Finite Group Databasebeta

← C13×#34978 #15721317

Subgroups — C13×#34978 #15721317

Order 3328.

1834 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#2612C214yesmaximal, complemented
2C13×#2571C211yesmaximal, characteristic, complemented
3C13×#2552C212yesmaximal, complemented
4C13×#2551C211yesmaximal, characteristic, complemented
5C13×#2441C214yesmaximal
6C13×#2439C214yesmaximal
7C13×#2396C214yesmaximal
8C4×C13×C4⋊Q8C214yesmaximal, complemented
9C4×C13×#125C214yesmaximal, complemented
10C13×#2285C211yesmaximal, characteristic
11C4×C13×#117C212yesmaximal
12C2×C13×C4⋊Q8C2214yes—
13C2×C13×#125C2214yes—
14C2×C4×Q8×C13C2214yes—
15C2×C13×#117C2212yes—
16C2×C13×#117C2212yes—
17C2×C13×#117C2212yes—
18C22×C42×C13C2211yescharacteristic
19C13×#400C2214yes—
20C13×#399C2214yes—
21C13×#398C2218yes—
22C13×#396C2218yes—
23C13×#395C2214yes—
24C13×#393C2214yes—
25C13×#391C2218yes—
26C13×#389C2214yes—
27C13×#389C2214yes—
28C13×#389C2214yes—
29C13×#389C2214yes—
30C13×#389C2218yes—
31C13×#387C2218yes—
32C13×#387C2218yes—
33C13×#384C2211yescharacteristic
34C13×#384C2211yescharacteristic
35C13×#384C2214yes—
36C13×#382C2212yes—
37C13×#382C2214yes—
38C13×#380C2214yes—
39C4×C13×C4⋊C4C2212yes—
40C4×C13×C4⋊C4C2212yes—
41C4×C13×C4⋊C4C2212yes—
42C4×C13×C4⋊C4C2212yes—
43C4×C13×C4⋊C4C2214yes—
44C4×C13×C4⋊C4C2214yes—
45C4×C13×C4⋊C4C2218yes—
46C4×C13×C22⋊C4C2214yes—
47C4×C13×C22⋊C4C2214yes—
48C13×#376C2214yes—
49C43×C13C2214yes—
50C22×Q8×C13C2314yes—
51C23×C4×C13C2312yes—
52C23×C4×C13C2311yescharacteristic
53C13×C4⋊Q8—216no—
54C13×#125—216no—
55C4×Q8×C13—48no—
56C13×#117—28no—
57C13×#117—28no—
58C13×#117—44no—
59C2×C13×C4⋊C4C2312yes—
60C2×C13×C4⋊C4C2312yes—
61C2×C13×C4⋊C4C2314yes—
62C2×C13×C4⋊C4C2314yes—
63C2×C13×C4⋊C4C2318yes—
64C2×C13×C4⋊C4C2318yes—
65C2×C13×C4⋊C4C2318yes—
66C2×C13×C4⋊C4C2312yes—
67C2×C13×C4⋊C4C2312yes—
68C2×C13×C4⋊C4C2318yes—
69C2×C13×C4⋊C4C2314yes—
70C2×C13×C4⋊C4C2312yes—
71C2×C13×C4⋊C4C2312yes—
72C2×C13×C22⋊C4C2314yes—
73C2×C13×C22⋊C4C2314yes—
74C2×C13×C22⋊C4C2314yes—
75C2×C42×C13Q818yescomplemented
76C2×C42×C13C2314yes—
77C2×C42×C13C2314yes—
78C2×C42×C13C2314yes—
79C2×C42×C13C2314yes—
80C2×C42×C13C2314yes—
81C2×C42×C13C2314yes—
82C2×C42×C13C2314yes—
83C2×C42×C13C2311yescharacteristic
84C2×C42×C13C2311yescharacteristic
85C2×C42×C13C2312yes—
86C13×#95C2314yes—
87C13×#95C2314yes—
88C13×#95C2314yes—
89C13×#95C2314yes—
90C13×#95C2318yes—
91C13×#95C2314yes—
92C13×#95C2318yes—
93C13×#95C2314yes—
94C13×#95C2318yes—
95#34978C1311yesmaximal, characteristic, direct product factor, Sylow
96C24×C13C2411yescharacteristic
97C2×Q8×C13—216no—
98C2×Q8×C13—44no—
99C22×C4×C13—24no—
100C22×C4×C13—24no—
101C22×C4×C13—22no—
102C22×C4×C13—22no—
103C22×C4×C13C2×Q818yes—
104C22×C4×C13C2×Q814yes—
105C22×C4×C13C2414yes—
106C22×C4×C13C2414yes—
107C22×C4×C13C2414yes—
108C22×C4×C13C2414yes—
109C22×C4×C13C2412yes—
110C22×C4×C13C2411yescharacteristic
111C22×C4×C13C2414yes—
112C22×C4×C13C2414yes—
113C22×C4×C13C2412yes—
114C22×C4×C13C2411yescharacteristic
115C13×C4⋊C4—24no—
116C13×C4⋊C4—24no—
117C13×C4⋊C4—216no—
118C13×C4⋊C4—216no—
119C13×C4⋊C4—28no—
120C13×C4⋊C4—216no—
121C13×C4⋊C4—28no—
122C13×C4⋊C4—42no—
123C13×C4⋊C4—42no—
124C13×C4⋊C4—48no—
125C13×C4⋊C4—44no—
126C13×C4⋊C4#4118yes—
127C13×C4⋊C4#4118yes—
128C13×C22⋊C4—28no—
129C13×C22⋊C4—28no—
130C13×C22⋊C4—44no—
131C42×C13—28no—
132C42×C13—28no—
133C42×C13—28no—
134C42×C13—28no—
135C42×C13—28no—
136C42×C13—28no—
137C42×C13—28no—
138C42×C13C2×Q814yes—
139C42×C13C2×Q814yes—
140C42×C13C2×Q818yes—
141#2612C2×C1314yescomplemented
142#2571C2×C1311yescharacteristic, complemented
143#2552C2×C1312yescomplemented
144#2551C2×C1311yescharacteristic, complemented
145#2441C2×C1314yes—
146#2439C2×C1314yes—
147#2396C2×C1314yes—
148C4×C4⋊Q8C2×C1314yescomplemented
149C4×#125C2×C1314yescomplemented
150#2285C2×C1311yescharacteristic
151C4×#117C2×C1312yes—
152C23×C13—22no—
153C23×C13—22no—
154C23×C13—21no—
155C23×C13—21no—
156C23×C13C22×Q812yes—
157C23×C13C2511yescharacteristic
158Q8×C13—416no—
159C2×C4×C13—22no—
160C2×C4×C13—22no—
161C2×C4×C13—24no—
162C2×C4×C13—24no—
163C2×C4×C13—24no—
164C2×C4×C13—21no—
165C2×C4×C13—24no—
166C2×C4×C13—21no—
167C2×C4×C13—216no—
168C2×C4×C13—28no—
169C2×C4×C13—24no—
170C2×C4×C13—24no—
171C2×C4×C13—24no—
172C2×C4×C13—24no—
173C2×C4×C13—28no—
174C2×C4×C13—28no—
175C2×C4×C13—24no—
176C2×C4×C13—24no—
177C2×C4×C13—24no—
178C2×C4×C13—24no—
179C2×C4×C13C22×Q814yes—
180C2×C4×C13C22×Q812yes—
181C2×C4×C13C22×Q814yes—
182C2×C4×C13C22×Q812yes—
183C2×C4×C13C2×#4118yes—
184C2×C4×C13C2×#4118yes—
185C2×C4×C13C2×#4114yes—
186C2×C4×C13C2×#4114yes—
187C2×C4×C13H(5,𝔽2)12yes—
188C2×C4×C132−1+412yes—
189C2×C4⋊Q8C22×C1314yes—
190C2×#125C22×C1314yes—
191C2×C4×Q8C22×C1314yes—
192C2×#117C22×C1312yes—
193C2×#117C22×C1312yes—
194C2×#117C22×C1312yes—
195C22×C42C22×C1311yescharacteristic
196#400C22×C1314yes—
197#399C22×C1314yes—
198#398C22×C1318yes—
199#396C22×C1318yes—
200#395C22×C1314yes—
201#393C22×C1314yes—
202#391C22×C1318yes—
203#389C22×C1314yes—
204#389C22×C1314yes—
205#389C22×C1314yes—
206#389C22×C1318yes—
207#389C22×C1314yes—
208#387C22×C1318yes—
209#387C22×C1318yes—
210#384C22×C1314yes—
211#384C22×C1311yescharacteristic
212#384C22×C1311yescharacteristic
213#382C22×C1314yes—
214#382C22×C1312yes—
215#380C22×C1314yes—
216C4×C4⋊C4C22×C1314yes—
217C4×C4⋊C4C22×C1312yes—
218C4×C4⋊C4C22×C1318yes—
219C4×C4⋊C4C22×C1314yes—
220C4×C4⋊C4C22×C1312yes—
221C4×C4⋊C4C22×C1312yes—
222C4×C4⋊C4C22×C1312yes—
223C4×C22⋊C4C22×C1314yes—
224C4×C22⋊C4C22×C1314yes—
225#376C22×C1314yes—
226C43C22×C1314yes—
227C22×C13—24no—
228C22×C13—22no—
229C22×C13—41no—
230C22×C13—42no—
231C22×C13—41no—
232C22×C13C23×Q811yescharacteristic
233C22×C13C22×#4112yes—
234C22×C13C22×#4112yes—
235C22×C13C2×H(5,𝔽2)11yescharacteristic
236C22×C13C2×2−1+411yescharacteristic
237C4×C13—24no—
238C4×C13—22no—
239C4×C13—28no—
240C4×C13—28no—
241C4×C13—44no—
242C4×C13—44no—
243C4×C13—44no—
244C4×C13—44no—
245C4×C13#53318yes—
246C4×C13#54414yes—
247C22×Q8C23×C1314yes—
248C23×C4C23×C1311yescharacteristic
249C23×C4C23×C1312yes—
250C4⋊Q8—216no—
251#125—216no—
252C4×Q8—48no—
253#117—28no—
254#117—28no—
255#117—44no—
256C2×C4⋊C4C23×C1312yes—
257C2×C4⋊C4C23×C1312yes—
258C2×C4⋊C4C23×C1314yes—
259C2×C4⋊C4C23×C1318yes—
260C2×C4⋊C4C23×C1318yes—
261C2×C4⋊C4C23×C1314yes—
262C2×C4⋊C4C23×C1318yes—
263C2×C4⋊C4C23×C1312yes—
264C2×C4⋊C4C23×C1312yes—
265C2×C4⋊C4C23×C1318yes—
266C2×C4⋊C4C23×C1314yes—
267C2×C4⋊C4C23×C1312yes—
268C2×C4⋊C4C23×C1312yes—
269C2×C22⋊C4C23×C1314yes—
270C2×C22⋊C4C23×C1314yes—
271C2×C22⋊C4C23×C1314yes—
272C2×C42Q8×C1318yescomplemented
273C2×C42C23×C1314yes—
274C2×C42C23×C1314yes—
275C2×C42C23×C1314yes—
276C2×C42C23×C1314yes—
277C2×C42C23×C1314yes—
278C2×C42C23×C1314yes—
279C2×C42C23×C1314yes—
280C2×C42C23×C1312yes—
281C2×C42C23×C1311yescharacteristic
282C2×C42C23×C1311yescharacteristic
283#95C23×C1314yes—
284#95C23×C1314yes—
285#95C23×C1314yes—
286#95C23×C1314yes—
287#95C23×C1318yes—
288#95C23×C1314yes—
289#95C23×C1318yes—
290#95C23×C1314yes—
291#95C23×C1318yes—
292C2×C13—42no—
293C2×C13C2×#53312yes—
294C2×C13C2×#54411yescharacteristic
295C2×C13#348111yescharacteristic
296C2×C13#348212yes—
297C2×C13#348311yescharacteristic
298C24C24×C1311yescharacteristic
299C2×Q8—216no—
300C2×Q8—44no—
301C22×C4—24no—
302C22×C4—24no—
303C22×C4—22no—
304C22×C4—22no—
305C22×C4C2×Q8×C1318yes—
306C22×C4C2×Q8×C1314yes—
307C22×C4C24×C1314yes—
308C22×C4C24×C1314yes—
309C22×C4C24×C1314yes—
310C22×C4C24×C1314yes—
311C22×C4C24×C1312yes—
312C22×C4C24×C1311yescharacteristic
313C22×C4C24×C1314yes—
314C22×C4C24×C1314yes—
315C22×C4C24×C1312yes—
316C22×C4C24×C1311yescharacteristic
317C4⋊C4—24no—
318C4⋊C4—24no—
319C4⋊C4—216no—
320C4⋊C4—216no—
321C4⋊C4—28no—
322C4⋊C4—216no—
323C4⋊C4—28no—
324C4⋊C4—42no—
325C4⋊C4—42no—
326C4⋊C4—48no—
327C4⋊C4—44no—
328C4⋊C4C13×#4118yes—
329C4⋊C4C13×#4118yes—
330C22⋊C4—28no—
331C22⋊C4—28no—
332C22⋊C4—44no—
333C42—28no—
334C42—28no—
335C42—28no—
336C42—28no—
337C42—28no—
338C42—28no—
339C42—28no—
340C42C2×Q8×C1314yes—
341C42C2×Q8×C1314yes—
342C42C2×Q8×C1318yes—
343C13#3497811yescharacteristic, direct product factor, Sylow
344C23—22no—
345C23—22no—
346C23—21no—
347C23—21no—
348C23C22×Q8×C1312yes—
349C23C25×C1311yescharacteristic
350Q8—416no—
351C2×C4—22no—
352C2×C4—22no—
353C2×C4—24no—
354C2×C4—24no—
355C2×C4—24no—
356C2×C4—21no—
357C2×C4—24no—
358C2×C4—21no—
359C2×C4—216no—
360C2×C4—28no—
361C2×C4—24no—
362C2×C4—24no—
363C2×C4—24no—
364C2×C4—24no—
365C2×C4—28no—
366C2×C4—28no—
367C2×C4—24no—
368C2×C4—24no—
369C2×C4—24no—
370C2×C4—24no—
371C2×C4C22×Q8×C1314yes—
372C2×C4C22×Q8×C1312yes—
373C2×C4C22×Q8×C1314yes—
374C2×C4C22×Q8×C1312yes—
375C2×C4C2×C13×#4118yes—
376C2×C4C2×C13×#4118yes—
377C2×C4C2×C13×#4114yes—
378C2×C4C2×C13×#4114yes—
379C2×C4C13×H(5,𝔽2)12yes—
380C2×C4C13×2−1+412yes—
381C22—24no—
382C22—22no—
383C22—41no—
384C22—42no—
385C22—41no—
386C22C23×Q8×C1311yescharacteristic
387C22C22×C13×#4112yes—
388C22C22×C13×#4112yes—
389C22C2×C13×H(5,𝔽2)11yescharacteristic
390C22C2×C13×2−1+411yescharacteristic
391C4—24no—
392C4—22no—
393C4—28no—
394C4—28no—
395C4—44no—
396C4—44no—
397C4—44no—
398C4—44no—
399C4C13×#53318yes—
400C4C13×#54414yes—
401C2—42no—
402C2C2×C13×#53312yes—
403C2C2×C13×#54411yescharacteristic
404C2C13×#348111yescharacteristic
405C2C13×#348212yes—
406C2C13×#348311yescharacteristic
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×#2612C2semidirect
2. C13×#2571C2semidirect
3. C13×#2552C2semidirect
4. C13×#2551C2semidirect
8. C4×C13×C4⋊Q8C2semidirect
9. C4×C13×#125C2semidirect
75. C2×C42×C13Q8semidirect
95. #34978C13direct (N × H)
141. #2612C2×C13semidirect
142. #2571C2×C13semidirect
143. #2552C2×C13semidirect
144. #2551C2×C13semidirect
148. C4×C4⋊Q8C2×C13semidirect
149. C4×#125C2×C13semidirect
272. C2×C42Q8×C13semidirect
343. C13#34978direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#26122
C13×#25712
C13×#25522
C13×#25512
C13×#24412
C13×#24392
C13×#23962
C4×C13×C4⋊Q82
C4×C13×#1252
C13×#22852
C4×C13×#1172
#3497813