Finite Group Databasebeta

← C13×#9451 #15695790

Subgroups — C13×#9451 #15695790

Order 3328.

518 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 518 conjugacy classes of subgroups — too many to draw. Only its 126 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×#2973C211yesmaximal, characteristic
2C13×#2547C211yesmaximal, characteristic
3C13×#1558C212yesmaximal, complemented
4C13×#1466C211yesmaximal, characteristic
5C13×#1285C212yesmaximal, complemented
6C2×C13×C4⋊Q8C2211yescharacteristic
7C2×C13×#124C412yes—
8C2×C4×D4×C13C2211yescharacteristic
9C13×#435—24no—
10C13×#432C2212yes—
11C13×#432C2212yes—
12C13×#407—21no—
13C2×C13×C22⋊C8—21no—
14C13×#397—21no—
15C13×#397—21no—
16C13×#391C412yes—
17C13×#380—21no—
18C13×#380—21no—
19C4×C13×C4⋊C4C2211yescharacteristic
20C13×#333—24no—
21C13×#323—21no—
22C13×#323—21no—
23C22×Q8×C13C2×C412yes—
24C22×D4×C13C2×C411yescharacteristic
25C23×C4×C13D411yescharacteristic
26C23×C4×C13D411yescharacteristic
27C2×C13×M16—22no—
28C22×C8×C13—22no—
29C13×C4⋊Q8—22no—
30C13×C4⋊Q8—22no—
31C13×#124—44no—
32C4×D4×C13—22no—
33C4×D4×C13—22no—
34C2×C13×C4⋊C4—21no—
35C2×C13×C4⋊C4—21no—
36C2×C13×C4⋊C4—21no—
37C2×C13×C4⋊C4C2×C411yescharacteristic
38C2×C13×C22⋊C4—22no—
39C2×C13×C22⋊C4—22no—
40C2×C13×C22⋊C4D411yescharacteristic
41C2×C13×C22⋊C4D411yescharacteristic
42C2×C42×C13C2×C412yes—
43C2×C42×C13C2311yescharacteristic
44C13×C4⋊C8—22no—
45C13×C4⋊C8D414yes—
46C13×C22⋊C8—22no—
47C13×C22⋊C8—22no—
48C13×C22⋊C8—22no—
49C13×C22⋊C8—22no—
50C13×#97—22no—
51C13×#97—22no—
52C13×#95—22no—
53C13×#95—22no—
54C13×#95—21no—
55#9451C1311yesmaximal, characteristic, direct product factor, Sylow
56C24×C13C22⋊C411yescharacteristic
57C24×C13C22⋊C411yescharacteristic
58C2×Q8×C13—24no—
59C2×Q8×C13—42no—
60C2×Q8×C13—42no—
61C2×D4×C13—22no—
62C2×D4×C13—22no—
63C2×D4×C13—41no—
64C22×C4×C13—21no—
65C22×C4×C13—21no—
66C22×C4×C13—21no—
67C22×C4×C13—21no—
68C22×C4×C13—22no—
69C22×C4×C13—22no—
70C22×C4×C13—42no—
71C22×C4×C13—42no—
72C22×C4×C13C22⋊C411yescharacteristic
73C22×C4×C13C22⋊C411yescharacteristic
74C22×C4×C13C22×C411yescharacteristic
75C22×C4×C13C2×D411yescharacteristic
76C22×C4×C13C2×D411yescharacteristic
77C13×M16—82no—
78C2×C8×C13—24no—
79C2×C8×C13—42no—
80C2×C8×C13—82no—
81C13×C4⋊C4—22no—
82C13×C4⋊C4—42no—
83C13×C4⋊C4—41no—
84C13×C4⋊C4—42no—
85C13×C4⋊C4—41no—
86C13×C22⋊C4—22no—
87C13×C22⋊C4—22no—
88C13×C22⋊C4—44no—
89C13×C22⋊C4—44no—
90C42×C13—42no—
91C42×C13C2×D412yes—
92C42×C13#4112yes—
93#2973C2×C1311yescharacteristic
94#2547C2×C1311yescharacteristic
95#1558C2×C1312yescomplemented
96#1466C2×C1311yescharacteristic
97#1285C2×C1312yescomplemented
98C23×C13—21no—
99C23×C13—21no—
100C23×C13—21no—
101C23×C13—21no—
102C23×C13—21no—
103C23×C13—41no—
104C23×C13—41no—
105C23×C13—41no—
106C23×C13—41no—
107C23×C13#10012yes—
108C23×C13C2×C22⋊C411yescharacteristic
109Q8×C13—84no—
110D4×C13—44no—
111C2×C4×C13—21no—
112C2×C4×C13—21no—
113C2×C4×C13—22no—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—41no—
117C2×C4×C13—42no—
118C2×C4×C13—42no—
119C2×C4×C13—41no—
120C2×C4×C13—41no—
121C2×C4×C13—42no—
122C2×C4×C13—42no—
123C2×C4×C13—42no—
124C2×C4×C13—42no—
125C2×C4×C13—42no—
126C2×C4×C13—42no—
127C2×C4×C13—81no—
128C2×C4×C13—81no—
129C2×C4×C13C4×D412yes—
130C2×C4×C13#12011yescharacteristic
131C2×C4×C13#12112yes—
132C2×C4×C13#12311yescharacteristic
133C8×C13—44no—
134C8×C13—82no—
135C2×C4⋊Q8C22×C1311yescharacteristic
136C2×#124C4×C1312yes—
137C2×C4×D4C22×C1311yescharacteristic
138#435—24no—
139#432C22×C1312yes—
140#432C22×C1312yes—
141#407—21no—
142C2×C22⋊C8—21no—
143#397—21no—
144#397—21no—
145#391C4×C1312yes—
146#380—21no—
147#380—21no—
148C4×C4⋊C4C22×C1311yescharacteristic
149#333—24no—
150#323—21no—
151#323—21no—
152C22×C13—21no—
153C22×C13—21no—
154C22×C13—22no—
155C22×C13—42no—
156C22×C13—42no—
157C22×C13—41no—
158C22×C13—41no—
159C22×C13—41no—
160C22×C13—41no—
161C22×C13—41no—
162C22×C13—81no—
163C22×C13—81no—
164C22×C13#38611yescharacteristic
165C22×C13C2×#10011yescharacteristic
166C22×C13#41311yescharacteristic
167C4×C13—21no—
168C4×C13—22no—
169C4×C13—22no—
170C4×C13—41no—
171C4×C13—41no—
172C4×C13—82no—
173C4×C13—82no—
174C4×C13#45512yes—
175C22×Q8C2×C4×C1312yes—
176C22×D4C2×C4×C1311yescharacteristic
177C23×C4D4×C1311yescharacteristic
178C23×C4D4×C1311yescharacteristic
179C2×M16—22no—
180C22×C8—22no—
181C4⋊Q8—22no—
182C4⋊Q8—22no—
183#124—44no—
184C4×D4—22no—
185C4×D4—22no—
186C2×C4⋊C4—21no—
187C2×C4⋊C4—21no—
188C2×C4⋊C4—21no—
189C2×C4⋊C4C2×C4×C1311yescharacteristic
190C2×C22⋊C4—22no—
191C2×C22⋊C4—22no—
192C2×C22⋊C4D4×C1311yescharacteristic
193C2×C22⋊C4D4×C1311yescharacteristic
194C2×C42C2×C4×C1312yes—
195C2×C42C23×C1311yescharacteristic
196C4⋊C8—22no—
197C4⋊C8D4×C1314yes—
198C22⋊C8—22no—
199C22⋊C8—22no—
200C22⋊C8—22no—
201C22⋊C8—22no—
202#97—22no—
203#97—22no—
204#95—22no—
205#95—22no—
206#95—21no—
207C2×C13—21no—
208C2×C13—21no—
209C2×C13—42no—
210C2×C13—81no—
211C2×C13#188511yescharacteristic
212C2×C13#190011yescharacteristic
213C2×C13#190911yescharacteristic
214C24C13×C22⋊C411yescharacteristic
215C24C13×C22⋊C411yescharacteristic
216C2×Q8—24no—
217C2×Q8—42no—
218C2×Q8—42no—
219C2×D4—22no—
220C2×D4—22no—
221C2×D4—41no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—22no—
227C22×C4—22no—
228C22×C4—42no—
229C22×C4—42no—
230C22×C4C13×C22⋊C411yescharacteristic
231C22×C4C13×C22⋊C411yescharacteristic
232C22×C4C22×C4×C1311yescharacteristic
233C22×C4C2×D4×C1311yescharacteristic
234C22×C4C2×D4×C1311yescharacteristic
235M16—82no—
236C2×C8—24no—
237C2×C8—42no—
238C2×C8—82no—
239C4⋊C4—22no—
240C4⋊C4—42no—
241C4⋊C4—41no—
242C4⋊C4—42no—
243C4⋊C4—41no—
244C22⋊C4—22no—
245C22⋊C4—22no—
246C22⋊C4—44no—
247C22⋊C4—44no—
248C42—42no—
249C42C2×D4×C1312yes—
250C42C13×#4112yes—
251C13#945111yescharacteristic, direct product factor, Sylow
252C23—21no—
253C23—21no—
254C23—21no—
255C23—21no—
256C23—21no—
257C23—41no—
258C23—41no—
259C23—41no—
260C23—41no—
261C23C13×#10012yes—
262C23C2×C13×C22⋊C411yescharacteristic
263Q8—84no—
264D4—44no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—22no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—41no—
271C2×C4—42no—
272C2×C4—42no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—42no—
276C2×C4—42no—
277C2×C4—42no—
278C2×C4—42no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—81no—
282C2×C4—81no—
283C2×C4C4×D4×C1312yes—
284C2×C4C13×#12011yescharacteristic
285C2×C4C13×#12112yes—
286C2×C4C13×#12311yescharacteristic
287C8—44no—
288C8—82no—
289C22—21no—
290C22—21no—
291C22—22no—
292C22—42no—
293C22—42no—
294C22—41no—
295C22—41no—
296C22—41no—
297C22—41no—
298C22—41no—
299C22—81no—
300C22—81no—
301C22C13×#38611yescharacteristic
302C22C2×C13×#10011yescharacteristic
303C22C13×#41311yescharacteristic
304C4—21no—
305C4—22no—
306C4—22no—
307C4—41no—
308C4—41no—
309C4—82no—
310C4—82no—
311C4C13×#45512yes—
312C2—21no—
313C2—21no—
314C2—42no—
315C2—81no—
316C2C13×#188511yescharacteristic
317C2C13×#190011yescharacteristic
318C2C13×#190911yescharacteristic
subgroupG/H
center, socleC22×C13#386
commutatorC22×C4C22×C4×C13
Frattini, cosocleC2×C42C23×C13
prime radicalC22×D4×C13C2×C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G

Complements

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

NH ≅ G/Ntype
3. C13×#1558C2semidirect
5. C13×#1285C2semidirect
55. #9451C13direct (N × H)
95. #1558C2×C13semidirect
97. #1285C2×C13semidirect
251. C13#9451direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#29732
C13×#25472
C13×#15582
C13×#14662
C13×#12852
#945113