Finite Group Databasebeta

← C13×#7710 #15694049

Subgroups — C13×#7710 #15694049

Order 3328.

570 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#2850C211yesmaximal, characteristic
2C13×#1797C211yesmaximal, characteristic, complemented
3C13×#1728C211yesmaximal, characteristic, complemented
4C13×#1272C212yesmaximal, complemented
5C13×#1270C212yesmaximal, complemented
6C22×C13×M16—21no—
7C2×C13×#124C411yescharacteristic
8C2×C13×C22⋊Q8C411yescharacteristic
9C2×C13×#121C411yescharacteristic
10C22×C42×C13C2211yescharacteristic
11C2×C13×C4⋊C8—21no—
12C2×C13×C22⋊C8—21no—
13C13×#391C2211yescharacteristic
14C13×#390C2211yescharacteristic
15C13×#388—21no—
16C13×#388—21no—
17C13×#386—21no—
18C13×#386—21no—
19C13×#382C411yescharacteristic
20C13×#336—21no—
21C13×#336C2212yes—
22C13×#336C2212yes—
23C22×Q8×C13C2×C411yescharacteristic
24C22×D4×C13—21no—
25C22×D4×C13C2×C411yescharacteristic
26C23×C4×C13C2×C411yescharacteristic
27C23×C4×C13D411yescharacteristic
28C23×C4×C13D411yescharacteristic
29C2×C13×M16—24no—
30C2×C13×M16—42no—
31C2×C13×M16—42no—
32C22×C8×C13—22no—
33C22×C8×C13—22no—
34C13×#124—42no—
35C13×C22⋊Q8—42no—
36C13×#121—42no—
37C2×C13×C4⋊C4—21no—
38C2×C13×C4⋊C4C2×C411yescharacteristic
39C2×C13×C4⋊C4C2×C411yescharacteristic
40C2×C13×C22⋊C4—21no—
41C2×C13×C22⋊C4—21no—
42C2×C13×C22⋊C4—21no—
43C2×C13×C22⋊C4—21no—
44C2×C13×C22⋊C4—21no—
45C2×C13×C22⋊C4—21no—
46C2×C42×C13—42no—
47C2×C42×C13C2×C411yescharacteristic
48C2×C42×C13D411yescharacteristic
49C2×C42×C13D411yescharacteristic
50C2×C42×C13C2311yescharacteristic
51C13×C4⋊C8—42no—
52C13×C22⋊C8—42no—
53C13×#95—21no—
54C13×#95—21no—
55C13×#95—21no—
56C13×#95—21no—
57#7710C1311yesmaximal, characteristic, direct product factor, Sylow
58C24×C13—21no—
59C24×C13C22⋊C411yescharacteristic
60C2×Q8×C13—22no—
61C2×Q8×C13—41no—
62C2×Q8×C13—41no—
63C2×D4×C13—22no—
64C2×D4×C13—41no—
65C2×D4×C13—41no—
66C2×D4×C13—42no—
67C2×D4×C13—42no—
68C2×D4×C13—42no—
69C22×C4×C13—22no—
70C22×C4×C13—22no—
71C22×C4×C13—21no—
72C22×C4×C13—21no—
73C22×C4×C13—22no—
74C22×C4×C13—22no—
75C22×C4×C13—21no—
76C22×C4×C13—21no—
77C22×C4×C13—21no—
78C22×C4×C13—21no—
79C22×C4×C13—21no—
80C22×C4×C13—41no—
81C22×C4×C13—41no—
82C22×C4×C13—41no—
83C22×C4×C13C22⋊C411yescharacteristic
84C22×C4×C13C22⋊C411yescharacteristic
85C22×C4×C13C22⋊C411yescharacteristic
86C22×C4×C13C22×C411yescharacteristic
87C22×C4×C13C2×D411yescharacteristic
88C22×C4×C13C2×D411yescharacteristic
89C13×M16—48no—
90C2×C8×C13—24no—
91C2×C8×C13—42no—
92C2×C8×C13—42no—
93C2×C8×C13—42no—
94C2×C8×C13—42no—
95C2×C8×C13—42no—
96C13×C4⋊C4—41no—
97C13×C4⋊C4—41no—
98C13×C4⋊C4—42no—
99C13×C22⋊C4—42no—
100C13×C22⋊C4—42no—
101C13×C22⋊C4—42no—
102C13×C22⋊C4—42no—
103C13×C22⋊C4—41no—
104C13×C22⋊C4—41no—
105C13×C22⋊C4—41no—
106C13×C22⋊C4—41no—
107C42×C13—22no—
108C42×C13—22no—
109C42×C13—41no—
110C42×C13—41no—
111#2850C2×C1311yescharacteristic
112#1797C2×C1311yescharacteristic, complemented
113#1728C2×C1311yescharacteristic, complemented
114#1272C2×C1312yescomplemented
115#1270C2×C1312yescomplemented
116C23×C13—21no—
117C23×C13—21no—
118C23×C13—21no—
119C23×C13—21no—
120C23×C13—21no—
121C23×C13—21no—
122C23×C13—41no—
123C23×C13—41no—
124C23×C13—41no—
125C23×C13—41no—
126C23×C13—41no—
127C23×C13—41no—
128C23×C13—41no—
129C23×C13#10412yes—
130C23×C13C2×C22⋊C411yescharacteristic
131Q8×C13—82no—
132D4×C13—82no—
133D4×C13—84no—
134C2×C4×C13—24no—
135C2×C4×C13—24no—
136C2×C4×C13—21no—
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—21no—
144C2×C4×C13—21no—
145C2×C4×C13—21no—
146C2×C4×C13—21no—
147C2×C4×C13—21no—
148C2×C4×C13—21no—
149C2×C4×C13—44no—
150C2×C4×C13—42no—
151C2×C4×C13—42no—
152C2×C4×C13—41no—
153C2×C4×C13—41no—
154C2×C4×C13—41no—
155C2×C4×C13—41no—
156C2×C4×C13—41no—
157C2×C4×C13—41no—
158C2×C4×C13—41no—
159C2×C4×C13—41no—
160C2×C4×C13—41no—
161C2×C4×C13#9912yes—
162C2×C4×C13#10012yes—
163C2×C4×C13#13112yes—
164C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
165C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
166C2×C4×C13#13711yescharacteristic
167C2×C4×C13#13711yescharacteristic
168C8×C13—44no—
169C8×C13—82no—
170C22×M16—21no—
171C2×#124C4×C1311yescharacteristic
172C2×C22⋊Q8C4×C1311yescharacteristic
173C2×#121C4×C1311yescharacteristic
174C22×C42C22×C1311yescharacteristic
175C2×C4⋊C8—21no—
176C2×C22⋊C8—21no—
177#391C22×C1311yescharacteristic
178#390C22×C1311yescharacteristic
179#388—21no—
180#388—21no—
181#386—21no—
182#386—21no—
183#382C4×C1311yescharacteristic
184#336—21no—
185#336C22×C1312yes—
186#336C22×C1312yes—
187C22×C13—22no—
188C22×C13—22no—
189C22×C13—22no—
190C22×C13—41no—
191C22×C13—41no—
192C22×C13—41no—
193C22×C13—41no—
194C22×C13—81no—
195C22×C13—81no—
196C22×C13—81no—
197C22×C13—81no—
198C22×C13—81no—
199C22×C13—81no—
200C22×C13—81no—
201C22×C13#40811yescharacteristic
202C22×C13C2×#9911yescharacteristic
203C22×C13C2×#10011yescharacteristic
204C22×C13#41711yescharacteristic
205C22×C13#41711yescharacteristic
206C22×C13C2×#10411yescharacteristic
207C22×C13#42111yescharacteristic
208C4×C13—22no—
209C4×C13—22no—
210C4×C13—21no—
211C4×C13—22no—
212C4×C13—21no—
213C4×C13—21no—
214C4×C13—21no—
215C4×C13—41no—
216C4×C13—81no—
217C4×C13—81no—
218C4×C13—81no—
219C22×Q8C2×C4×C1311yescharacteristic
220C22×D4—21no—
221C22×D4C2×C4×C1311yescharacteristic
222C23×C4C2×C4×C1311yescharacteristic
223C23×C4D4×C1311yescharacteristic
224C23×C4D4×C1311yescharacteristic
225C2×M16—24no—
226C2×M16—42no—
227C2×M16—42no—
228C22×C8—22no—
229C22×C8—22no—
230#124—42no—
231C22⋊Q8—42no—
232#121—42no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4C2×C4×C1311yescharacteristic
235C2×C4⋊C4C2×C4×C1311yescharacteristic
236C2×C22⋊C4—21no—
237C2×C22⋊C4—21no—
238C2×C22⋊C4—21no—
239C2×C22⋊C4—21no—
240C2×C22⋊C4—21no—
241C2×C22⋊C4—21no—
242C2×C42—42no—
243C2×C42C2×C4×C1311yescharacteristic
244C2×C42D4×C1311yescharacteristic
245C2×C42D4×C1311yescharacteristic
246C2×C42C23×C1311yescharacteristic
247C4⋊C8—42no—
248C22⋊C8—42no—
249#95—21no—
250#95—21no—
251#95—21no—
252#95—21no—
253C2×C13—42no—
254C2×C13—161no—
255C2×C13#147111yescharacteristic
256C2×C13#148311yescharacteristic
257C2×C13#149511yescharacteristic
258C2×C13#150411yescharacteristic
259C2×C13#151311yescharacteristic
260C2×C13#152711yescharacteristic
261C2×C13#156011yescharacteristic
262C24—21no—
263C24C13×C22⋊C411yescharacteristic
264C2×Q8—22no—
265C2×Q8—41no—
266C2×Q8—41no—
267C2×D4—22no—
268C2×D4—41no—
269C2×D4—41no—
270C2×D4—42no—
271C2×D4—42no—
272C2×D4—42no—
273C22×C4—22no—
274C22×C4—22no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—22no—
278C22×C4—22no—
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—21no—
283C22×C4—21no—
284C22×C4—41no—
285C22×C4—41no—
286C22×C4—41no—
287C22×C4C13×C22⋊C411yescharacteristic
288C22×C4C13×C22⋊C411yescharacteristic
289C22×C4C13×C22⋊C411yescharacteristic
290C22×C4C22×C4×C1311yescharacteristic
291C22×C4C2×D4×C1311yescharacteristic
292C22×C4C2×D4×C1311yescharacteristic
293M16—48no—
294C2×C8—24no—
295C2×C8—42no—
296C2×C8—42no—
297C2×C8—42no—
298C2×C8—42no—
299C2×C8—42no—
300C4⋊C4—41no—
301C4⋊C4—41no—
302C4⋊C4—42no—
303C22⋊C4—42no—
304C22⋊C4—42no—
305C22⋊C4—42no—
306C22⋊C4—42no—
307C22⋊C4—41no—
308C22⋊C4—41no—
309C22⋊C4—41no—
310C22⋊C4—41no—
311C42—22no—
312C42—22no—
313C42—41no—
314C42—41no—
315C13#771011yescharacteristic, direct product factor, Sylow
316C23—21no—
317C23—21no—
318C23—21no—
319C23—21no—
320C23—21no—
321C23—21no—
322C23—41no—
323C23—41no—
324C23—41no—
325C23—41no—
326C23—41no—
327C23—41no—
328C23—41no—
329C23C13×#10412yes—
330C23C2×C13×C22⋊C411yescharacteristic
331Q8—82no—
332D4—82no—
333D4—84no—
334C2×C4—24no—
335C2×C4—24no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—44no—
350C2×C4—42no—
351C2×C4—42no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4C13×#9912yes—
362C2×C4C13×#10012yes—
363C2×C4C13×#13112yes—
364C2×C4C13×AGL(1,ℤ/8)11yescharacteristic
365C2×C4C13×AGL(1,ℤ/8)11yescharacteristic
366C2×C4C13×#13711yescharacteristic
367C2×C4C13×#13711yescharacteristic
368C8—44no—
369C8—82no—
370C22—22no—
371C22—22no—
372C22—22no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—81no—
378C22—81no—
379C22—81no—
380C22—81no—
381C22—81no—
382C22—81no—
383C22—81no—
384C22C13×#40811yescharacteristic
385C22C2×C13×#9911yescharacteristic
386C22C2×C13×#10011yescharacteristic
387C22C13×#41711yescharacteristic
388C22C13×#41711yescharacteristic
389C22C2×C13×#10411yescharacteristic
390C22C13×#42111yescharacteristic
391C4—22no—
392C4—22no—
393C4—21no—
394C4—22no—
395C4—21no—
396C4—21no—
397C4—21no—
398C4—41no—
399C4—81no—
400C4—81no—
401C4—81no—
402C2—42no—
403C2—161no—
404C2C13×#147111yescharacteristic
405C2C13×#148311yescharacteristic
406C2C13×#149511yescharacteristic
407C2C13×#150411yescharacteristic
408C2C13×#151311yescharacteristic
409C2C13×#152711yescharacteristic
410C2C13×#156011yescharacteristic
subgroupG/H
center, socleC23×C13C2×C22⋊C4
commutatorC22×C4C22×C4×C13
Frattini, cosocleC2×C42C23×C13
prime radicalC2×C13×#121C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C13 ◁ C22×C42×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C13×#1797C2semidirect
3. C13×#1728C2semidirect
4. C13×#1272C2semidirect
5. C13×#1270C2semidirect
57. #7710C13direct (N × H)
112. #1797C2×C13semidirect
113. #1728C2×C13semidirect
114. #1272C2×C13semidirect
115. #1270C2×C13semidirect
315. C13#7710direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#28502
C13×#17972
C13×#17282
C13×#12722
C13×#12702
#771013