Finite Group Databasebeta

← C13×#13408 #15699747

Subgroups — C13×#13408 #15699747

Order 3328.

482 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#495C211yesmaximal, characteristic
2C2×C13×#358C211yesmaximal, characteristic, complemented
3C2×C13×#358C211yesmaximal, characteristic, complemented
4C2×C13×#357C211yesmaximal, characteristic
5C2×C13×#357C211yesmaximal, characteristic
6C13×#1942C211yesmaximal, characteristic, complemented
7C13×#1374C211yesmaximal, characteristic, complemented
8C22×C13×Q16C2211yescharacteristic
9C22×C13×SD16—21no—
10C22×C13×D8C2211yescharacteristic
11C2×C13×#124—21no—
12C22×C13×C16C2211yescharacteristic
13C22×C13×C16C2211yescharacteristic
14C13×#495—22no—
15C13×#495—22no—
16C2×C13×#107C2211yescharacteristic
17C2×C13×#107C2211yescharacteristic
18C2×C4×C8×C13C2211yescharacteristic
19C13×#389—21no—
20C13×#358—22no—
21C13×#358—22no—
22C13×#357—22no—
23C13×#357—22no—
24C13×#340—21no—
25C22×Q8×C13—21no—
26C22×D4×C13—21no—
27C2×C13×Q16—21no—
28C2×C13×Q16—21no—
29C2×C13×Q16—21no—
30C2×C13×Q16—21no—
31C2×C13×Q16—21no—
32C2×C13×Q16D412yes—
33C2×C13×SD16—24no—
34C2×C13×SD16—42no—
35C2×C13×SD16—42no—
36C2×C13×D8—21no—
37C2×C13×D8—21no—
38C2×C13×D8—21no—
39C2×C13×D8—21no—
40C2×C13×D8—21no—
41C2×C13×D8D412yes—
42C22×C8×C13D411yescharacteristic
43C22×C8×C13C2311yescharacteristic
44C13×#124—24no—
45C13×#124—42no—
46C2×C13×C4⋊C4—21no—
47C2×C13×C4⋊C4—21no—
48C2×C13×C4⋊C4—41no—
49C2×C13×C22⋊C4—41no—
50C2×C13×C22⋊C4—41no—
51C2×C42×C13D411yescharacteristic
52C2×C13×C16—21no—
53C2×C13×C16—21no—
54C2×C13×C16—21no—
55C2×C13×C16—21no—
56C2×C13×C16—21no—
57C2×C13×C16—21no—
58C13×#107—21no—
59C13×#107—21no—
60C13×#107—21no—
61C13×#107D412yes—
62C4×C8×C13—21no—
63C4×C8×C13—21no—
64C13×#95—41no—
65#13408C1311yesmaximal, characteristic, direct product factor, Sylow
66C24×C13—41no—
67C2×Q8×C13—22no—
68C2×Q8×C13—41no—
69C2×Q8×C13—41no—
70C2×Q8×C13—41no—
71C2×Q8×C13—41no—
72C2×Q8×C13—41no—
73C2×D4×C13—22no—
74C2×D4×C13—41no—
75C2×D4×C13—41no—
76C2×D4×C13—41no—
77C2×D4×C13—41no—
78C2×D4×C13—41no—
79C22×C4×C13—41no—
80C22×C4×C13—41no—
81C22×C4×C13—41no—
82C22×C4×C13D811yescharacteristic
83C22×C4×C13D811yescharacteristic
84C22×C4×C13C2×D411yescharacteristic
85C13×Q16—22no—
86C13×Q16—22no—
87C13×Q16—41no—
88C13×Q16—41no—
89C13×SD16—48no—
90C13×D8—22no—
91C13×D8—22no—
92C13×D8—41no—
93C13×D8—41no—
94C2×C8×C13—21no—
95C2×C8×C13—21no—
96C2×C8×C13SD1612yes—
97C2×C8×C13C2×D411yescharacteristic
98C2×C8×C13C2×D411yescharacteristic
99C2×C8×C13C2×D411yescharacteristic
100C2×C8×C13#4111yescharacteristic
101C2×C8×C13#4111yescharacteristic
102C2×C8×C13#4111yescharacteristic
103C13×C4⋊C4—22no—
104C13×C4⋊C4—41no—
105C13×C4⋊C4—41no—
106C13×C4⋊C4—41no—
107C13×C4⋊C4—82no—
108C13×C22⋊C4—44no—
109C13×C22⋊C4—44no—
110C42×C13—21no—
111C42×C13—21no—
112C13×C16—41no—
113C13×C16—41no—
114C2×#495C2×C1311yescharacteristic
115C2×#358C2×C1311yescharacteristic, complemented
116C2×#358C2×C1311yescharacteristic, complemented
117C2×#357C2×C1311yescharacteristic
118C2×#357C2×C1311yescharacteristic
119#1942C2×C1311yescharacteristic, complemented
120#1374C2×C1311yescharacteristic, complemented
121C23×C13—42no—
122C23×C13—81no—
123C23×C13—81no—
124C23×C13—81no—
125C23×C13—81no—
126C23×C13—81no—
127C23×C13—81no—
128C23×C13C2×D811yescharacteristic
129Q8×C13—42no—
130Q8×C13—42no—
131Q8×C13—81no—
132Q8×C13—81no—
133D4×C13—42no—
134D4×C13—42no—
135D4×C13—81no—
136D4×C13—81no—
137C2×C4×C13—21no—
138C2×C4×C13—21no—
139C2×C4×C13—21no—
140C2×C4×C13—21no—
141C2×C4×C13—21no—
142C2×C4×C13—21no—
143C2×C4×C13—42no—
144C2×C4×C13—42no—
145C2×C4×C13—81no—
146C2×C4×C13—81no—
147C2×C4×C13—81no—
148C2×C4×C13—81no—
149C2×C4×C13—81no—
150C2×C4×C13—81no—
151C2×C4×C13—81no—
152C2×C4×C13#12011yescharacteristic
153C2×C4×C13#12111yescharacteristic
154C2×C4×C13#12411yescharacteristic
155C2×C4×C13C2×SD1611yescharacteristic
156C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
157C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
158C8×C13—22no—
159C8×C13#12111yescharacteristic
160C8×C13#12111yescharacteristic
161C8×C13#12311yescharacteristic
162C8×C13#12311yescharacteristic
163C22×Q16C22×C1311yescharacteristic
164C22×SD16—21no—
165C22×D8C22×C1311yescharacteristic
166C2×#124—21no—
167C22×C16C22×C1311yescharacteristic
168C22×C16C22×C1311yescharacteristic
169#495—22no—
170#495—22no—
171C2×#107C22×C1311yescharacteristic
172C2×#107C22×C1311yescharacteristic
173C2×C4×C8C22×C1311yescharacteristic
174#389—21no—
175#358—22no—
176#358—22no—
177#357—22no—
178#357—22no—
179#340—21no—
180C22×C13—82no—
181C22×C13—82no—
182C22×C13—82no—
183C22×C13—161no—
184C22×C13—161no—
185C22×C13—161no—
186C22×C13—161no—
187C22×C13#44711yescharacteristic
188C22×C13#45911yescharacteristic
189C22×C13#48611yescharacteristic
190C22×C13#50811yescharacteristic
191C22×C13#50811yescharacteristic
192C22×C13#50911yescharacteristic
193C22×C13#51011yescharacteristic
194C4×C13—41no—
195C4×C13—41no—
196C4×C13—82no—
197C4×C13—82no—
198C4×C13—161no—
199C4×C13#39411yescharacteristic
200C4×C13#45011yescharacteristic
201C4×C13#46011yescharacteristic
202C4×C13#49011yescharacteristic
203C22×Q8—21no—
204C22×D4—21no—
205C2×Q16—21no—
206C2×Q16—21no—
207C2×Q16—21no—
208C2×Q16—21no—
209C2×Q16—21no—
210C2×Q16D4×C1312yes—
211C2×SD16—24no—
212C2×SD16—42no—
213C2×SD16—42no—
214C2×D8—21no—
215C2×D8—21no—
216C2×D8—21no—
217C2×D8—21no—
218C2×D8—21no—
219C2×D8D4×C1312yes—
220C22×C8D4×C1311yescharacteristic
221C22×C8C23×C1311yescharacteristic
222#124—24no—
223#124—42no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—41no—
227C2×C22⋊C4—41no—
228C2×C22⋊C4—41no—
229C2×C42D4×C1311yescharacteristic
230C2×C16—21no—
231C2×C16—21no—
232C2×C16—21no—
233C2×C16—21no—
234C2×C16—21no—
235C2×C16—21no—
236#107—21no—
237#107—21no—
238#107—21no—
239#107D4×C1312yes—
240C4×C8—21no—
241C4×C8—21no—
242#95—41no—
243C2×C13—162no—
244C2×C13#204111yescharacteristic
245C2×C13#218611yescharacteristic
246C2×C13#218911yescharacteristic
247C2×C13#221011yescharacteristic
248C2×C13#221111yescharacteristic
249C2×C13#224211yescharacteristic
250C2×C13#224311yescharacteristic
251C24—41no—
252C2×Q8—22no—
253C2×Q8—41no—
254C2×Q8—41no—
255C2×Q8—41no—
256C2×Q8—41no—
257C2×Q8—41no—
258C2×D4—22no—
259C2×D4—41no—
260C2×D4—41no—
261C2×D4—41no—
262C2×D4—41no—
263C2×D4—41no—
264C22×C4—41no—
265C22×C4—41no—
266C22×C4—41no—
267C22×C4C13×D811yescharacteristic
268C22×C4C13×D811yescharacteristic
269C22×C4C2×D4×C1311yescharacteristic
270Q16—22no—
271Q16—22no—
272Q16—41no—
273Q16—41no—
274SD16—48no—
275D8—22no—
276D8—22no—
277D8—41no—
278D8—41no—
279C2×C8—21no—
280C2×C8—21no—
281C2×C8C13×SD1612yes—
282C2×C8C2×D4×C1311yescharacteristic
283C2×C8C2×D4×C1311yescharacteristic
284C2×C8C2×D4×C1311yescharacteristic
285C2×C8C13×#4111yescharacteristic
286C2×C8C13×#4111yescharacteristic
287C2×C8C13×#4111yescharacteristic
288C4⋊C4—22no—
289C4⋊C4—41no—
290C4⋊C4—41no—
291C4⋊C4—41no—
292C4⋊C4—82no—
293C22⋊C4—44no—
294C22⋊C4—44no—
295C42—21no—
296C42—21no—
297C16—41no—
298C16—41no—
299C13#1340811yescharacteristic, direct product factor, Sylow
300C23—42no—
301C23—81no—
302C23—81no—
303C23—81no—
304C23—81no—
305C23—81no—
306C23—81no—
307C23C2×C13×D811yescharacteristic
308Q8—42no—
309Q8—42no—
310Q8—81no—
311Q8—81no—
312D4—42no—
313D4—42no—
314D4—81no—
315D4—81no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4—81no—
325C2×C4—81no—
326C2×C4—81no—
327C2×C4—81no—
328C2×C4—81no—
329C2×C4—81no—
330C2×C4—81no—
331C2×C4C13×#12011yescharacteristic
332C2×C4C13×#12111yescharacteristic
333C2×C4C13×#12411yescharacteristic
334C2×C4C2×C13×SD1611yescharacteristic
335C2×C4C13×AGL(1,ℤ/8)11yescharacteristic
336C2×C4C13×AGL(1,ℤ/8)11yescharacteristic
337C8—22no—
338C8C13×#12111yescharacteristic
339C8C13×#12111yescharacteristic
340C8C13×#12311yescharacteristic
341C8C13×#12311yescharacteristic
342C22—82no—
343C22—82no—
344C22—82no—
345C22—161no—
346C22—161no—
347C22—161no—
348C22—161no—
349C22C13×#44711yescharacteristic
350C22C13×#45911yescharacteristic
351C22C13×#48611yescharacteristic
352C22C13×#50811yescharacteristic
353C22C13×#50811yescharacteristic
354C22C13×#50911yescharacteristic
355C22C13×#51011yescharacteristic
356C4—41no—
357C4—41no—
358C4—82no—
359C4—82no—
360C4—161no—
361C4C13×#39411yescharacteristic
362C4C13×#45011yescharacteristic
363C4C13×#46011yescharacteristic
364C4C13×#49011yescharacteristic
365C2—162no—
366C2C13×#204111yescharacteristic
367C2C13×#218611yescharacteristic
368C2C13×#218911yescharacteristic
369C2C13×#221011yescharacteristic
370C2C13×#221111yescharacteristic
371C2C13×#224211yescharacteristic
372C2C13×#224311yescharacteristic
subgroupG/H
center, socleC23×C13C2×D8
commutator, Frattini, cosocleC22×C8C23×C13
prime radicalC22×C13×D8C22
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C13 ◁ C2×C42×C13 ◁ C2×C4×C8×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C13×#358C2semidirect
3. C2×C13×#358C2semidirect
6. C13×#1942C2semidirect
7. C13×#1374C2semidirect
65. #13408C13direct (N × H)
115. C2×#358C2×C13semidirect
116. C2×#358C2×C13semidirect
119. #1942C2×C13semidirect
120. #1374C2×C13semidirect
299. C13#13408direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#4952
C2×C13×#3582
C2×C13×#3572
C13×#19422
C13×#13742
#1340813