Finite Group Databasebeta

← C13×#9531 #15695870

Subgroups — C13×#9531 #15695870

Order 3328.

412 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3117C211yesmaximal, characteristic
2C13×#2967C211yesmaximal, characteristic
3C13×#1535C211yesmaximal, characteristic
4C13×#1491C211yesmaximal, characteristic, complemented
5C13×#1467C211yesmaximal, characteristic, complemented
6C13×#1308C211yesmaximal, characteristic, complemented
7C13×#1291C211yesmaximal, characteristic, complemented
8C13×#529C2211yescharacteristic
9C2×C4×Q8×C13C2211yescharacteristic
10C13×#484C411yescharacteristic
11C13×#481C411yescharacteristic
12C13×#479—21no—
13C13×#464—21no—
14C13×#451C411yescharacteristic
15C13×#448C411yescharacteristic
16C13×#446—21no—
17C13×#441—21no—
18C13×#440—21no—
19C13×#436—21no—
20C13×#435—21no—
21C13×#435—21no—
22C13×#433—21no—
23C13×#432C2211yescharacteristic
24C13×#432C2211yescharacteristic
25C13×#432C2211yescharacteristic
26C13×#432C2211yescharacteristic
27C13×#405—21no—
28C4×C13×M16C2211yescharacteristic
29C13×#330—21no—
30C13×#329—21no—
31C13×Q8⋊C8—21no—
32C13×Q8⋊C8—21no—
33C13×#324—21no—
34C13×#324—21no—
35C22×Q8×C13C2×C411yescharacteristic
36C2×C13×Q16—21no—
37C2×C13×SD16—21no—
38C2×C13×M16—21no—
39C2×C13×M16—21no—
40C22×C8×C13—21no—
41C13×#126—21no—
42C13×#125D411yescharacteristic
43C13×#124D411yescharacteristic
44C13×#123—21no—
45C13×C22⋊Q8C2×C411yescharacteristic
46C13×#121C2×C411yescharacteristic
47C4×Q8×C13—21no—
48C4×Q8×C13—21no—
49C4×Q8×C13—21no—
50C4×Q8×C13—21no—
51C4×Q8×C13D411yescharacteristic
52C4×D4×C13—21no—
53C4×D4×C13D411yescharacteristic
54C13×#117—21no—
55C2×C13×C4⋊C4—21no—
56C2×C13×C4⋊C4C2×C411yescharacteristic
57C2×C42×C13—21no—
58C2×C42×C13C2311yescharacteristic
59C13×#107—21no—
60C13×#106—21no—
61C13×C4⋊C8—21no—
62C13×C4⋊C8—21no—
63C13×C4⋊C8—21no—
64C13×C4⋊C8—21no—
65C13×C4⋊C8—21no—
66C13×C4⋊C8—21no—
67C13×#103—21no—
68C13×#103—21no—
69C13×#103—21no—
70C13×#102—21no—
71C13×C22⋊C8—21no—
72C13×C22⋊C8—21no—
73C13×C22⋊C8—21no—
74C13×C22⋊C8—21no—
75C13×C22⋊C8C2×C411yescharacteristic
76C13×C22⋊C8C2×C411yescharacteristic
77C13×C22⋊C8D411yescharacteristic
78C13×C22⋊C8D411yescharacteristic
79C13×#97—21no—
80C13×#97—21no—
81C13×#97—21no—
82C13×#97—21no—
83C13×#97—21no—
84C13×#97—21no—
85C4×C8×C13—21no—
86C4×C8×C13D411yescharacteristic
87C4×C8×C13D411yescharacteristic
88#9531C1311yesmaximal, characteristic, direct product factor, Sylow
89C2×Q8×C13—21no—
90C2×Q8×C13—21no—
91C2×Q8×C13—42no—
92C2×Q8×C13C22⋊C411yescharacteristic
93C2×D4×C13—21no—
94C2×D4×C13C22⋊C411yescharacteristic
95C22×C4×C13—21no—
96C22×C4×C13—21no—
97C22×C4×C13—21no—
98C22×C4×C13C22×C411yescharacteristic
99C22×C4×C13C2×D411yescharacteristic
100C22×C4×C13#4111yescharacteristic
101C13×Q16—42no—
102C13×SD16—42no—
103C13×M16—42no—
104C13×M16—42no—
105C2×C8×C13—21no—
106C2×C8×C13—21no—
107C2×C8×C13—21no—
108C2×C8×C13—21no—
109C2×C8×C13—21no—
110C2×C8×C13—21no—
111C2×C8×C13—42no—
112C2×C8×C13—41no—
113C2×C8×C13—41no—
114C13×C4⋊C4—21no—
115C13×C4⋊C4—21no—
116C13×C4⋊C4—21no—
117C13×C4⋊C4—21no—
118C13×C4⋊C4—21no—
119C13×C4⋊C4—21no—
120C13×C4⋊C4—41no—
121C13×C4⋊C4—41no—
122C13×C4⋊C4C22⋊C411yescharacteristic
123C13×C4⋊C4C22⋊C411yescharacteristic
124C13×C22⋊C4—21no—
125C13×C22⋊C4—21no—
126C13×C22⋊C4—21no—
127C13×C22⋊C4—21no—
128C13×C22⋊C4—21no—
129C42×C13—21no—
130C42×C13—41no—
131C42×C13—41no—
132C42×C13C2×D411yescharacteristic
133C42×C13C2×D411yescharacteristic
134C42×C13C2×D411yescharacteristic
135C42×C13#4111yescharacteristic
136#3117C2×C1311yescharacteristic
137#2967C2×C1311yescharacteristic
138#1535C2×C1311yescharacteristic
139#1491C2×C1311yescharacteristic, complemented
140#1467C2×C1311yescharacteristic, complemented
141#1308C2×C1311yescharacteristic, complemented
142#1291C2×C1311yescharacteristic, complemented
143C23×C13—21no—
144C23×C13C4×D411yescharacteristic
145Q8×C13—22no—
146Q8×C13—22no—
147Q8×C13—41no—
148Q8×C13—41no—
149Q8×C13—41no—
150D4×C13—41no—
151D4×C13—81no—
152C2×C4×C13—22no—
153C2×C4×C13—21no—
154C2×C4×C13—21no—
155C2×C4×C13—21no—
156C2×C4×C13—41no—
157C2×C4×C13—41no—
158C2×C4×C13—41no—
159C2×C4×C13—41no—
160C2×C4×C13—41no—
161C2×C4×C13—41no—
162C2×C4×C13—41no—
163C2×C4×C13—41no—
164C2×C4×C13—81no—
165C2×C4×C13C2×C22⋊C411yescharacteristic
166C2×C4×C13C4×D411yescharacteristic
167C2×C4×C13#12011yescharacteristic
168C2×C4×C13#12111yescharacteristic
169C2×C4×C13#12111yescharacteristic
170C2×C4×C13#12311yescharacteristic
171C8×C13—22no—
172C8×C13—41no—
173C8×C13—41no—
174C8×C13—41no—
175C8×C13—41no—
176C8×C13—41no—
177C8×C13—81no—
178C8×C13—81no—
179#529C22×C1311yescharacteristic
180C2×C4×Q8C22×C1311yescharacteristic
181#484C4×C1311yescharacteristic
182#481C4×C1311yescharacteristic
183#479—21no—
184#464—21no—
185#451C4×C1311yescharacteristic
186#448C4×C1311yescharacteristic
187#446—21no—
188#441—21no—
189#440—21no—
190#436—21no—
191#435—21no—
192#435—21no—
193#433—21no—
194#432C22×C1311yescharacteristic
195#432C22×C1311yescharacteristic
196#432C22×C1311yescharacteristic
197#432C22×C1311yescharacteristic
198#405—21no—
199C4×M16C22×C1311yescharacteristic
200#330—21no—
201#329—21no—
202Q8⋊C8—21no—
203Q8⋊C8—21no—
204#324—21no—
205#324—21no—
206C22×C13—21no—
207C22×C13—21no—
208C22×C13—21no—
209C22×C13—41no—
210C22×C13—41no—
211C22×C13—41no—
212C22×C13#38611yescharacteristic
213C4×C13—21no—
214C4×C13—21no—
215C4×C13—21no—
216C4×C13—21no—
217C4×C13—21no—
218C4×C13—21no—
219C4×C13—42no—
220C4×C13—41no—
221C4×C13—41no—
222C4×C13—41no—
223C4×C13—81no—
224C22×Q8C2×C4×C1311yescharacteristic
225C2×Q16—21no—
226C2×SD16—21no—
227C2×M16—21no—
228C2×M16—21no—
229C22×C8—21no—
230#126—21no—
231#125D4×C1311yescharacteristic
232#124D4×C1311yescharacteristic
233#123—21no—
234C22⋊Q8C2×C4×C1311yescharacteristic
235#121C2×C4×C1311yescharacteristic
236C4×Q8—21no—
237C4×Q8—21no—
238C4×Q8—21no—
239C4×Q8—21no—
240C4×Q8D4×C1311yescharacteristic
241C4×D4—21no—
242C4×D4D4×C1311yescharacteristic
243#117—21no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4C2×C4×C1311yescharacteristic
246C2×C42—21no—
247C2×C42C23×C1311yescharacteristic
248#107—21no—
249#106—21no—
250C4⋊C8—21no—
251C4⋊C8—21no—
252C4⋊C8—21no—
253C4⋊C8—21no—
254C4⋊C8—21no—
255C4⋊C8—21no—
256#103—21no—
257#103—21no—
258#103—21no—
259#102—21no—
260C22⋊C8—21no—
261C22⋊C8—21no—
262C22⋊C8—21no—
263C22⋊C8—21no—
264C22⋊C8C2×C4×C1311yescharacteristic
265C22⋊C8C2×C4×C1311yescharacteristic
266C22⋊C8D4×C1311yescharacteristic
267C22⋊C8D4×C1311yescharacteristic
268#97—21no—
269#97—21no—
270#97—21no—
271#97—21no—
272#97—21no—
273#97—21no—
274C4×C8—21no—
275C4×C8D4×C1311yescharacteristic
276C4×C8D4×C1311yescharacteristic
277C2×C13—41no—
278C2×C13—81no—
279C2×C13#189111yescharacteristic
280C2×C13#190211yescharacteristic
281C2×C13#190611yescharacteristic
282C2×Q8—21no—
283C2×Q8—21no—
284C2×Q8—42no—
285C2×Q8C13×C22⋊C411yescharacteristic
286C2×D4—21no—
287C2×D4C13×C22⋊C411yescharacteristic
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—21no—
291C22×C4C22×C4×C1311yescharacteristic
292C22×C4C2×D4×C1311yescharacteristic
293C22×C4C13×#4111yescharacteristic
294Q16—42no—
295SD16—42no—
296M16—42no—
297M16—42no—
298C2×C8—21no—
299C2×C8—21no—
300C2×C8—21no—
301C2×C8—21no—
302C2×C8—21no—
303C2×C8—21no—
304C2×C8—42no—
305C2×C8—41no—
306C2×C8—41no—
307C4⋊C4—21no—
308C4⋊C4—21no—
309C4⋊C4—21no—
310C4⋊C4—21no—
311C4⋊C4—21no—
312C4⋊C4—21no—
313C4⋊C4—41no—
314C4⋊C4—41no—
315C4⋊C4C13×C22⋊C411yescharacteristic
316C4⋊C4C13×C22⋊C411yescharacteristic
317C22⋊C4—21no—
318C22⋊C4—21no—
319C22⋊C4—21no—
320C22⋊C4—21no—
321C22⋊C4—21no—
322C42—21no—
323C42—41no—
324C42—41no—
325C42C2×D4×C1311yescharacteristic
326C42C2×D4×C1311yescharacteristic
327C42C2×D4×C1311yescharacteristic
328C42C13×#4111yescharacteristic
329C13#953111yescharacteristic, direct product factor, Sylow
330C23—21no—
331C23C4×D4×C1311yescharacteristic
332Q8—22no—
333Q8—22no—
334Q8—41no—
335Q8—41no—
336Q8—41no—
337D4—41no—
338D4—81no—
339C2×C4—22no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—81no—
352C2×C4C2×C13×C22⋊C411yescharacteristic
353C2×C4C4×D4×C1311yescharacteristic
354C2×C4C13×#12011yescharacteristic
355C2×C4C13×#12111yescharacteristic
356C2×C4C13×#12111yescharacteristic
357C2×C4C13×#12311yescharacteristic
358C8—22no—
359C8—41no—
360C8—41no—
361C8—41no—
362C8—41no—
363C8—41no—
364C8—81no—
365C8—81no—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—41no—
370C22—41no—
371C22—41no—
372C22C13×#38611yescharacteristic
373C4—21no—
374C4—21no—
375C4—21no—
376C4—21no—
377C4—21no—
378C4—21no—
379C4—42no—
380C4—41no—
381C4—41no—
382C4—41no—
383C4—81no—
384C2—41no—
385C2—81no—
386C2C13×#189111yescharacteristic
387C2C13×#190211yescharacteristic
388C2C13×#190611yescharacteristic
subgroupG/H
center, socleC22×C13#386
commutatorC22×C4C22×C4×C13
Frattini, cosocleC2×C42C23×C13
prime radicalC13×#121C2×C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G

Complements

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

NH ≅ G/Ntype
4. C13×#1491C2semidirect
5. C13×#1467C2semidirect
6. C13×#1308C2semidirect
7. C13×#1291C2semidirect
88. #9531C13direct (N × H)
139. #1491C2×C13semidirect
140. #1467C2×C13semidirect
141. #1308C2×C13semidirect
142. #1291C2×C13semidirect
329. C13#9531direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#31172
C13×#29672
C13×#15352
C13×#14912
C13×#14672
C13×#13082
C13×#12912
#953113