Finite Group Databasebeta

← C13×#9200 #15695539

Subgroups — C13×#9200 #15695539

Order 3328.

560 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#2627C211yesmaximal, characteristic
2C13×#2316C211yesmaximal, characteristic
3C13×#1520C212yesmaximal
4C2×C13×#324C211yesmaximal, characteristic
5C13×#1289C212yesmaximal
6C2×C13×C22⋊Q8C2211yescharacteristic
7C2×C13×#117—21no—
8C22×C13×C4⋊C4C2211yescharacteristic
9C2×C13×C22⋊C8C2212yes—
10C13×#400C412yescomplemented
11C13×#398—22no—
12C13×#395C412yescomplemented
13C13×#389—24no—
14C13×#385—21no—
15C13×#381—21no—
16C13×#380—21no—
17C13×#380C2211yescharacteristic
18C13×#380C2212yes—
19C13×#328—24no—
20C13×#324—22no—
21C22×Q8×C13C2×C411yescharacteristic
22C23×C4×C13D411yescharacteristic
23C23×C4×C13D411yescharacteristic
24C23×C4×C13C2311yescharacteristic
25C22×C8×C13—22no—
26C13×C22⋊Q8—22no—
27C13×C22⋊Q8—22no—
28C13×#117—42no—
29C13×#117—42no—
30C2×C13×C4⋊C4—22no—
31C2×C13×C4⋊C4—22no—
32C2×C13×C4⋊C4—22no—
33C2×C13×C4⋊C4—21no—
34C2×C13×C4⋊C4—22no—
35C2×C13×C4⋊C4—22no—
36C2×C13×C4⋊C4—22no—
37C2×C13×C4⋊C4—21no—
38C2×C13×C4⋊C4C2×C411yescharacteristic
39C2×C13×C4⋊C4C2×C412yes—
40C2×C13×C4⋊C4D412yes—
41C2×C13×C22⋊C4—22no—
42C2×C13×C22⋊C4—21no—
43C2×C13×C22⋊C4—21no—
44C2×C42×C13—22no—
45C13×C22⋊C8—22no—
46C13×C22⋊C8—22no—
47C13×#95—22no—
48C13×#95—22no—
49C13×#95—22no—
50C13×#95—22no—
51C13×#95C2×C412yes—
52C13×#95D414yes—
53#9200C1311yesmaximal, characteristic, direct product factor, Sylow
54C24×C13C2×D411yescharacteristic
55C2×Q8×C13—22no—
56C2×Q8×C13—81no—
57C22×C4×C13—21no—
58C22×C4×C13—21no—
59C22×C4×C13—21no—
60C22×C4×C13—21no—
61C22×C4×C13—21no—
62C22×C4×C13—21no—
63C22×C4×C13—21no—
64C22×C4×C13—22no—
65C22×C4×C13—21no—
66C22×C4×C13—24no—
67C22×C4×C13—81no—
68C22×C4×C13—81no—
69C22×C4×C13C22⋊C412yes—
70C22×C4×C13C22⋊C412yes—
71C22×C4×C13SD1612yes—
72C22×C4×C13Q1612yes—
73C22×C4×C13C22×C411yescharacteristic
74C22×C4×C13C2×D412yes—
75C22×C4×C13C2×D411yescharacteristic
76C22×C4×C13#4112yes—
77C2×C8×C13—42no—
78C2×C8×C13—82no—
79C13×C4⋊C4—24no—
80C13×C4⋊C4—24no—
81C13×C4⋊C4—22no—
82C13×C4⋊C4—44no—
83C13×C4⋊C4—42no—
84C13×C4⋊C4—82no—
85C13×C4⋊C4—81no—
86C13×C4⋊C4—82no—
87C13×C4⋊C4—82no—
88C13×C22⋊C4—41no—
89C13×C22⋊C4—41no—
90C13×C22⋊C4—42no—
91C13×C22⋊C4—41no—
92C13×C22⋊C4—42no—
93C13×C22⋊C4—41no—
94C42×C13—44no—
95#2627C2×C1311yescharacteristic
96#2316C2×C1311yescharacteristic
97#1520C2×C1312yes—
98C2×#324C2×C1311yescharacteristic
99#1289C2×C1312yes—
100C23×C13—41no—
101C23×C13—41no—
102C23×C13C2×C22⋊C411yescharacteristic
103C23×C13#12011yescharacteristic
104C23×C13#12311yescharacteristic
105C23×C13C2×SD1611yescharacteristic
106C23×C13C2×Q1611yescharacteristic
107C23×C13AGL(1,ℤ/8)11yescharacteristic
108C23×C13#13711yescharacteristic
109Q8×C13—82no—
110C2×C4×C13—22no—
111C2×C4×C13—22no—
112C2×C4×C13—22no—
113C2×C4×C13—22no—
114C2×C4×C13—22no—
115C2×C4×C13—22no—
116C2×C4×C13—22no—
117C2×C4×C13—41no—
118C2×C4×C13—42no—
119C2×C4×C13—42no—
120C2×C4×C13—41no—
121C2×C4×C13—42no—
122C2×C4×C13—42no—
123C2×C4×C13—42no—
124C2×C4×C13—44no—
125C2×C4×C13—42no—
126C2×C4×C13—42no—
127C2×C4×C13—44no—
128C2×C4×C13—42no—
129C2×C4×C13—41no—
130C2×C4×C13—41no—
131C2×C4×C13—42no—
132C2×C4×C13—44no—
133C2×C4×C13—81no—
134C2×C4×C13#10314yes—
135C2×C4×C13C4×D412yes—
136C2×C4×C13#12112yes—
137C8×C13—82no—
138C2×C22⋊Q8C22×C1311yescharacteristic
139C2×#117—21no—
140C22×C4⋊C4C22×C1311yescharacteristic
141C2×C22⋊C8C22×C1312yes—
142#400C4×C1312yescomplemented
143#398—22no—
144#395C4×C1312yescomplemented
145#389—24no—
146#385—21no—
147#381—21no—
148#380—21no—
149#380C22×C1311yescharacteristic
150#380C22×C1312yes—
151#328—24no—
152#324—22no—
153C22×C13—21no—
154C22×C13—21no—
155C22×C13—21no—
156C22×C13—21no—
157C22×C13—21no—
158C22×C13—21no—
159C22×C13—41no—
160C22×C13—41no—
161C22×C13—41no—
162C22×C13—41no—
163C22×C13#38611yescharacteristic
164C22×C13C2×#10311yescharacteristic
165C22×C13#41711yescharacteristic
166C22×C13#45011yescharacteristic
167C22×C13#45111yescharacteristic
168C22×C13#48311yescharacteristic
169C22×C13#48411yescharacteristic
170C4×C13—24no—
171C4×C13—22no—
172C4×C13—22no—
173C4×C13—42no—
174C4×C13—84no—
175C4×C13—82no—
176C4×C13—81no—
177C4×C13—81no—
178C22×Q8C2×C4×C1311yescharacteristic
179C23×C4D4×C1311yescharacteristic
180C23×C4D4×C1311yescharacteristic
181C23×C4C23×C1311yescharacteristic
182C22×C8—22no—
183C22⋊Q8—22no—
184C22⋊Q8—22no—
185#117—42no—
186#117—42no—
187C2×C4⋊C4—22no—
188C2×C4⋊C4—22no—
189C2×C4⋊C4—22no—
190C2×C4⋊C4—21no—
191C2×C4⋊C4—22no—
192C2×C4⋊C4—22no—
193C2×C4⋊C4—22no—
194C2×C4⋊C4—21no—
195C2×C4⋊C4C2×C4×C1311yescharacteristic
196C2×C4⋊C4C2×C4×C1312yes—
197C2×C4⋊C4D4×C1312yes—
198C2×C22⋊C4—22no—
199C2×C22⋊C4—21no—
200C2×C22⋊C4—21no—
201C2×C42—22no—
202C22⋊C8—22no—
203C22⋊C8—22no—
204#95—22no—
205#95—22no—
206#95—22no—
207#95—22no—
208#95C2×C4×C1312yes—
209#95D4×C1314yes—
210C2×C13—21no—
211C2×C13—21no—
212C2×C13—21no—
213C2×C13—21no—
214C2×C13—21no—
215C2×C13—21no—
216C2×C13#187211yescharacteristic
217C2×C13#191211yescharacteristic
218C2×C13#191311yescharacteristic
219C24C2×D4×C1311yescharacteristic
220C2×Q8—22no—
221C2×Q8—81no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—22no—
230C22×C4—21no—
231C22×C4—24no—
232C22×C4—81no—
233C22×C4—81no—
234C22×C4C13×C22⋊C412yes—
235C22×C4C13×C22⋊C412yes—
236C22×C4C13×SD1612yes—
237C22×C4C13×Q1612yes—
238C22×C4C22×C4×C1311yescharacteristic
239C22×C4C2×D4×C1312yes—
240C22×C4C2×D4×C1311yescharacteristic
241C22×C4C13×#4112yes—
242C2×C8—42no—
243C2×C8—82no—
244C4⋊C4—24no—
245C4⋊C4—24no—
246C4⋊C4—22no—
247C4⋊C4—44no—
248C4⋊C4—42no—
249C4⋊C4—82no—
250C4⋊C4—81no—
251C4⋊C4—82no—
252C4⋊C4—82no—
253C22⋊C4—41no—
254C22⋊C4—41no—
255C22⋊C4—42no—
256C22⋊C4—42no—
257C22⋊C4—41no—
258C22⋊C4—41no—
259C42—44no—
260C13#920011yescharacteristic, direct product factor, Sylow
261C23—41no—
262C23—41no—
263C23C2×C13×C22⋊C411yescharacteristic
264C23C13×#12011yescharacteristic
265C23C13×#12311yescharacteristic
266C23C2×C13×SD1611yescharacteristic
267C23C2×C13×Q1611yescharacteristic
268C23C13×AGL(1,ℤ/8)11yescharacteristic
269C23C13×#13711yescharacteristic
270Q8—82no—
271C2×C4—22no—
272C2×C4—22no—
273C2×C4—22no—
274C2×C4—22no—
275C2×C4—22no—
276C2×C4—22no—
277C2×C4—22no—
278C2×C4—41no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—41no—
282C2×C4—42no—
283C2×C4—42no—
284C2×C4—42no—
285C2×C4—44no—
286C2×C4—42no—
287C2×C4—42no—
288C2×C4—44no—
289C2×C4—42no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—42no—
293C2×C4—44no—
294C2×C4—81no—
295C2×C4C13×#10314yes—
296C2×C4C4×D4×C1312yes—
297C2×C4C13×#12112yes—
298C8—82no—
299C22—21no—
300C22—21no—
301C22—21no—
302C22—21no—
303C22—21no—
304C22—21no—
305C22—41no—
306C22—41no—
307C22—41no—
308C22—41no—
309C22C13×#38611yescharacteristic
310C22C2×C13×#10311yescharacteristic
311C22C13×#41711yescharacteristic
312C22C13×#45011yescharacteristic
313C22C13×#45111yescharacteristic
314C22C13×#48311yescharacteristic
315C22C13×#48411yescharacteristic
316C4—24no—
317C4—22no—
318C4—22no—
319C4—42no—
320C4—84no—
321C4—82no—
322C4—81no—
323C4—81no—
324C2—21no—
325C2—21no—
326C2—21no—
327C2—21no—
328C2—21no—
329C2—21no—
330C2C13×#187211yescharacteristic
331C2C13×#191211yescharacteristic
332C2C13×#191311yescharacteristic
subgroupG/H
center, socleC22×C13#386
commutatorC22×C4C22×C4×C13
Frattini, cosocleC23×C4C23×C13
prime radicalC24×C13C2×D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ C23×C4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
10. C13×#400C4semidirect
12. C13×#395C4semidirect
53. #9200C13direct (N × H)
142. #400C4×C13semidirect
144. #395C4×C13semidirect
260. C13#9200direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#26272
C13×#23162
C13×#15202
C2×C13×#3242
C13×#12892
#920013