Finite Group Databasebeta

← C13×#11529 #15697868

Subgroups — C13×#11529 #15697868

Order 3328.

596 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 596 conjugacy classes of subgroups — too many to draw. Only its 110 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
1C4×C13×#127C211yesmaximal, characteristic
2C13×#1465C212yesmaximal, complemented
3C13×#1325C212yesmaximal, complemented
4C13×#1318C212yesmaximal, complemented
5C2×C13×#127C411yescharacteristic
6C2×C4×D4×C13—22no—
7C2×C4×D4×C13C411yescharacteristic
8C2×C4×D4×C13C2211yescharacteristic
9C13×#407—22no—
10C13×#390—22no—
11C13×#390C411yescharacteristic
12C13×#390C2211yescharacteristic
13C13×#384C2211yescharacteristic
14C43×C13C411yescharacteristic
15C13×#324C2214yes—
16C13×#323—22no—
17C22×D4×C13—22no—
18C22×D4×C13C2×C411yescharacteristic
19C22×D4×C13C2×C411yescharacteristic
20C23×C4×C13—21no—
21C23×C4×C13D412yes—
22C2×C13×M16—42no—
23C13×#127—22no—
24C13×#127—22no—
25C4×D4×C13—41no—
26C4×D4×C13—41no—
27C4×D4×C13—48no—
28C4×D4×C13—41no—
29C4×D4×C13—41no—
30C2×C13×C4⋊C4—22no—
31C2×C13×C4⋊C4C2×C411yescharacteristic
32C2×C13×C4⋊C4C2311yescharacteristic
33C2×C13×C22⋊C4—22no—
34C2×C13×C22⋊C4—21no—
35C2×C13×C22⋊C4—22no—
36C2×C13×C22⋊C4D412yes—
37C2×C42×C13—21no—
38C2×C42×C13—21no—
39C2×C42×C13C2×C411yescharacteristic
40C2×C42×C13C2×C411yescharacteristic
41C2×C42×C13C2×C411yescharacteristic
42C13×C22⋊C8—24no—
43C13×C22⋊C8—42no—
44#11529C1311yesmaximal, characteristic, direct product factor, Sylow
45C24×C13—21no—
46C24×C13C22⋊C412yes—
47C2×D4×C13—28no—
48C2×D4×C13—21no—
49C2×D4×C13—21no—
50C2×D4×C13—21no—
51C2×D4×C13—41no—
52C2×D4×C13—41no—
53C2×D4×C13—41no—
54C2×D4×C13—41no—
55C2×D4×C13—44no—
56C2×D4×C13—44no—
57C2×D4×C13M1612yescomplemented
58C22×C4×C13—21no—
59C22×C4×C13—21no—
60C22×C4×C13—22no—
61C22×C4×C13—22no—
62C22×C4×C13—21no—
63C22×C4×C13—44no—
64C22×C4×C13—44no—
65C22×C4×C13—41no—
66C22×C4×C13—41no—
67C22×C4×C13C22⋊C411yescharacteristic
68C22×C4×C13C22⋊C411yescharacteristic
69C22×C4×C13C22×C411yescharacteristic
70C22×C4×C13C2×D412yes—
71C13×M16—84no—
72C2×C8×C13—44no—
73C13×C4⋊C4—41no—
74C13×C4⋊C4—41no—
75C13×C4⋊C4—44no—
76C13×C22⋊C4—42no—
77C13×C22⋊C4—44no—
78C13×C22⋊C4—44no—
79C13×C22⋊C4—42no—
80C42×C13—24no—
81C42×C13—21no—
82C42×C13—21no—
83C42×C13—21no—
84C42×C13—41no—
85C42×C13—42no—
86C42×C13M1612yescomplemented
87C4×#127C2×C1311yescharacteristic
88#1465C2×C1312yescomplemented
89#1325C2×C1312yescomplemented
90#1318C2×C1312yescomplemented
91C23×C13—22no—
92C23×C13—22no—
93C23×C13—22no—
94C23×C13—22no—
95C23×C13—42no—
96C23×C13—42no—
97C23×C13—42no—
98C23×C13—42no—
99C23×C13—41no—
100C23×C13—41no—
101C23×C13C2×C22⋊C411yescharacteristic
102D4×C13—416no—
103D4×C13—42no—
104D4×C13—42no—
105D4×C13—42no—
106D4×C13—42no—
107C2×C4×C13—22no—
108C2×C4×C13—22no—
109C2×C4×C13—22no—
110C2×C4×C13—21no—
111C2×C4×C13—21no—
112C2×C4×C13—22no—
113C2×C4×C13—22no—
114C2×C4×C13—21no—
115C2×C4×C13—22no—
116C2×C4×C13—41no—
117C2×C4×C13—41no—
118C2×C4×C13—44no—
119C2×C4×C13—41no—
120C2×C4×C13—42no—
121C2×C4×C13—42no—
122C2×C4×C13—41no—
123C2×C4×C13—82no—
124C2×C4×C13—82no—
125C2×C4×C13—82no—
126C2×C4×C13#9911yescharacteristic
127C2×C4×C13#9911yescharacteristic
128C2×C4×C13C2×M1611yescharacteristic
129C2×C4×C13C2×M1611yescharacteristic
130C8×C13—84no—
131C2×#127C4×C1311yescharacteristic
132C2×C4×D4—22no—
133C2×C4×D4C4×C1311yescharacteristic
134C2×C4×D4C22×C1311yescharacteristic
135#407—22no—
136#390—22no—
137#390C4×C1311yescharacteristic
138#390C22×C1311yescharacteristic
139#384C22×C1311yescharacteristic
140C43C4×C1311yescharacteristic
141#324C22×C1314yes—
142#323—22no—
143C22×C13—21no—
144C22×C13—21no—
145C22×C13—44no—
146C22×C13—44no—
147C22×C13—42no—
148C22×C13—42no—
149C22×C13—42no—
150C22×C13—42no—
151C22×C13—82no—
152C22×C13—82no—
153C22×C13—81no—
154C22×C13—81no—
155C22×C13#40711yescharacteristic
156C22×C13C2×#9911yescharacteristic
157C22×C13#41311yescharacteristic
158C4×C13—24no—
159C4×C13—21no—
160C4×C13—21no—
161C4×C13—21no—
162C4×C13—42no—
163C4×C13—42no—
164C4×C13—41no—
165C4×C13—81no—
166C4×C13#35312yes—
167C22×D4—22no—
168C22×D4C2×C4×C1311yescharacteristic
169C22×D4C2×C4×C1311yescharacteristic
170C23×C4—21no—
171C23×C4D4×C1312yes—
172C2×M16—42no—
173#127—22no—
174#127—22no—
175C4×D4—41no—
176C4×D4—41no—
177C4×D4—48no—
178C4×D4—41no—
179C4×D4—41no—
180C2×C4⋊C4—22no—
181C2×C4⋊C4C2×C4×C1311yescharacteristic
182C2×C4⋊C4C23×C1311yescharacteristic
183C2×C22⋊C4—22no—
184C2×C22⋊C4—21no—
185C2×C22⋊C4—22no—
186C2×C22⋊C4D4×C1312yes—
187C2×C42—21no—
188C2×C42—21no—
189C2×C42C2×C4×C1311yescharacteristic
190C2×C42C2×C4×C1311yescharacteristic
191C2×C42C2×C4×C1311yescharacteristic
192C22⋊C8—24no—
193C22⋊C8—42no—
194C2×C13—21no—
195C2×C13—21no—
196C2×C13—82no—
197C2×C13—82no—
198C2×C13#146511yescharacteristic
199C2×C13C2×#35311yescharacteristic
200C2×C13#213211yescharacteristic
201C24—21no—
202C24C13×C22⋊C412yes—
203C2×D4—28no—
204C2×D4—21no—
205C2×D4—21no—
206C2×D4—21no—
207C2×D4—41no—
208C2×D4—41no—
209C2×D4—41no—
210C2×D4—41no—
211C2×D4—44no—
212C2×D4—44no—
213C2×D4C13×M1612yescomplemented
214C22×C4—21no—
215C22×C4—21no—
216C22×C4—22no—
217C22×C4—22no—
218C22×C4—21no—
219C22×C4—44no—
220C22×C4—44no—
221C22×C4—41no—
222C22×C4—41no—
223C22×C4C13×C22⋊C411yescharacteristic
224C22×C4C13×C22⋊C411yescharacteristic
225C22×C4C22×C4×C1311yescharacteristic
226C22×C4C2×D4×C1312yes—
227M16—84no—
228C2×C8—44no—
229C4⋊C4—41no—
230C4⋊C4—41no—
231C4⋊C4—44no—
232C22⋊C4—42no—
233C22⋊C4—44no—
234C22⋊C4—44no—
235C22⋊C4—42no—
236C42—24no—
237C42—21no—
238C42—21no—
239C42—21no—
240C42—41no—
241C42—42no—
242C42C13×M1612yescomplemented
243C13#1152911yescharacteristic, direct product factor, Sylow
244C23—22no—
245C23—22no—
246C23—22no—
247C23—22no—
248C23—42no—
249C23—42no—
250C23—42no—
251C23—42no—
252C23—41no—
253C23—41no—
254C23C2×C13×C22⋊C411yescharacteristic
255D4—42no—
256D4—416no—
257D4—42no—
258D4—42no—
259D4—42no—
260C2×C4—22no—
261C2×C4—22no—
262C2×C4—22no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—22no—
266C2×C4—22no—
267C2×C4—21no—
268C2×C4—22no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—44no—
272C2×C4—41no—
273C2×C4—42no—
274C2×C4—42no—
275C2×C4—41no—
276C2×C4—82no—
277C2×C4—82no—
278C2×C4—82no—
279C2×C4C13×#9911yescharacteristic
280C2×C4C13×#9911yescharacteristic
281C2×C4C2×C13×M1611yescharacteristic
282C2×C4C2×C13×M1611yescharacteristic
283C8—84no—
284C22—21no—
285C22—21no—
286C22—44no—
287C22—44no—
288C22—42no—
289C22—42no—
290C22—42no—
291C22—42no—
292C22—82no—
293C22—82no—
294C22—81no—
295C22—81no—
296C22C13×#40711yescharacteristic
297C22C2×C13×#9911yescharacteristic
298C22C13×#41311yescharacteristic
299C4—24no—
300C4—21no—
301C4—21no—
302C4—21no—
303C4—42no—
304C4—42no—
305C4—41no—
306C4—81no—
307C4C13×#35312yes—
308C2—21no—
309C2—21no—
310C2—82no—
311C2—82no—
312C2C13×#146511yescharacteristic
313C2C2×C13×#35311yescharacteristic
314C2C13×#213211yescharacteristic
subgroupG/H
center, socleC22×C13C2×#99
commutatorC22×C4C22×C4×C13
Frattini, cosocleC2×C4⋊C4C23×C13
prime radicalC2×C13×#127C4
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C22×C4×C13 ◁ C2×C4×D4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C13×#1465C2semidirect
3. C13×#1325C2semidirect
4. C13×#1318C2semidirect
44. #11529C13direct (N × H)
57. C2×D4×C13M16semidirect
86. C42×C13M16semidirect
88. #1465C2×C13semidirect
89. #1325C2×C13semidirect
90. #1318C2×C13semidirect
213. C2×D4C13×M16semidirect
242. C42C13×M16semidirect
243. C13#11529direct (N × H)

Maximal subgroups

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

subgroupindex
C4×C13×#1272
C13×#14652
C13×#13252
C13×#13182
#1152913