Finite Group Databasebeta

← C13×#2745 #13111803

Subgroups — C13×#2745 #13111803

Order 1664.

400 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#401C211yesmaximal, characteristic, complemented
2C13×#400C211yesmaximal, characteristic, complemented
3C13×#400C211yesmaximal, characteristic, complemented
4C13×#397C211yesmaximal, characteristic
5C13×#395C211yesmaximal, characteristic, complemented
6C13×#393C211yesmaximal, characteristic
7C13×#391C211yesmaximal, characteristic, complemented
8C13×#388C211yesmaximal, characteristic
9C13×#388C211yesmaximal, characteristic
10C13×#387C211yesmaximal, characteristic, complemented
11C13×#387C211yesmaximal, characteristic, complemented
12C13×#387C211yesmaximal, characteristic, complemented
13C13×#385C211yesmaximal, characteristic
14C13×#381C211yesmaximal, characteristic
15C13×#380C211yesmaximal, characteristic
16C22×Q8×C13C2211yescharacteristic
17C23×C4×C13C2211yescharacteristic
18C2×C13×C4⋊C4C2211yescharacteristic
19C2×C13×C4⋊C4C2211yescharacteristic
20C2×C13×C4⋊C4C2211yescharacteristic
21C2×C13×C4⋊C4C2211yescharacteristic
22C2×C13×C4⋊C4C2211yescharacteristic
23C2×C13×C4⋊C4C2211yescharacteristic
24C2×C13×C4⋊C4C2211yescharacteristic
25C2×C13×C22⋊C4C2211yescharacteristic
26C2×C13×C22⋊C4C2211yescharacteristic
27C2×C13×C22⋊C4C2211yescharacteristic
28C2×C13×C22⋊C4C2211yescharacteristic
29C2×C13×C22⋊C4C2211yescharacteristic
30C2×C13×C22⋊C4C2211yescharacteristic
31C2×C42×C13C2211yescharacteristic
32C2×C42×C13C2211yescharacteristic
33C13×#95C2211yescharacteristic
34C13×#95C2211yescharacteristic
35C13×#95C2211yescharacteristic
36C13×#95C2211yescharacteristic
37C13×#95C2211yescharacteristic
38C13×#95C2211yescharacteristic
39C13×#95C2211yescharacteristic
40C13×#95C2211yescharacteristic
41C13×#95C2211yescharacteristic
42C13×#95C2211yescharacteristic
43C13×#95C2211yescharacteristic
44C13×#95C2211yescharacteristic
45C13×#95C2211yescharacteristic
46C13×#95C2211yescharacteristic
47C13×#95C2211yescharacteristic
48C13×#95C2211yescharacteristic
49C13×#95C2211yescharacteristic
50C13×#95C2211yescharacteristic
51C24×C13C2311yescharacteristic
52C2×Q8×C13—22no—
53C2×Q8×C13—41no—
54C2×Q8×C13—41no—
55C22×C4×C13—22no—
56C22×C4×C13—22no—
57C22×C4×C13—41no—
58C22×C4×C13C2311yescharacteristic
59C22×C4×C13C2311yescharacteristic
60C22×C4×C13C2311yescharacteristic
61C22×C4×C13C2311yescharacteristic
62C22×C4×C13C2311yescharacteristic
63C22×C4×C13C2311yescharacteristic
64C22×C4×C13C2311yescharacteristic
65C22×C4×C13C2311yescharacteristic
66C22×C4×C13C2311yescharacteristic
67C22×C4×C13C2311yescharacteristic
68C22×C4×C13C2311yescharacteristic
69C22×C4×C13C2311yescharacteristic
70C22×C4×C13C2311yescharacteristic
71C22×C4×C13C2311yescharacteristic
72C13×C4⋊C4—22no—
73C13×C4⋊C4—22no—
74C13×C4⋊C4—22no—
75C13×C4⋊C4—41no—
76C13×C4⋊C4—41no—
77C13×C4⋊C4—41no—
78C13×C4⋊C4—41no—
79C13×C22⋊C4—22no—
80C13×C22⋊C4—22no—
81C13×C22⋊C4—22no—
82C13×C22⋊C4—41no—
83C13×C22⋊C4—41no—
84C13×C22⋊C4—41no—
85C42×C13—41no—
86C42×C13—41no—
87#2745C1311yesmaximal, characteristic, direct product factor, Sylow
88C23×C13—21no—
89C23×C13—21no—
90C23×C13—21no—
91C23×C13—21no—
92C23×C13—21no—
93C23×C13—21no—
94C23×C13#4112yes—
95C23×C13C2411yescharacteristic
96Q8×C13—44no—
97C2×C4×C13—21no—
98C2×C4×C13—21no—
99C2×C4×C13—21no—
100C2×C4×C13—21no—
101C2×C4×C13—21no—
102C2×C4×C13—21no—
103C2×C4×C13—21no—
104C2×C4×C13—21no—
105C2×C4×C13—21no—
106C2×C4×C13—21no—
107C2×C4×C13—21no—
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—21no—
124C2×C4×C13—21no—
125C2×C4×C13—21no—
126C2×C4×C13—21no—
127C2×C4×C13—21no—
128C2×C4×C13—21no—
129C2×C4×C13—21no—
130C2×C4×C13—21no—
131C2×C4×C13—21no—
132C2×C4×C13—21no—
133C2×C4×C13—21no—
134C2×C4×C13—21no—
135C2×C4×C13—21no—
136C2×C4×C13—21no—
137C2×C4×C13—44no—
138C2×C4×C13#4112yes—
139C2×C4×C13#4112yes—
140#401C2×C1311yescharacteristic, complemented
141#400C2×C1311yescharacteristic, complemented
142#400C2×C1311yescharacteristic, complemented
143#397C2×C1311yescharacteristic
144#395C2×C1311yescharacteristic, complemented
145#393C2×C1311yescharacteristic
146#391C2×C1311yescharacteristic, complemented
147#388C2×C1311yescharacteristic
148#388C2×C1311yescharacteristic
149#387C2×C1311yescharacteristic, complemented
150#387C2×C1311yescharacteristic, complemented
151#387C2×C1311yescharacteristic, complemented
152#385C2×C1311yescharacteristic
153#381C2×C1311yescharacteristic
154#380C2×C1311yescharacteristic
155C22×C13—22no—
156C22×C13—22no—
157C22×C13—22no—
158C22×C13—41no—
159C22×C13—41no—
160C22×C13—41no—
161C22×C13—41no—
162C22×C13C2×#4111yescharacteristic
163C22×C13C2×#4111yescharacteristic
164C22×C13C2×#4111yescharacteristic
165C22×C13H(5,𝔽2)11yescharacteristic
166C22×C13H(5,𝔽2)11yescharacteristic
167C22×C132−1+411yescharacteristic
168C22×C132−1+411yescharacteristic
169C4×C13—22no—
170C4×C13—22no—
171C4×C13—41no—
172C4×C13—41no—
173C4×C13—41no—
174C4×C13—41no—
175C4×C13—41no—
176C4×C13—41no—
177C4×C13—41no—
178C4×C13—41no—
179C4×C13—41no—
180C4×C13—41no—
181C4×C13—41no—
182C4×C13—41no—
183C22×Q8C22×C1311yescharacteristic
184C23×C4C22×C1311yescharacteristic
185C2×C4⋊C4C22×C1311yescharacteristic
186C2×C4⋊C4C22×C1311yescharacteristic
187C2×C4⋊C4C22×C1311yescharacteristic
188C2×C4⋊C4C22×C1311yescharacteristic
189C2×C4⋊C4C22×C1311yescharacteristic
190C2×C4⋊C4C22×C1311yescharacteristic
191C2×C4⋊C4C22×C1311yescharacteristic
192C2×C22⋊C4C22×C1311yescharacteristic
193C2×C22⋊C4C22×C1311yescharacteristic
194C2×C22⋊C4C22×C1311yescharacteristic
195C2×C22⋊C4C22×C1311yescharacteristic
196C2×C22⋊C4C22×C1311yescharacteristic
197C2×C22⋊C4C22×C1311yescharacteristic
198C2×C42C22×C1311yescharacteristic
199C2×C42C22×C1311yescharacteristic
200#95C22×C1311yescharacteristic
201#95C22×C1311yescharacteristic
202#95C22×C1311yescharacteristic
203#95C22×C1311yescharacteristic
204#95C22×C1311yescharacteristic
205#95C22×C1311yescharacteristic
206#95C22×C1311yescharacteristic
207#95C22×C1311yescharacteristic
208#95C22×C1311yescharacteristic
209#95C22×C1311yescharacteristic
210#95C22×C1311yescharacteristic
211#95C22×C1311yescharacteristic
212#95C22×C1311yescharacteristic
213#95C22×C1311yescharacteristic
214#95C22×C1311yescharacteristic
215#95C22×C1311yescharacteristic
216#95C22×C1311yescharacteristic
217#95C22×C1311yescharacteristic
218C2×C13—42no—
219C2×C13#53811yescharacteristic
220C2×C13#53911yescharacteristic
221C2×C13#54211yescharacteristic
222C2×C13#55111yescharacteristic
223C2×C13#55211yescharacteristic
224C2×C13#55611yescharacteristic
225C2×C13#56311yescharacteristic
226C24C23×C1311yescharacteristic
227C2×Q8—22no—
228C2×Q8—41no—
229C2×Q8—41no—
230C22×C4—22no—
231C22×C4—22no—
232C22×C4—41no—
233C22×C4C23×C1311yescharacteristic
234C22×C4C23×C1311yescharacteristic
235C22×C4C23×C1311yescharacteristic
236C22×C4C23×C1311yescharacteristic
237C22×C4C23×C1311yescharacteristic
238C22×C4C23×C1311yescharacteristic
239C22×C4C23×C1311yescharacteristic
240C22×C4C23×C1311yescharacteristic
241C22×C4C23×C1311yescharacteristic
242C22×C4C23×C1311yescharacteristic
243C22×C4C23×C1311yescharacteristic
244C22×C4C23×C1311yescharacteristic
245C22×C4C23×C1311yescharacteristic
246C22×C4C23×C1311yescharacteristic
247C4⋊C4—22no—
248C4⋊C4—22no—
249C4⋊C4—22no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C22⋊C4—22no—
255C22⋊C4—22no—
256C22⋊C4—22no—
257C22⋊C4—41no—
258C22⋊C4—41no—
259C22⋊C4—41no—
260C42—41no—
261C42—41no—
262C13#274511yescharacteristic, direct product factor, Sylow
263C23—21no—
264C23—21no—
265C23—21no—
266C23—21no—
267C23—21no—
268C23—21no—
269C23C13×#4112yes—
270C23C24×C1311yescharacteristic
271Q8—44no—
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—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—44no—
313C2×C4C13×#4112yes—
314C2×C4C13×#4112yes—
315C22—22no—
316C22—22no—
317C22—22no—
318C22—41no—
319C22—41no—
320C22—41no—
321C22—41no—
322C22C2×C13×#4111yescharacteristic
323C22C2×C13×#4111yescharacteristic
324C22C2×C13×#4111yescharacteristic
325C22C13×H(5,𝔽2)11yescharacteristic
326C22C13×H(5,𝔽2)11yescharacteristic
327C22C13×2−1+411yescharacteristic
328C22C13×2−1+411yescharacteristic
329C4—22no—
330C4—22no—
331C4—41no—
332C4—41no—
333C4—41no—
334C4—41no—
335C4—41no—
336C4—41no—
337C4—41no—
338C4—41no—
339C4—41no—
340C4—41no—
341C4—41no—
342C4—41no—
343C2—42no—
344C2C13×#53811yescharacteristic
345C2C13×#53911yescharacteristic
346C2C13×#54211yescharacteristic
347C2C13×#55111yescharacteristic
348C2C13×#55211yescharacteristic
349C2C13×#55611yescharacteristic
350C2C13×#56311yescharacteristic
subgroupG/H
center, socleC23×C13C24
commutator, Frattini, cosocleC23C24×C13
prime radicalC24×C13C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C13 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×#401C2semidirect
2. C13×#400C2semidirect
3. C13×#400C2semidirect
5. C13×#395C2semidirect
7. C13×#391C2semidirect
10. C13×#387C2semidirect
11. C13×#387C2semidirect
12. C13×#387C2semidirect
87. #2745C13direct (N × H)
140. #401C2×C13semidirect
141. #400C2×C13semidirect
142. #400C2×C13semidirect
144. #395C2×C13semidirect
146. #391C2×C13semidirect
149. #387C2×C13semidirect
150. #387C2×C13semidirect
151. #387C2×C13semidirect
262. C13#2745direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#4012
C13×#4002
C13×#3972
C13×#3952
C13×#3932
C13×#3912
C13×#3882
C13×#3872
C13×#3852
C13×#3812
C13×#3802
#274513