Finite Group Databasebeta

← C13×#9453 #15695792

Subgroups — C13×#9453 #15695792

Order 3328.

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

normal subgroups only

This group has 498 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×#2563C211yesmaximal, characteristic
3C13×#1556C212yesmaximal, complemented
4C13×#1466C211yesmaximal, characteristic
5C13×#1285C212yesmaximal, complemented
6C2×C13×C4⋊Q8C2211yescharacteristic
7C2×C4×D4×C13C2211yescharacteristic
8C13×#435—24no—
9C13×#432C2212yes—
10C13×#432C2212yes—
11C13×#407—21no—
12C2×C13×C22⋊C8—21no—
13C13×#393—21no—
14C13×#393—21no—
15C13×#390C412yes—
16C13×#382C412yes—
17C13×#380—21no—
18C13×#380—21no—
19C4×C13×C4⋊C4C2211yescharacteristic
20C13×#332—24no—
21C13×#323—21no—
22C13×#323—21no—
23C22×Q8×C13—21no—
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—
31C4×D4×C13—22no—
32C4×D4×C13—22no—
33C2×C13×C4⋊C4—21no—
34C2×C13×C4⋊C4—21no—
35C2×C13×C4⋊C4C2×C412yes—
36C2×C13×C4⋊C4C2×C411yescharacteristic
37C2×C13×C22⋊C4—22no—
38C2×C13×C22⋊C4—22no—
39C2×C13×C22⋊C4D411yescharacteristic
40C2×C13×C22⋊C4D411yescharacteristic
41C2×C42×C13C2×C412yes—
42C2×C42×C13C2311yescharacteristic
43C13×C4⋊C8—22no—
44C13×C4⋊C8D414yes—
45C13×C22⋊C8—22no—
46C13×C22⋊C8—22no—
47C13×C22⋊C8—22no—
48C13×C22⋊C8—22no—
49C13×#97—22no—
50C13×#97—22no—
51C13×#95—22no—
52C13×#95—22no—
53C13×#95—21no—
54#9453C1311yesmaximal, characteristic, direct product factor, Sylow
55C24×C13C22⋊C411yescharacteristic
56C24×C13C22⋊C411yescharacteristic
57C2×Q8×C13—42no—
58C2×Q8×C13—82no—
59C2×D4×C13—22no—
60C2×D4×C13—22no—
61C2×D4×C13—41no—
62C22×C4×C13—21no—
63C22×C4×C13—21no—
64C22×C4×C13—21no—
65C22×C4×C13—21no—
66C22×C4×C13—22no—
67C22×C4×C13—22no—
68C22×C4×C13—42no—
69C22×C4×C13—42no—
70C22×C4×C13C22⋊C411yescharacteristic
71C22×C4×C13C22⋊C411yescharacteristic
72C22×C4×C13C22×C411yescharacteristic
73C22×C4×C13C2×D411yescharacteristic
74C22×C4×C13C2×D411yescharacteristic
75C13×M16—82no—
76C2×C8×C13—24no—
77C2×C8×C13—42no—
78C2×C8×C13—82no—
79C13×C4⋊C4—22no—
80C13×C4⋊C4—24no—
81C13×C4⋊C4—42no—
82C13×C4⋊C4—41no—
83C13×C4⋊C4—41no—
84C13×C22⋊C4—22no—
85C13×C22⋊C4—22no—
86C13×C22⋊C4—82no—
87C13×C22⋊C4—82no—
88C42×C13—42no—
89C42×C13C2×D412yes—
90C42×C13#4112yes—
91#2973C2×C1311yescharacteristic
92#2563C2×C1311yescharacteristic
93#1556C2×C1312yescomplemented
94#1466C2×C1311yescharacteristic
95#1285C2×C1312yescomplemented
96C23×C13—21no—
97C23×C13—21no—
98C23×C13—21no—
99C23×C13—21no—
100C23×C13—21no—
101C23×C13—41no—
102C23×C13—41no—
103C23×C13—41no—
104C23×C13—41no—
105C23×C13#10112yes—
106C23×C13C2×C22⋊C411yescharacteristic
107Q8×C13—84no—
108D4×C13—44no—
109C2×C4×C13—21no—
110C2×C4×C13—21no—
111C2×C4×C13—22no—
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—41no—
115C2×C4×C13—42no—
116C2×C4×C13—42no—
117C2×C4×C13—41no—
118C2×C4×C13—41no—
119C2×C4×C13—42no—
120C2×C4×C13—42no—
121C2×C4×C13—42no—
122C2×C4×C13—42no—
123C2×C4×C13—42no—
124C2×C4×C13—42no—
125C2×C4×C13—81no—
126C2×C4×C13—81no—
127C2×C4×C13C4×D412yes—
128C2×C4×C13#12011yescharacteristic
129C2×C4×C13#12112yes—
130C2×C4×C13#12311yescharacteristic
131C8×C13—44no—
132C8×C13—82no—
133C2×C4⋊Q8C22×C1311yescharacteristic
134C2×C4×D4C22×C1311yescharacteristic
135#435—24no—
136#432C22×C1312yes—
137#432C22×C1312yes—
138#407—21no—
139C2×C22⋊C8—21no—
140#393—21no—
141#393—21no—
142#390C4×C1312yes—
143#382C4×C1312yes—
144#380—21no—
145#380—21no—
146C4×C4⋊C4C22×C1311yescharacteristic
147#332—24no—
148#323—21no—
149#323—21no—
150C22×C13—21no—
151C22×C13—21no—
152C22×C13—22no—
153C22×C13—42no—
154C22×C13—42no—
155C22×C13—41no—
156C22×C13—41no—
157C22×C13—41no—
158C22×C13—41no—
159C22×C13—41no—
160C22×C13—81no—
161C22×C13—81no—
162C22×C13#38611yescharacteristic
163C22×C13C2×#10111yescharacteristic
164C22×C13#41311yescharacteristic
165C4×C13—21no—
166C4×C13—22no—
167C4×C13—22no—
168C4×C13—41no—
169C4×C13—41no—
170C4×C13—82no—
171C4×C13—82no—
172C4×C13#45512yes—
173C22×Q8—21no—
174C22×D4C2×C4×C1311yescharacteristic
175C23×C4D4×C1311yescharacteristic
176C23×C4D4×C1311yescharacteristic
177C2×M16—22no—
178C22×C8—22no—
179C4⋊Q8—22no—
180C4⋊Q8—22no—
181C4×D4—22no—
182C4×D4—22no—
183C2×C4⋊C4—21no—
184C2×C4⋊C4—21no—
185C2×C4⋊C4C2×C4×C1312yes—
186C2×C4⋊C4C2×C4×C1311yescharacteristic
187C2×C22⋊C4—22no—
188C2×C22⋊C4—22no—
189C2×C22⋊C4D4×C1311yescharacteristic
190C2×C22⋊C4D4×C1311yescharacteristic
191C2×C42C2×C4×C1312yes—
192C2×C42C23×C1311yescharacteristic
193C4⋊C8—22no—
194C4⋊C8D4×C1314yes—
195C22⋊C8—22no—
196C22⋊C8—22no—
197C22⋊C8—22no—
198C22⋊C8—22no—
199#97—22no—
200#97—22no—
201#95—22no—
202#95—22no—
203#95—21no—
204C2×C13—21no—
205C2×C13—21no—
206C2×C13—42no—
207C2×C13—81no—
208C2×C13#188511yescharacteristic
209C2×C13#190111yescharacteristic
210C2×C13#191011yescharacteristic
211C24C13×C22⋊C411yescharacteristic
212C24C13×C22⋊C411yescharacteristic
213C2×Q8—42no—
214C2×Q8—82no—
215C2×D4—22no—
216C2×D4—22no—
217C2×D4—41no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—21no—
222C22×C4—22no—
223C22×C4—22no—
224C22×C4—42no—
225C22×C4—42no—
226C22×C4C13×C22⋊C411yescharacteristic
227C22×C4C13×C22⋊C411yescharacteristic
228C22×C4C22×C4×C1311yescharacteristic
229C22×C4C2×D4×C1311yescharacteristic
230C22×C4C2×D4×C1311yescharacteristic
231M16—82no—
232C2×C8—24no—
233C2×C8—42no—
234C2×C8—82no—
235C4⋊C4—22no—
236C4⋊C4—24no—
237C4⋊C4—42no—
238C4⋊C4—41no—
239C4⋊C4—41no—
240C22⋊C4—22no—
241C22⋊C4—22no—
242C22⋊C4—82no—
243C22⋊C4—82no—
244C42—42no—
245C42C2×D4×C1312yes—
246C42C13×#4112yes—
247C13#945311yescharacteristic, direct product factor, Sylow
248C23—21no—
249C23—21no—
250C23—21no—
251C23—21no—
252C23—21no—
253C23—41no—
254C23—41no—
255C23—41no—
256C23—41no—
257C23C13×#10112yes—
258C23C2×C13×C22⋊C411yescharacteristic
259Q8—84no—
260D4—44no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—22no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—41no—
267C2×C4—42no—
268C2×C4—42no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—42no—
272C2×C4—42no—
273C2×C4—42no—
274C2×C4—42no—
275C2×C4—42no—
276C2×C4—42no—
277C2×C4—81no—
278C2×C4—81no—
279C2×C4C4×D4×C1312yes—
280C2×C4C13×#12011yescharacteristic
281C2×C4C13×#12112yes—
282C2×C4C13×#12311yescharacteristic
283C8—44no—
284C8—82no—
285C22—21no—
286C22—21no—
287C22—22no—
288C22—42no—
289C22—42no—
290C22—41no—
291C22—41no—
292C22—41no—
293C22—41no—
294C22—41no—
295C22—81no—
296C22—81no—
297C22C13×#38611yescharacteristic
298C22C2×C13×#10111yescharacteristic
299C22C13×#41311yescharacteristic
300C4—21no—
301C4—22no—
302C4—22no—
303C4—41no—
304C4—41no—
305C4—82no—
306C4—82no—
307C4C13×#45512yes—
308C2—21no—
309C2—21no—
310C2—42no—
311C2—81no—
312C2C13×#188511yescharacteristic
313C2C13×#190111yescharacteristic
314C2C13×#191011yescharacteristic
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×#1556C2semidirect
5. C13×#1285C2semidirect
54. #9453C13direct (N × H)
93. #1556C2×C13semidirect
95. #1285C2×C13semidirect
247. C13#9453direct (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×#25632
C13×#15562
C13×#14662
C13×#12852
#945313