Finite Group Databasebeta

← C13×#7721 #15694060

Subgroups — C13×#7721 #15694060

Order 3328.

444 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#2855C211yesmaximal, characteristic
2C13×#1817C211yesmaximal, characteristic
3C13×#1817C211yesmaximal, characteristic
4C13×#1272C212yesmaximal, complemented
5C13×#1271C212yesmaximal, complemented
6C2×C13×C22⋊Q8C411yescharacteristic
7C22×C42×C13C2211yescharacteristic
8C2×C13×C22⋊C8—21no—
9C2×C13×C22⋊C8—21no—
10C13×#391C411yescharacteristic
11C13×#391C2211yescharacteristic
12C13×#389C411yescharacteristic
13C13×#389C2211yescharacteristic
14C13×#387—21no—
15C13×#387—21no—
16C13×#385—21no—
17C13×#381—21no—
18C13×#380C411yescharacteristic
19C13×#336—21no—
20C13×#336—21no—
21C13×#336C2212yes—
22C13×#336C2212yes—
23C22×Q8×C13C2×C411yescharacteristic
24C23×C4×C13C2×C411yescharacteristic
25C23×C4×C13D411yescharacteristic
26C23×C4×C13D411yescharacteristic
27C22×C8×C13—22no—
28C22×C8×C13—22no—
29C13×C22⋊Q8—42no—
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4—21no—
33C2×C13×C4⋊C4C2×C411yescharacteristic
34C2×C13×C4⋊C4C2×C411yescharacteristic
35C2×C13×C4⋊C4C2×C411yescharacteristic
36C2×C13×C22⋊C4—21no—
37C2×C13×C22⋊C4—21no—
38C2×C42×C13—42no—
39C2×C42×C13C2×C411yescharacteristic
40C2×C42×C13D411yescharacteristic
41C2×C42×C13D411yescharacteristic
42C2×C42×C13C2311yescharacteristic
43C13×C22⋊C8—42no—
44C13×C22⋊C8—42no—
45C13×#95—21no—
46C13×#95—21no—
47C13×#95—21no—
48C13×#95—21no—
49C13×#95—21no—
50C13×#95—21no—
51C13×#95—21no—
52#7721C1311yesmaximal, characteristic, direct product factor, Sylow
53C24×C13C22⋊C411yescharacteristic
54C2×Q8×C13—22no—
55C2×Q8×C13—41no—
56C2×Q8×C13—41no—
57C22×C4×C13—22no—
58C22×C4×C13—22no—
59C22×C4×C13—22no—
60C22×C4×C13—22no—
61C22×C4×C13—22no—
62C22×C4×C13—22no—
63C22×C4×C13—21no—
64C22×C4×C13—21no—
65C22×C4×C13—21no—
66C22×C4×C13—21no—
67C22×C4×C13—41no—
68C22×C4×C13—41no—
69C22×C4×C13—41no—
70C22×C4×C13C22⋊C411yescharacteristic
71C22×C4×C13C22⋊C411yescharacteristic
72C22×C4×C13C22⋊C411yescharacteristic
73C22×C4×C13C22×C411yescharacteristic
74C22×C4×C13C2×D411yescharacteristic
75C22×C4×C13C2×D411yescharacteristic
76C2×C8×C13—42no—
77C2×C8×C13—42no—
78C2×C8×C13—42no—
79C2×C8×C13—42no—
80C2×C8×C13—42no—
81C2×C8×C13—42no—
82C13×C4⋊C4—22no—
83C13×C4⋊C4—41no—
84C13×C4⋊C4—41no—
85C13×C4⋊C4—42no—
86C13×C4⋊C4—42no—
87C13×C4⋊C4—42no—
88C13×C22⋊C4—42no—
89C13×C22⋊C4—42no—
90C42×C13—41no—
91C42×C13—41no—
92C42×C13—41no—
93C42×C13—41no—
94#2855C2×C1311yescharacteristic
95#1817C2×C1311yescharacteristic
96#1817C2×C1311yescharacteristic
97#1272C2×C1312yescomplemented
98#1271C2×C1312yescomplemented
99C23×C13—21no—
100C23×C13—21no—
101C23×C13—21no—
102C23×C13—21no—
103C23×C13—21no—
104C23×C13—21no—
105C23×C13#9912yes—
106C23×C13C2×C22⋊C411yescharacteristic
107Q8×C13—82no—
108C2×C4×C13—21no—
109C2×C4×C13—21no—
110C2×C4×C13—21no—
111C2×C4×C13—21no—
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13—44no—
124C2×C4×C13—44no—
125C2×C4×C13—44no—
126C2×C4×C13—41no—
127C2×C4×C13—41no—
128C2×C4×C13—41no—
129C2×C4×C13—41no—
130C2×C4×C13—41no—
131C2×C4×C13—41no—
132C2×C4×C13—41no—
133C2×C4×C13—41no—
134C2×C4×C13—41no—
135C2×C4×C13—41no—
136C2×C4×C13—41no—
137C2×C4×C13—41no—
138C2×C4×C13#13112yes—
139C2×C4×C13#13512yes—
140C2×C4×C13#13712yes—
141C8×C13—82no—
142C8×C13—82no—
143C2×C22⋊Q8C4×C1311yescharacteristic
144C22×C42C22×C1311yescharacteristic
145C2×C22⋊C8—21no—
146C2×C22⋊C8—21no—
147#391C4×C1311yescharacteristic
148#391C22×C1311yescharacteristic
149#389C4×C1311yescharacteristic
150#389C22×C1311yescharacteristic
151#387—21no—
152#387—21no—
153#385—21no—
154#381—21no—
155#380C4×C1311yescharacteristic
156#336—21no—
157#336—21no—
158#336C22×C1312yes—
159#336C22×C1312yes—
160C22×C13—22no—
161C22×C13—22no—
162C22×C13—22no—
163C22×C13—41no—
164C22×C13—41no—
165C22×C13—41no—
166C22×C13—41no—
167C22×C13#40811yescharacteristic
168C22×C13C2×#9911yescharacteristic
169C22×C13#41311yescharacteristic
170C22×C13#41611yescharacteristic
171C22×C13#41911yescharacteristic
172C22×C13#42111yescharacteristic
173C22×C13#42111yescharacteristic
174C4×C13—22no—
175C4×C13—22no—
176C4×C13—22no—
177C4×C13—41no—
178C4×C13—41no—
179C4×C13—41no—
180C4×C13—81no—
181C4×C13—81no—
182C4×C13—81no—
183C4×C13—81no—
184C22×Q8C2×C4×C1311yescharacteristic
185C23×C4C2×C4×C1311yescharacteristic
186C23×C4D4×C1311yescharacteristic
187C23×C4D4×C1311yescharacteristic
188C22×C8—22no—
189C22×C8—22no—
190C22⋊Q8—42no—
191C2×C4⋊C4—21no—
192C2×C4⋊C4—21no—
193C2×C4⋊C4—21no—
194C2×C4⋊C4C2×C4×C1311yescharacteristic
195C2×C4⋊C4C2×C4×C1311yescharacteristic
196C2×C4⋊C4C2×C4×C1311yescharacteristic
197C2×C22⋊C4—21no—
198C2×C22⋊C4—21no—
199C2×C42—42no—
200C2×C42C2×C4×C1311yescharacteristic
201C2×C42D4×C1311yescharacteristic
202C2×C42D4×C1311yescharacteristic
203C2×C42C23×C1311yescharacteristic
204C22⋊C8—42no—
205C22⋊C8—42no—
206#95—21no—
207#95—21no—
208#95—21no—
209#95—21no—
210#95—21no—
211#95—21no—
212#95—21no—
213C2×C13—42no—
214C2×C13#146811yescharacteristic
215C2×C13#148211yescharacteristic
216C2×C13#149711yescharacteristic
217C2×C13#151111yescharacteristic
218C2×C13#151611yescharacteristic
219C2×C13#153511yescharacteristic
220C2×C13#155411yescharacteristic
221C24C13×C22⋊C411yescharacteristic
222C2×Q8—22no—
223C2×Q8—41no—
224C2×Q8—41no—
225C22×C4—22no—
226C22×C4—22no—
227C22×C4—22no—
228C22×C4—22no—
229C22×C4—22no—
230C22×C4—22no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—41no—
236C22×C4—41no—
237C22×C4—41no—
238C22×C4C13×C22⋊C411yescharacteristic
239C22×C4C13×C22⋊C411yescharacteristic
240C22×C4C13×C22⋊C411yescharacteristic
241C22×C4C22×C4×C1311yescharacteristic
242C22×C4C2×D4×C1311yescharacteristic
243C22×C4C2×D4×C1311yescharacteristic
244C2×C8—42no—
245C2×C8—42no—
246C2×C8—42no—
247C2×C8—42no—
248C2×C8—42no—
249C2×C8—42no—
250C4⋊C4—22no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—42no—
254C4⋊C4—42no—
255C4⋊C4—42no—
256C22⋊C4—42no—
257C22⋊C4—42no—
258C42—41no—
259C42—41no—
260C42—41no—
261C42—41no—
262C13#772111yescharacteristic, direct product factor, Sylow
263C23—21no—
264C23—21no—
265C23—21no—
266C23—21no—
267C23—21no—
268C23—21no—
269C23C13×#9912yes—
270C23C2×C13×C22⋊C411yescharacteristic
271Q8—82no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—44no—
288C2×C4—44no—
289C2×C4—44no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4C13×#13112yes—
303C2×C4C13×#13512yes—
304C2×C4C13×#13712yes—
305C8—82no—
306C8—82no—
307C22—22no—
308C22—22no—
309C22—22no—
310C22—41no—
311C22—41no—
312C22—41no—
313C22—41no—
314C22C13×#40811yescharacteristic
315C22C2×C13×#9911yescharacteristic
316C22C13×#41311yescharacteristic
317C22C13×#41611yescharacteristic
318C22C13×#41911yescharacteristic
319C22C13×#42111yescharacteristic
320C22C13×#42111yescharacteristic
321C4—22no—
322C4—22no—
323C4—22no—
324C4—41no—
325C4—41no—
326C4—41no—
327C4—81no—
328C4—81no—
329C4—81no—
330C4—81no—
331C2—42no—
332C2C13×#146811yescharacteristic
333C2C13×#148211yescharacteristic
334C2C13×#149711yescharacteristic
335C2C13×#151111yescharacteristic
336C2C13×#151611yescharacteristic
337C2C13×#153511yescharacteristic
338C2C13×#155411yescharacteristic
subgroupG/H
center, socleC23×C13C2×C22⋊C4
commutatorC22×C4C22×C4×C13
Frattini, cosocleC2×C42C23×C13
prime radicalC24×C13C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C13 ◁ C22×C42×C13 ◁ G

Complements

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

NH ≅ G/Ntype
4. C13×#1272C2semidirect
5. C13×#1271C2semidirect
52. #7721C13direct (N × H)
97. #1272C2×C13semidirect
98. #1271C2×C13semidirect
262. C13#7721direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#28552
C13×#18172
C13×#12722
C13×#12712
#772113