311yescharacteristic, direct product factor, Sylow
237C23—24no—
238C23—28no—
239C23—24no—
240C23—41no—
241C23—44no—
242C23—42no—
243C23—48no—
244C23—42no—
245C23—48no—
246C23—84no—
247C23—816no—
248C23C13×#12012yes—
249C23C13×#12111yescharacteristic
250Q8—44no—
251Q8—82no—
252D4—44no—
253D4—48no—
254D4—44no—
255C2×C4—24no—
256C2×C4—22no—
257C2×C4—42no—
258C2×C4—41no—
259C2×C4—44no—
260C2×C4—44no—
261C2×C4—44no—
262C2×C4—42no—
263C2×C4—42no—
264C2×C4—44no—
265C2×C4—44no—
266C2×C4C13×#12011yescharacteristic
267C2×C4C13×#12112yes—
268C2×C4C13×#12711yescharacteristic
269C8—42no—
270C8—81no—
271C22—22no—
272C22—22no—
273C22—22no—
274C22—21no—
275C22—44no—
276C22—416no—
277C22—44no—
278C22—88no—
279C22—84no—
280C22—84no—
281C22—84no—
282C22C13×#39211yescharacteristic
283C22C13×#45514yes—
284C4—21no—
285C4—22no—
286C4—84no—
287C4—82no—
288C4—82no—
289C4C13×B(4,𝔽2)12yes—
290C2—24no—
291C2—41no—
292C2—84no—
293C2C13×#200412yes—
294C2C13×#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×#1508C2semidirect
5. C13×#1297C2semidirect
49. #10333C13direct (N × H)
90. #3195C2×C13semidirect
93. #1508C2×C13semidirect
94. #1297C2×C13semidirect
236. C13#10333direct (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×#24352
C13×#17832
C13×#15082
C13×#12972
#1033313