Finite Group Databasebeta

← C13×#36700 #15723039

Subgroups — C13×#36700 #15723039

Order 3328.

1356 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#2839C214yesmaximal, complemented
2C13×#2836C214yesmaximal
3C13×#2833C214yesmaximal, complemented
4C13×#2831C214yesmaximal
5C13×#2402C211yesmaximal, characteristic, complemented
6C13×#2402C214yesmaximal, complemented
7C13×#2401C214yesmaximal
8C13×#2399C211yesmaximal, characteristic, complemented
9C13×#2396C212yesmaximal
10C13×#2298C211yesmaximal, characteristic
11C13×#2295C212yesmaximal, complemented
12C2×C4×Q8×C13C2212yes—
13C2×C13×#117C2211yescharacteristic
14C13×#401C2214yes—
15C13×#400C2214yes—
16C13×#400C2214yes—
17C13×#400C2214yes—
18C13×#400C2214yes—
19C13×#400C2214yes—
20C13×#400C2214yes—
21C13×#400C2214yes—
22C13×#400C2212yes—
23C13×#400C2214yes—
24C13×#399C2212yes—
25C13×#398C2214yes—
26C13×#398C2214yes—
27C13×#398C2214yes—
28C13×#398C2214yes—
29C13×#398C2214yes—
30C13×#398C2214yes—
31C13×#398C2214yes—
32C13×#397C2214yes—
33C13×#397C2214yes—
34C13×#397C2214yes—
35C13×#396C2214yes—
36C13×#396C2214yes—
37C13×#395C2214yes—
38C13×#395C2212yes—
39C13×#393C2212yes—
40C13×#391C2214yes—
41C13×#389C2214yes—
42C13×#388C2214yes—
43C13×#387C2214yes—
44C13×#387C2214yes—
45C13×#387C2214yes—
46C4×C13×C4⋊C4C2212yes—
47C4×C13×C4⋊C4C2214yes—
48C4×C13×C4⋊C4C2212yes—
49C4×C13×C4⋊C4C2214yes—
50C4×C13×C4⋊C4C2214yes—
51C4×C13×C4⋊C4C2214yes—
52C4×C13×C22⋊C4C2212yes—
53C4×C13×C22⋊C4C2214yes—
54C13×#376C2214yes—
55C13×#376C2211yescharacteristic
56C43×C13C2211yescharacteristic
57C22×Q8×C13C2312yes—
58C23×C4×C13C2311yescharacteristic
59C4×Q8×C13—28no—
60C13×#117—24no—
61C2×C13×C4⋊C4C2314yes—
62C2×C13×C4⋊C4C2312yes—
63C2×C13×C4⋊C4C2312yes—
64C2×C13×C4⋊C4C2314yes—
65C2×C13×C4⋊C4C2314yes—
66C2×C13×C4⋊C4C2314yes—
67C2×C13×C4⋊C4C2314yes—
68C2×C13×C4⋊C4C2314yes—
69C2×C13×C4⋊C4C2314yes—
70C2×C13×C4⋊C4C2314yes—
71C2×C13×C4⋊C4C2314yes—
72C2×C13×C4⋊C4C2314yes—
73C2×C13×C4⋊C4C2314yes—
74C2×C13×C22⋊C4C2312yes—
75C2×C13×C22⋊C4C2314yes—
76C2×C13×C22⋊C4C2314yes—
77C2×C13×C22⋊C4C2314yes—
78C2×C42×C13C2312yes—
79C2×C42×C13C2314yes—
80C2×C42×C13C2314yes—
81C2×C42×C13C2312yes—
82C2×C42×C13C2311yescharacteristic
83C2×C42×C13C2314yes—
84C2×C42×C13C2311yescharacteristic
85C13×#95C2314yes—
86C13×#95C2314yes—
87C13×#95C2314yes—
88C13×#95C2312yes—
89C13×#95C2312yes—
90C13×#95C2314yes—
91C13×#95C2314yes—
92C13×#95C2314yes—
93C13×#95C2314yes—
94C13×#95C2314yes—
95C13×#95C2314yes—
96C13×#95C2314yes—
97C13×#95C2314yes—
98C13×#95C2314yes—
99C13×#95C2314yes—
100C13×#95C2314yes—
101C13×#95C2314yes—
102C13×#95C2314yes—
103C13×#95C2314yes—
104#36700C1311yesmaximal, characteristic, direct product factor, Sylow
105C24×C13C2411yescharacteristic
106C2×Q8×C13—24no—
107C2×Q8×C13—44no—
108C22×C4×C13—22no—
109C22×C4×C13—24no—
110C22×C4×C13C2411yescharacteristic
111C22×C4×C13C2414yes—
112C22×C4×C13C2414yes—
113C22×C4×C13C2414yes—
114C22×C4×C13C2414yes—
115C22×C4×C13C2414yes—
116C22×C4×C13C2412yes—
117C22×C4×C13C2414yes—
118C22×C4×C13C2412yes—
119C22×C4×C13C2411yescharacteristic
120C13×C4⋊C4—24no—
121C13×C4⋊C4—24no—
122C13×C4⋊C4—28no—
123C13×C4⋊C4—44no—
124C13×C4⋊C4—44no—
125C13×C4⋊C4—44no—
126C13×C4⋊C4—44no—
127C13×C4⋊C4—44no—
128C13×C4⋊C4—44no—
129C13×C4⋊C4—44no—
130C13×C4⋊C4—44no—
131C13×C4⋊C4—44no—
132C13×C4⋊C4—44no—
133C13×C22⋊C4—24no—
134C13×C22⋊C4—44no—
135C13×C22⋊C4—44no—
136C13×C22⋊C4—44no—
137C42×C13—22no—
138C42×C13—28no—
139C42×C13—24no—
140C42×C13—28no—
141C42×C13—24no—
142C42×C13—44no—
143C42×C13#4114yes—
144#2839C2×C1314yescomplemented
145#2836C2×C1314yes—
146#2833C2×C1314yescomplemented
147#2831C2×C1314yes—
148#2402C2×C1311yescharacteristic, complemented
149#2402C2×C1314yescomplemented
150#2401C2×C1314yes—
151#2399C2×C1311yescharacteristic, complemented
152#2396C2×C1312yes—
153#2298C2×C1311yescharacteristic
154#2295C2×C1312yescomplemented
155C23×C13—21no—
156C23×C13—22no—
157C23×C13—24no—
158C23×C13C2511yescharacteristic
159Q8×C13—48no—
160C2×C4×C13—24no—
161C2×C4×C13—22no—
162C2×C4×C13—24no—
163C2×C4×C13—24no—
164C2×C4×C13—21no—
165C2×C4×C13—24no—
166C2×C4×C13—24no—
167C2×C4×C13—24no—
168C2×C4×C13—24no—
169C2×C4×C13—22no—
170C2×C4×C13—24no—
171C2×C4×C13—24no—
172C2×C4×C13—24no—
173C2×C4×C13—24no—
174C2×C4×C13—24no—
175C2×C4×C13—24no—
176C2×C4×C13—24no—
177C2×C4×C13—24no—
178C2×C4×C13—24no—
179C2×C4×C13—24no—
180C2×C4×C13—24no—
181C2×C4×C13—24no—
182C2×C4×C13—24no—
183C2×C4×C13—44no—
184C2×C4×C13C2×#4114yes—
185C2×C4×C13C2×#4112yes—
186C2×C4×C132−1+414yes—
187C2×C4×Q8C22×C1312yes—
188C2×#117C22×C1311yescharacteristic
189#401C22×C1314yes—
190#400C22×C1314yes—
191#400C22×C1314yes—
192#400C22×C1314yes—
193#400C22×C1314yes—
194#400C22×C1314yes—
195#400C22×C1314yes—
196#400C22×C1314yes—
197#400C22×C1312yes—
198#400C22×C1314yes—
199#399C22×C1312yes—
200#398C22×C1314yes—
201#398C22×C1314yes—
202#398C22×C1314yes—
203#398C22×C1314yes—
204#398C22×C1314yes—
205#398C22×C1314yes—
206#398C22×C1314yes—
207#397C22×C1314yes—
208#397C22×C1314yes—
209#397C22×C1314yes—
210#396C22×C1314yes—
211#396C22×C1314yes—
212#395C22×C1314yes—
213#395C22×C1312yes—
214#393C22×C1312yes—
215#391C22×C1314yes—
216#389C22×C1314yes—
217#388C22×C1314yes—
218#387C22×C1314yes—
219#387C22×C1314yes—
220#387C22×C1314yes—
221C4×C4⋊C4C22×C1314yes—
222C4×C4⋊C4C22×C1312yes—
223C4×C4⋊C4C22×C1314yes—
224C4×C4⋊C4C22×C1314yes—
225C4×C4⋊C4C22×C1314yes—
226C4×C4⋊C4C22×C1312yes—
227C4×C22⋊C4C22×C1314yes—
228C4×C22⋊C4C22×C1312yes—
229#376C22×C1311yescharacteristic
230#376C22×C1314yes—
231C43C22×C1311yescharacteristic
232C22×C13—41no—
233C22×C13—42no—
234C22×C13—44no—
235C22×C13C22×#4111yescharacteristic
236C22×C13C2×2−1+412yes—
237C22×C13#58514yes—
238C4×C13—24no—
239C4×C13—41no—
240C4×C13—42no—
241C4×C13—44no—
242C4×C13—44no—
243C4×C13—44no—
244C4×C13—44no—
245C4×C13—44no—
246C4×C13—44no—
247C4×C13#54114yes—
248C22×Q8C23×C1312yes—
249C23×C4C23×C1311yescharacteristic
250C4×Q8—28no—
251#117—24no—
252C2×C4⋊C4C23×C1312yes—
253C2×C4⋊C4C23×C1314yes—
254C2×C4⋊C4C23×C1312yes—
255C2×C4⋊C4C23×C1314yes—
256C2×C4⋊C4C23×C1314yes—
257C2×C4⋊C4C23×C1314yes—
258C2×C4⋊C4C23×C1314yes—
259C2×C4⋊C4C23×C1314yes—
260C2×C4⋊C4C23×C1314yes—
261C2×C4⋊C4C23×C1314yes—
262C2×C4⋊C4C23×C1314yes—
263C2×C4⋊C4C23×C1314yes—
264C2×C4⋊C4C23×C1314yes—
265C2×C22⋊C4C23×C1312yes—
266C2×C22⋊C4C23×C1314yes—
267C2×C22⋊C4C23×C1314yes—
268C2×C22⋊C4C23×C1314yes—
269C2×C42C23×C1311yescharacteristic
270C2×C42C23×C1314yes—
271C2×C42C23×C1312yes—
272C2×C42C23×C1312yes—
273C2×C42C23×C1314yes—
274C2×C42C23×C1314yes—
275C2×C42C23×C1311yescharacteristic
276#95C23×C1314yes—
277#95C23×C1314yes—
278#95C23×C1314yes—
279#95C23×C1314yes—
280#95C23×C1314yes—
281#95C23×C1314yes—
282#95C23×C1314yes—
283#95C23×C1314yes—
284#95C23×C1312yes—
285#95C23×C1312yes—
286#95C23×C1314yes—
287#95C23×C1314yes—
288#95C23×C1314yes—
289#95C23×C1314yes—
290#95C23×C1314yes—
291#95C23×C1314yes—
292#95C23×C1314yes—
293#95C23×C1314yes—
294#95C23×C1314yes—
295C2×C13—81no—
296C2×C13C2×#54111yescharacteristic
297C2×C13#345512yes—
298C2×C13#353114yes—
299C24C24×C1311yescharacteristic
300C2×Q8—24no—
301C2×Q8—44no—
302C22×C4—22no—
303C22×C4—24no—
304C22×C4C24×C1311yescharacteristic
305C22×C4C24×C1314yes—
306C22×C4C24×C1314yes—
307C22×C4C24×C1314yes—
308C22×C4C24×C1314yes—
309C22×C4C24×C1314yes—
310C22×C4C24×C1312yes—
311C22×C4C24×C1314yes—
312C22×C4C24×C1312yes—
313C22×C4C24×C1311yescharacteristic
314C4⋊C4—24no—
315C4⋊C4—24no—
316C4⋊C4—28no—
317C4⋊C4—44no—
318C4⋊C4—44no—
319C4⋊C4—44no—
320C4⋊C4—44no—
321C4⋊C4—44no—
322C4⋊C4—44no—
323C4⋊C4—44no—
324C4⋊C4—44no—
325C4⋊C4—44no—
326C4⋊C4—44no—
327C22⋊C4—24no—
328C22⋊C4—44no—
329C22⋊C4—44no—
330C22⋊C4—44no—
331C42—22no—
332C42—28no—
333C42—24no—
334C42—24no—
335C42—28no—
336C42—44no—
337C42C13×#4114yes—
338C13#3670011yescharacteristic, direct product factor, Sylow
339C23—21no—
340C23—22no—
341C23—24no—
342C23C25×C1311yescharacteristic
343Q8—48no—
344C2×C4—24no—
345C2×C4—22no—
346C2×C4—24no—
347C2×C4—24no—
348C2×C4—21no—
349C2×C4—24no—
350C2×C4—24no—
351C2×C4—24no—
352C2×C4—24no—
353C2×C4—22no—
354C2×C4—24no—
355C2×C4—24no—
356C2×C4—24no—
357C2×C4—24no—
358C2×C4—24no—
359C2×C4—24no—
360C2×C4—24no—
361C2×C4—24no—
362C2×C4—24no—
363C2×C4—24no—
364C2×C4—24no—
365C2×C4—24no—
366C2×C4—24no—
367C2×C4—44no—
368C2×C4C2×C13×#4114yes—
369C2×C4C2×C13×#4112yes—
370C2×C4C13×2−1+414yes—
371C22—44no—
372C22—41no—
373C22—42no—
374C22C22×C13×#4111yescharacteristic
375C22C2×C13×2−1+412yes—
376C22C13×#58514yes—
377C4—24no—
378C4—44no—
379C4—44no—
380C4—44no—
381C4—44no—
382C4—41no—
383C4—42no—
384C4—44no—
385C4—44no—
386C4C13×#54114yes—
387C2—81no—
388C2C2×C13×#54111yescharacteristic
389C2C13×#345512yes—
390C2C13×#353114yes—
subgroupG/H
centerC22×C4×C13C24
commutator, Frattini, cosocleC23C25×C13
socleC23×C13C25
prime radicalC24×C13C24
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×#2839C2semidirect
3. C13×#2833C2semidirect
5. C13×#2402C2semidirect
6. C13×#2402C2semidirect
8. C13×#2399C2semidirect
11. C13×#2295C2semidirect
104. #36700C13direct (N × H)
144. #2839C2×C13semidirect
146. #2833C2×C13semidirect
148. #2402C2×C13semidirect
149. #2402C2×C13semidirect
151. #2399C2×C13semidirect
154. #2295C2×C13semidirect
338. C13#36700direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#28392
C13×#28362
C13×#28332
C13×#28312
C13×#24022
C13×#24012
C13×#23992
C13×#23962
C13×#22982
C13×#22952
#3670013