Finite Group Databasebeta

← C13×#61013 #15747352

Subgroups — C13×#61013 #15747352

Order 3328.

1656 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3509C212yesmaximal
2C13×#3261C214yesmaximal, complemented
3C13×#3231C214yesmaximal, complemented
4C13×#3209C214yesmaximal, complemented
5C13×#3202C214yesmaximal
6C13×#3185C212yesmaximal, complemented
7C13×#3170C212yesmaximal, complemented
8C13×#3127C218yesmaximal, complemented
9C13×#2922C211yesmaximal, characteristic
10C13×#557—24no—
11C13×#556—24no—
12C13×#552—24no—
13C13×#552—24no—
14C13×#541C2214yes—
15C13×#541C2214yes—
16C13×#536C2214yes—
17C13×#533C2214yes—
18C13×#533C2214yes—
19C13×#533C2212yes—
20C2×C13×C4⋊Q8C2212yes—
21C13×#519C2214yes—
22C4×C13×#41C2211yescharacteristic
23C13×#500C2212yes—
24C13×#498C2212yes—
25C13×#494C2212yes—
26C13×#494C2212yes—
27C13×#487C2214yes—
28C13×#487C2214yes—
29C13×#485C22116yes—
30C13×#479C22116yes—
31C13×#470C2218yes—
32C13×#467C2218yes—
33C13×#462C22116yes—
34C13×#451C22116yes—
35C13×#441C2218yes—
36C4×C13×Q16C2218yes—
37C13×#433C2214yes—
38C13×#431C2214yes—
39C13×#424C2212yes—
40C13×#408C2212yes—
41C4×C13×M16C2211yescharacteristic
42C2×C4×C8×C13C2211yescharacteristic
43C2×C13×#41C2311yescharacteristic
44C22×Q8×C13C2314yes—
45C2×C13×Q16C2318yes—
46C2×C13×Q16C2318yes—
47C2×C13×M16C2312yes—
48C22×C8×C13C2312yes—
49C13×C4⋊Q8—24no—
50C13×C4⋊Q8—24no—
51C13×C4⋊Q8C2314yes—
52C13×C4⋊Q8C2314yes—
53C13×C4⋊Q8C2314yes—
54C13×#126—28no—
55C13×#126—28no—
56C13×#125—28no—
57C13×#125—28no—
58C13×#125—24no—
59C13×#125—24no—
60C13×#125C2314yes—
61C13×#124—24no—
62C13×#123—24no—
63C13×#123—24no—
64C13×C22⋊Q8—24no—
65C13×C22⋊Q8—24no—
66C13×C22⋊Q8—24no—
67C13×C22⋊Q8C2318yes—
68C13×C22⋊Q8C2318yes—
69C4×Q8×C13—28no—
70C4×Q8×C13—24no—
71C4×Q8×C13—24no—
72C4×Q8×C13—24no—
73C4×Q8×C13D412yes—
74C4×Q8×C13C2318yes—
75C4×Q8×C13C2318yes—
76C4×D4×C13D412yes—
77C4×D4×C13D414yes—
78C13×#117—24no—
79C13×#117—24no—
80C13×#117—28no—
81C13×#117C2314yes—
82C13×#117C2311yescharacteristic
83C13×#117C2312yes—
84C2×C13×C4⋊C4—24no—
85C2×C42×C13C2311yescharacteristic
86C2×C42×C13C2312yes—
87C13×#107C2318yes—
88C13×#106C2318yes—
89C13×C4⋊C8C2318yes—
90C13×#103C23116yes—
91C13×#103C23116yes—
92C13×C22⋊C8C2318yes—
93C13×#97C2312yes—
94C4×C8×C13C2312yes—
95C4×C8×C13C2312yes—
96C4×C8×C13C2312yes—
97#61013C1311yesmaximal, characteristic, direct product factor, Sylow
98C13×#41—42no—
99C2×Q8×C13—24no—
100C2×Q8×C13—24no—
101C2×Q8×C13—48no—
102C2×Q8×C13C2×D411yescharacteristic
103C2×Q8×C13C2418yes—
104C2×D4×C13C2×D411yescharacteristic
105C2×D4×C13C2×D412yes—
106C22×C4×C13—24no—
107C22×C4×C13C2×D414yes—
108C22×C4×C13C2×D412yes—
109C22×C4×C13C2412yes—
110C22×C4×C13C2411yescharacteristic
111C13×Q16—48no—
112C13×Q16—48no—
113C13×M16—42no—
114C2×C8×C13—42no—
115C2×C8×C13C2414yes—
116C2×C8×C13C2414yes—
117C13×C4⋊C4—24no—
118C13×C4⋊C4—24no—
119C13×C4⋊C4—28no—
120C13×C4⋊C4—24no—
121C13×C4⋊C4—28no—
122C13×C4⋊C4—28no—
123C13×C4⋊C4—28no—
124C13×C4⋊C4—28no—
125C13×C4⋊C4—28no—
126C13×C4⋊C4C2×D414yes—
127C13×C4⋊C4C2×D412yes—
128C13×C4⋊C4C2418yes—
129C13×C22⋊C4—24no—
130C13×C22⋊C4—28no—
131C13×C22⋊C4—28no—
132C13×C22⋊C4C2×D414yes—
133C13×C22⋊C4C2×D412yes—
134C42×C13—28no—
135C42×C13—28no—
136C42×C13—24no—
137C42×C13C2×D412yes—
138C42×C13C2×D414yes—
139C42×C13C2411yescharacteristic
140C42×C13C2411yescharacteristic
141C42×C13C2412yes—
142#3509C2×C1312yes—
143#3261C2×C1314yescomplemented
144#3231C2×C1314yescomplemented
145#3209C2×C1314yescomplemented
146#3202C2×C1314yes—
147#3185C2×C1312yescomplemented
148#3170C2×C1312yescomplemented
149#3127C2×C1318yescomplemented
150#2922C2×C1311yescharacteristic
151C23×C13C22×D411yescharacteristic
152C23×C13C22×D412yes—
153Q8×C13—216no—
154Q8×C13—41no—
155Q8×C13—48no—
156Q8×C13—48no—
157D4×C13—41no—
158D4×C13—42no—
159C2×C4×C13—28no—
160C2×C4×C13—24no—
161C2×C4×C13—22no—
162C2×C4×C13—24no—
163C2×C4×C13—28no—
164C2×C4×C13—28no—
165C2×C4×C13—48no—
166C2×C4×C13C22×D412yes—
167C2×C4×C13C22×D412yes—
168C2×C4×C13C22×D414yes—
169C2×C4×C13C22×D411yescharacteristic
170C2×C4×C13C22×D412yes—
171C2×C4×C13C2511yescharacteristic
172C8×C13—24no—
173C8×C13—24no—
174#557—24no—
175#556—24no—
176#552—24no—
177#552—24no—
178#541C22×C1314yes—
179#541C22×C1314yes—
180#536C22×C1314yes—
181#533C22×C1314yes—
182#533C22×C1314yes—
183#533C22×C1312yes—
184C2×C4⋊Q8C22×C1312yes—
185#519C22×C1314yes—
186C4×#41C22×C1311yescharacteristic
187#500C22×C1312yes—
188#498C22×C1312yes—
189#494C22×C1312yes—
190#494C22×C1312yes—
191#487C22×C1314yes—
192#487C22×C1314yes—
193#485C22×C13116yes—
194#479C22×C13116yes—
195#470C22×C1318yes—
196#467C22×C1318yes—
197#462C22×C13116yes—
198#451C22×C13116yes—
199#441C22×C1318yes—
200C4×Q16C22×C1318yes—
201#433C22×C1314yes—
202#431C22×C1314yes—
203#424C22×C1312yes—
204#408C22×C1312yes—
205C4×M16C22×C1311yescharacteristic
206C2×C4×C8C22×C1311yescharacteristic
207C22×C13—22no—
208C22×C13—21no—
209C22×C13—22no—
210C22×C13—24no—
211C22×C13C23×D411yescharacteristic
212C4×C13—21no—
213C4×C13—22no—
214C4×C13—22no—
215C4×C13—24no—
216C4×C13—48no—
217C4×C13—48no—
218C4×C13#57814yes—
219C4×C13#58512yes—
220C2×#41C23×C1311yescharacteristic
221C22×Q8C23×C1314yes—
222C2×Q16C23×C1318yes—
223C2×Q16C23×C1318yes—
224C2×M16C23×C1312yes—
225C22×C8C23×C1312yes—
226C4⋊Q8—24no—
227C4⋊Q8—24no—
228C4⋊Q8C23×C1314yes—
229C4⋊Q8C23×C1314yes—
230C4⋊Q8C23×C1314yes—
231#126—28no—
232#126—28no—
233#125—28no—
234#125—28no—
235#125—24no—
236#125—24no—
237#125C23×C1314yes—
238#124—24no—
239#123—24no—
240#123—24no—
241C22⋊Q8—24no—
242C22⋊Q8—24no—
243C22⋊Q8—24no—
244C22⋊Q8C23×C1318yes—
245C22⋊Q8C23×C1318yes—
246C4×Q8—28no—
247C4×Q8—24no—
248C4×Q8—24no—
249C4×Q8—24no—
250C4×Q8D4×C1312yes—
251C4×Q8C23×C1318yes—
252C4×Q8C23×C1318yes—
253C4×D4D4×C1312yes—
254C4×D4D4×C1314yes—
255#117—24no—
256#117—24no—
257#117—28no—
258#117C23×C1314yes—
259#117C23×C1312yes—
260#117C23×C1311yescharacteristic
261C2×C4⋊C4—24no—
262C2×C42C23×C1312yes—
263C2×C42C23×C1311yescharacteristic
264#107C23×C1318yes—
265#106C23×C1318yes—
266C4⋊C8C23×C1318yes—
267#103C23×C13116yes—
268#103C23×C13116yes—
269C22⋊C8C23×C1318yes—
270#97C23×C1312yes—
271C4×C8C23×C1312yes—
272C4×C8C23×C1312yes—
273C4×C8C23×C1312yes—
274C2×C13—42no—
275C2×C13—41no—
276C2×C13#344911yescharacteristic
277C2×C13C2×#57812yes—
278#41—42no—
279C2×Q8—24no—
280C2×Q8—24no—
281C2×Q8—48no—
282C2×Q8C2×D4×C1311yescharacteristic
283C2×Q8C24×C1318yes—
284C2×D4C2×D4×C1311yescharacteristic
285C2×D4C2×D4×C1312yes—
286C22×C4—24no—
287C22×C4C2×D4×C1314yes—
288C22×C4C2×D4×C1312yes—
289C22×C4C24×C1312yes—
290C22×C4C24×C1311yescharacteristic
291Q16—48no—
292Q16—48no—
293M16—42no—
294C2×C8—42no—
295C2×C8C24×C1314yes—
296C2×C8C24×C1314yes—
297C4⋊C4—24no—
298C4⋊C4—24no—
299C4⋊C4—28no—
300C4⋊C4—24no—
301C4⋊C4—28no—
302C4⋊C4—28no—
303C4⋊C4—28no—
304C4⋊C4—28no—
305C4⋊C4—28no—
306C4⋊C4C2×D4×C1314yes—
307C4⋊C4C2×D4×C1312yes—
308C4⋊C4C24×C1318yes—
309C22⋊C4—24no—
310C22⋊C4—28no—
311C22⋊C4—28no—
312C22⋊C4C2×D4×C1314yes—
313C22⋊C4C2×D4×C1312yes—
314C42—28no—
315C42—28no—
316C42—24no—
317C42C2×D4×C1312yes—
318C42C2×D4×C1314yes—
319C42C24×C1311yescharacteristic
320C42C24×C1311yescharacteristic
321C42C24×C1312yes—
322C13#6101311yescharacteristic, direct product factor, Sylow
323C23C22×D4×C1311yescharacteristic
324C23C22×D4×C1312yes—
325Q8—216no—
326Q8—41no—
327Q8—48no—
328Q8—48no—
329D4—41no—
330D4—42no—
331C2×C4—28no—
332C2×C4—24no—
333C2×C4—22no—
334C2×C4—24no—
335C2×C4—28no—
336C2×C4—28no—
337C2×C4—48no—
338C2×C4C22×D4×C1312yes—
339C2×C4C22×D4×C1312yes—
340C2×C4C22×D4×C1314yes—
341C2×C4C22×D4×C1311yescharacteristic
342C2×C4C22×D4×C1312yes—
343C2×C4C25×C1311yescharacteristic
344C8—24no—
345C8—24no—
346C22—22no—
347C22—24no—
348C22—22no—
349C22—21no—
350C22C23×D4×C1311yescharacteristic
351C4—22no—
352C4—24no—
353C4—21no—
354C4—22no—
355C4—48no—
356C4—48no—
357C4C13×#57814yes—
358C4C13×#58512yes—
359C2—42no—
360C2—41no—
361C2C13×#344911yescharacteristic
362C2C2×C13×#57812yes—
subgroupG/H
center, socleC22×C13C23×D4
commutator, Frattini, cosocleC2×C4C25×C13
prime radicalC2×C13×#41C23
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C4×C13×#41 ◁ G

Complements

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

NH ≅ G/Ntype
2. C13×#3261C2semidirect
3. C13×#3231C2semidirect
4. C13×#3209C2semidirect
6. C13×#3185C2semidirect
7. C13×#3170C2semidirect
8. C13×#3127C2semidirect
97. #61013C13direct (N × H)
143. #3261C2×C13semidirect
144. #3231C2×C13semidirect
145. #3209C2×C13semidirect
147. #3185C2×C13semidirect
148. #3170C2×C13semidirect
149. #3127C2×C13semidirect
322. C13#61013direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#35092
C13×#32612
C13×#32312
C13×#32092
C13×#32022
C13×#31852
C13×#31702
C13×#31272
C13×#29222
#6101313