Finite Group Databasebeta

← C13×#9462 #15695801

Subgroups — C13×#9462 #15695801

Order 3328.

700 conjugacy classes of subgroups; only the 130 normal subgroups are shown.

normal subgroups only

This group has 700 conjugacy classes of subgroups — too many to draw. Only its 130 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×#2434C211yesmaximal, characteristic
2C13×#2310C211yesmaximal, characteristic
3C13×#1784C211yesmaximal, characteristic
4C13×#1511C212yesmaximal
5C13×#1284C212yesmaximal
6C23×Q8×C13C2211yescharacteristic
7C2×C13×C4⋊Q8C412yescomplemented
8C2×C13×C22⋊Q8C2211yescharacteristic
9C2×C13×#117—21no—
10C2×C13×#101—22no—
11C13×#407C2212yes—
12C13×#395—22no—
13C13×#391—24no—
14C13×#391C412yescomplemented
15C13×#385—21no—
16C13×#385—21no—
17C13×#381—21no—
18C13×#381C2212yes—
19C4×C13×C22⋊C4C2211yescharacteristic
20C13×#328—24no—
21C22×Q8×C13—22no—
22C22×Q8×C13—22no—
23C22×Q8×C13—44no—
24C22×Q8×C13C2×C411yescharacteristic
25C22×Q8×C13C2×C412yes—
26C22×Q8×C13D412yes—
27C23×C4×C13D411yescharacteristic
28C23×C4×C13D411yescharacteristic
29C23×C4×C13C2311yescharacteristic
30C2×C13×M16—22no—
31C13×C4⋊Q8—44no—
32C13×C22⋊Q8—22no—
33C13×C22⋊Q8—22no—
34C13×#117—44no—
35C2×C13×C4⋊C4—22no—
36C2×C13×C4⋊C4—22no—
37C2×C13×C4⋊C4—22no—
38C2×C13×C4⋊C4—21no—
39C2×C13×C4⋊C4C2×C411yescharacteristic
40C2×C13×C22⋊C4—21no—
41C2×C13×C22⋊C4—22no—
42C2×C13×C22⋊C4—21no—
43C2×C42×C13—22no—
44C2×C42×C13C2×C412yes—
45C13×#101—44no—
46C13×C22⋊C8—22no—
47C13×C22⋊C8—22no—
48C13×#95—24no—
49C13×#95—22no—
50C13×#95—22no—
51C13×#95—21no—
52C13×#95—22no—
53C13×#95D414yes—
54#9462C1311yesmaximal, characteristic, direct product factor, Sylow
55C24×C13C2×D411yescharacteristic
56C2×Q8×C13—24no—
57C2×Q8×C13—24no—
58C2×Q8×C13—24no—
59C2×Q8×C13—24no—
60C2×Q8×C13—22no—
61C2×Q8×C13—42no—
62C2×Q8×C13—42no—
63C2×Q8×C13—44no—
64C2×Q8×C13—44no—
65C2×Q8×C13—48no—
66C2×Q8×C13—42no—
67C22×C4×C13—21no—
68C22×C4×C13—21no—
69C22×C4×C13—24no—
70C22×C4×C13—22no—
71C22×C4×C13—21no—
72C22×C4×C13—21no—
73C22×C4×C13—21no—
74C22×C4×C13—21no—
75C22×C4×C13—24no—
76C22×C4×C13—42no—
77C22×C4×C13—42no—
78C22×C4×C13C22⋊C412yes—
79C22×C4×C13C22⋊C412yes—
80C22×C4×C13C22×C411yescharacteristic
81C22×C4×C13C2×D411yescharacteristic
82C22×C4×C13C2×D412yes—
83C22×C4×C13#4112yes—
84C13×M16—44no—
85C2×C8×C13—42no—
86C13×C4⋊C4—22no—
87C13×C4⋊C4—44no—
88C13×C4⋊C4—44no—
89C13×C4⋊C4—44no—
90C13×C4⋊C4—42no—
91C13×C22⋊C4—24no—
92C13×C22⋊C4—44no—
93C13×C22⋊C4—41no—
94C13×C22⋊C4—41no—
95C42×C13—42no—
96C42×C13—44no—
97#2434C2×C1311yescharacteristic
98#2310C2×C1311yescharacteristic
99#1784C2×C1311yescharacteristic
100#1511C2×C1312yes—
101#1284C2×C1312yes—
102C23×C13—22no—
103C23×C13—22no—
104C23×C13—41no—
105C23×C13C2×C22⋊C411yescharacteristic
106C23×C13#12011yescharacteristic
107C23×C13#12311yescharacteristic
108Q8×C13—48no—
109Q8×C13—48no—
110Q8×C13—82no—
111C2×C4×C13—22no—
112C2×C4×C13—22no—
113C2×C4×C13—24no—
114C2×C4×C13—22no—
115C2×C4×C13—22no—
116C2×C4×C13—22no—
117C2×C4×C13—22no—
118C2×C4×C13—24no—
119C2×C4×C13—22no—
120C2×C4×C13—22no—
121C2×C4×C13—22no—
122C2×C4×C13—42no—
123C2×C4×C13—42no—
124C2×C4×C13—42no—
125C2×C4×C13—42no—
126C2×C4×C13—42no—
127C2×C4×C13—42no—
128C2×C4×C13—44no—
129C2×C4×C13—44no—
130C2×C4×C13—42no—
131C2×C4×C13—41no—
132C2×C4×C13—41no—
133C2×C4×C13—42no—
134C2×C4×C13—44no—
135C2×C4×C13#9914yes—
136C2×C4×C13C4×D412yes—
137C2×C4×C13#12112yes—
138C8×C13—82no—
139C23×Q8C22×C1311yescharacteristic
140C2×C4⋊Q8C4×C1312yescomplemented
141C2×C22⋊Q8C22×C1311yescharacteristic
142C2×#117—21no—
143C2×#101—22no—
144#407C22×C1312yes—
145#395—22no—
146#391—24no—
147#391C4×C1312yescomplemented
148#385—21no—
149#385—21no—
150#381—21no—
151#381C22×C1312yes—
152C4×C22⋊C4C22×C1311yescharacteristic
153#328—24no—
154C22×C13—21no—
155C22×C13—21no—
156C22×C13—21no—
157C22×C13—21no—
158C22×C13—21no—
159C22×C13—21no—
160C22×C13—21no—
161C22×C13—44no—
162C22×C13#38611yescharacteristic
163C22×C13C2×#9912yes—
164C22×C13#45612yes—
165C4×C13—22no—
166C4×C13—24no—
167C4×C13—22no—
168C4×C13—44no—
169C4×C13—42no—
170C4×C13—84no—
171C4×C13—81no—
172C4×C13—81no—
173C22×Q8—22no—
174C22×Q8—22no—
175C22×Q8—44no—
176C22×Q8C2×C4×C1311yescharacteristic
177C22×Q8C2×C4×C1312yes—
178C22×Q8D4×C1312yes—
179C23×C4D4×C1311yescharacteristic
180C23×C4D4×C1311yescharacteristic
181C23×C4C23×C1311yescharacteristic
182C2×M16—22no—
183C4⋊Q8—44no—
184C22⋊Q8—22no—
185C22⋊Q8—22no—
186#117—44no—
187C2×C4⋊C4—22no—
188C2×C4⋊C4—22no—
189C2×C4⋊C4—22no—
190C2×C4⋊C4—21no—
191C2×C4⋊C4C2×C4×C1311yescharacteristic
192C2×C22⋊C4—21no—
193C2×C22⋊C4—22no—
194C2×C22⋊C4—21no—
195C2×C42—22no—
196C2×C42C2×C4×C1312yes—
197#101—44no—
198C22⋊C8—22no—
199C22⋊C8—22no—
200#95—24no—
201#95—22no—
202#95—22no—
203#95—21no—
204#95—22no—
205#95D4×C1314yes—
206C2×C13—22no—
207C2×C13—22no—
208C2×C13—41no—
209C2×C13#188611yescharacteristic
210C2×C13#189811yescharacteristic
211C2×C13#191211yescharacteristic
212C24C2×D4×C1311yescharacteristic
213C2×Q8—24no—
214C2×Q8—24no—
215C2×Q8—24no—
216C2×Q8—24no—
217C2×Q8—22no—
218C2×Q8—42no—
219C2×Q8—42no—
220C2×Q8—44no—
221C2×Q8—44no—
222C2×Q8—48no—
223C2×Q8—42no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—24no—
227C22×C4—22no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—24no—
233C22×C4—42no—
234C22×C4—42no—
235C22×C4C13×C22⋊C412yes—
236C22×C4C13×C22⋊C412yes—
237C22×C4C22×C4×C1311yescharacteristic
238C22×C4C2×D4×C1311yescharacteristic
239C22×C4C2×D4×C1312yes—
240C22×C4C13×#4112yes—
241M16—44no—
242C2×C8—42no—
243C4⋊C4—22no—
244C4⋊C4—44no—
245C4⋊C4—44no—
246C4⋊C4—44no—
247C4⋊C4—42no—
248C22⋊C4—24no—
249C22⋊C4—44no—
250C22⋊C4—41no—
251C22⋊C4—41no—
252C42—42no—
253C42—44no—
254C13#946211yescharacteristic, direct product factor, Sylow
255C23—22no—
256C23—22no—
257C23—41no—
258C23C2×C13×C22⋊C411yescharacteristic
259C23C13×#12011yescharacteristic
260C23C13×#12311yescharacteristic
261Q8—48no—
262Q8—48no—
263Q8—82no—
264C2×C4—22no—
265C2×C4—22no—
266C2×C4—24no—
267C2×C4—22no—
268C2×C4—22no—
269C2×C4—22no—
270C2×C4—22no—
271C2×C4—24no—
272C2×C4—22no—
273C2×C4—22no—
274C2×C4—22no—
275C2×C4—42no—
276C2×C4—42no—
277C2×C4—42no—
278C2×C4—42no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—44no—
282C2×C4—44no—
283C2×C4—42no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—42no—
287C2×C4—44no—
288C2×C4C13×#9914yes—
289C2×C4C4×D4×C1312yes—
290C2×C4C13×#12112yes—
291C8—82no—
292C22—21no—
293C22—21no—
294C22—21no—
295C22—21no—
296C22—21no—
297C22—21no—
298C22—21no—
299C22—44no—
300C22C13×#38611yescharacteristic
301C22C2×C13×#9912yes—
302C22C13×#45612yes—
303C4—22no—
304C4—24no—
305C4—22no—
306C4—44no—
307C4—42no—
308C4—84no—
309C4—81no—
310C4—81no—
311C2—22no—
312C2—22no—
313C2—41no—
314C2C13×#188611yescharacteristic
315C2C13×#189811yescharacteristic
316C2C13×#191211yescharacteristic
subgroupG/H
center, socleC22×C13#386
commutatorC22×C4C22×C4×C13
Frattini, cosocleC23×C4C23×C13
prime radicalC24×C13C2×D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ C23×C4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
7. C2×C13×C4⋊Q8C4semidirect
14. C13×#391C4semidirect
54. #9462C13direct (N × H)
140. C2×C4⋊Q8C4×C13semidirect
147. #391C4×C13semidirect
254. C13#9462direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#24342
C13×#23102
C13×#17842
C13×#15112
C13×#12842
#946213