Finite Group Databasebeta

← C13×#7714 #15694053

Subgroups — C13×#7714 #15694053

Order 3328.

526 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#2854C211yesmaximal, characteristic
2C13×#1797C211yesmaximal, characteristic, complemented
3C13×#1797C211yesmaximal, characteristic, complemented
4C13×#1271C212yesmaximal, complemented
5C13×#1270C212yesmaximal, complemented
6C2×C13×#123—21no—
7C2×C13×#121C411yescharacteristic
8C22×C42×C13C2211yescharacteristic
9C2×C13×C4⋊C8—21no—
10C2×C13×C4⋊C8—21no—
11C2×C13×C22⋊C8—21no—
12C2×C13×C22⋊C8—21no—
13C13×#390C411yescharacteristic
14C13×#390C2211yescharacteristic
15C13×#389C411yescharacteristic
16C13×#389C2211yescharacteristic
17C13×#388—21no—
18C13×#388—21no—
19C13×#386—21no—
20C13×#380C411yescharacteristic
21C13×#336C2212yes—
22C13×#336C2212yes—
23C22×D4×C13—21no—
24C22×D4×C13C2×C411yescharacteristic
25C23×C4×C13C2×C411yescharacteristic
26C23×C4×C13D411yescharacteristic
27C23×C4×C13D411yescharacteristic
28C22×C8×C13—22no—
29C22×C8×C13—22no—
30C13×#123—42no—
31C13×#123—42no—
32C13×#121—42no—
33C2×C13×C4⋊C4—21no—
34C2×C13×C4⋊C4—21no—
35C2×C13×C4⋊C4C2×C411yescharacteristic
36C2×C13×C4⋊C4C2×C411yescharacteristic
37C2×C13×C4⋊C4C2×C411yescharacteristic
38C2×C13×C22⋊C4—21no—
39C2×C13×C22⋊C4—21no—
40C2×C13×C22⋊C4—21no—
41C2×C13×C22⋊C4—21no—
42C2×C13×C22⋊C4—21no—
43C2×C13×C22⋊C4—21no—
44C2×C42×C13—42no—
45C2×C42×C13C2×C411yescharacteristic
46C2×C42×C13D411yescharacteristic
47C2×C42×C13D411yescharacteristic
48C2×C42×C13C2311yescharacteristic
49C13×C4⋊C8—42no—
50C13×C4⋊C8—42no—
51C13×C22⋊C8—42no—
52C13×C22⋊C8—42no—
53C13×#95—21no—
54C13×#95—21no—
55C13×#95—21no—
56#7714C1311yesmaximal, characteristic, direct product factor, Sylow
57C24×C13—21no—
58C24×C13C22⋊C411yescharacteristic
59C2×D4×C13—22no—
60C2×D4×C13—41no—
61C2×D4×C13—41no—
62C2×D4×C13—42no—
63C2×D4×C13—42no—
64C2×D4×C13—42no—
65C22×C4×C13—22no—
66C22×C4×C13—22no—
67C22×C4×C13—21no—
68C22×C4×C13—21no—
69C22×C4×C13—21no—
70C22×C4×C13—21no—
71C22×C4×C13—21no—
72C22×C4×C13—41no—
73C22×C4×C13—41no—
74C22×C4×C13—41no—
75C22×C4×C13—41no—
76C22×C4×C13—41no—
77C22×C4×C13C22⋊C411yescharacteristic
78C22×C4×C13C22⋊C411yescharacteristic
79C22×C4×C13C22⋊C411yescharacteristic
80C22×C4×C13D812yes—
81C22×C4×C13SD1612yes—
82C22×C4×C13C22×C411yescharacteristic
83C22×C4×C13C2×D411yescharacteristic
84C22×C4×C13C2×D411yescharacteristic
85C2×C8×C13—42no—
86C2×C8×C13—42no—
87C2×C8×C13—42no—
88C2×C8×C13—42no—
89C2×C8×C13—42no—
90C2×C8×C13—42no—
91C13×C4⋊C4—22no—
92C13×C4⋊C4—41no—
93C13×C4⋊C4—41no—
94C13×C4⋊C4—42no—
95C13×C4⋊C4—41no—
96C13×C4⋊C4—41no—
97C13×C22⋊C4—42no—
98C13×C22⋊C4—42no—
99C13×C22⋊C4—42no—
100C13×C22⋊C4—42no—
101C13×C22⋊C4—41no—
102C13×C22⋊C4—41no—
103C13×C22⋊C4—41no—
104C13×C22⋊C4—41no—
105C42×C13—22no—
106C42×C13—22no—
107C42×C13—41no—
108C42×C13—41no—
109#2854C2×C1311yescharacteristic
110#1797C2×C1311yescharacteristic, complemented
111#1797C2×C1311yescharacteristic, complemented
112#1271C2×C1312yescomplemented
113#1270C2×C1312yescomplemented
114C23×C13—21no—
115C23×C13—21no—
116C23×C13—21no—
117C23×C13—21no—
118C23×C13—21no—
119C23×C13—21no—
120C23×C13—41no—
121C23×C13—41no—
122C23×C13—41no—
123C23×C13—41no—
124C23×C13—41no—
125C23×C13—41no—
126C23×C13—41no—
127C23×C13#10212yes—
128C23×C13C2×C22⋊C411yescharacteristic
129D4×C13—82no—
130D4×C13—84no—
131C2×C4×C13—21no—
132C2×C4×C13—21no—
133C2×C4×C13—21no—
134C2×C4×C13—21no—
135C2×C4×C13—21no—
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—42no—
145C2×C4×C13—42no—
146C2×C4×C13—44no—
147C2×C4×C13—42no—
148C2×C4×C13—42no—
149C2×C4×C13—41no—
150C2×C4×C13—41no—
151C2×C4×C13—41no—
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#9912yes—
159C2×C4×C13#10212yes—
160C2×C4×C13#13112yes—
161C2×C4×C13C2×D811yescharacteristic
162C2×C4×C13C2×SD1611yescharacteristic
163C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
164C2×C4×C13#13711yescharacteristic
165C8×C13—82no—
166C8×C13—82no—
167C2×#123—21no—
168C2×#121C4×C1311yescharacteristic
169C22×C42C22×C1311yescharacteristic
170C2×C4⋊C8—21no—
171C2×C4⋊C8—21no—
172C2×C22⋊C8—21no—
173C2×C22⋊C8—21no—
174#390C4×C1311yescharacteristic
175#390C22×C1311yescharacteristic
176#389C4×C1311yescharacteristic
177#389C22×C1311yescharacteristic
178#388—21no—
179#388—21no—
180#386—21no—
181#380C4×C1311yescharacteristic
182#336C22×C1312yes—
183#336C22×C1312yes—
184C22×C13—22no—
185C22×C13—22no—
186C22×C13—22no—
187C22×C13—41no—
188C22×C13—41no—
189C22×C13—41no—
190C22×C13—41no—
191C22×C13—81no—
192C22×C13—81no—
193C22×C13—81no—
194C22×C13—81no—
195C22×C13—81no—
196C22×C13—81no—
197C22×C13—81no—
198C22×C13#40811yescharacteristic
199C22×C13C2×#9911yescharacteristic
200C22×C13#41311yescharacteristic
201C22×C13C2×#10211yescharacteristic
202C22×C13#41711yescharacteristic
203C22×C13#42111yescharacteristic
204C22×C13#42111yescharacteristic
205C4×C13—22no—
206C4×C13—22no—
207C4×C13—21no—
208C4×C13—21no—
209C4×C13—21no—
210C4×C13—22no—
211C4×C13—21no—
212C4×C13—41no—
213C4×C13—81no—
214C4×C13—81no—
215C4×C13—81no—
216C22×D4—21no—
217C22×D4C2×C4×C1311yescharacteristic
218C23×C4C2×C4×C1311yescharacteristic
219C23×C4D4×C1311yescharacteristic
220C23×C4D4×C1311yescharacteristic
221C22×C8—22no—
222C22×C8—22no—
223#123—42no—
224#123—42no—
225#121—42no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4C2×C4×C1311yescharacteristic
229C2×C4⋊C4C2×C4×C1311yescharacteristic
230C2×C4⋊C4C2×C4×C1311yescharacteristic
231C2×C22⋊C4—21no—
232C2×C22⋊C4—21no—
233C2×C22⋊C4—21no—
234C2×C22⋊C4—21no—
235C2×C22⋊C4—21no—
236C2×C22⋊C4—21no—
237C2×C42—42no—
238C2×C42C2×C4×C1311yescharacteristic
239C2×C42D4×C1311yescharacteristic
240C2×C42D4×C1311yescharacteristic
241C2×C42C23×C1311yescharacteristic
242C4⋊C8—42no—
243C4⋊C8—42no—
244C22⋊C8—42no—
245C22⋊C8—42no—
246#95—21no—
247#95—21no—
248#95—21no—
249C2×C13—42no—
250C2×C13—161no—
251C2×C13#146811yescharacteristic
252C2×C13#148011yescharacteristic
253C2×C13#149511yescharacteristic
254C2×C13#151311yescharacteristic
255C2×C13#151911yescharacteristic
256C2×C13#153511yescharacteristic
257C2×C13#154711yescharacteristic
258C24—21no—
259C24C13×C22⋊C411yescharacteristic
260C2×D4—22no—
261C2×D4—41no—
262C2×D4—41no—
263C2×D4—42no—
264C2×D4—42no—
265C2×D4—42no—
266C22×C4—22no—
267C22×C4—22no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—41no—
274C22×C4—41no—
275C22×C4—41no—
276C22×C4—41no—
277C22×C4—41no—
278C22×C4C13×C22⋊C411yescharacteristic
279C22×C4C13×C22⋊C411yescharacteristic
280C22×C4C13×C22⋊C411yescharacteristic
281C22×C4C13×D812yes—
282C22×C4C13×SD1612yes—
283C22×C4C22×C4×C1311yescharacteristic
284C22×C4C2×D4×C1311yescharacteristic
285C22×C4C2×D4×C1311yescharacteristic
286C2×C8—42no—
287C2×C8—42no—
288C2×C8—42no—
289C2×C8—42no—
290C2×C8—42no—
291C2×C8—42no—
292C4⋊C4—22no—
293C4⋊C4—41no—
294C4⋊C4—41no—
295C4⋊C4—42no—
296C4⋊C4—41no—
297C4⋊C4—41no—
298C22⋊C4—42no—
299C22⋊C4—42no—
300C22⋊C4—42no—
301C22⋊C4—42no—
302C22⋊C4—41no—
303C22⋊C4—41no—
304C22⋊C4—41no—
305C22⋊C4—41no—
306C42—22no—
307C42—22no—
308C42—41no—
309C42—41no—
310C13#771411yescharacteristic, direct product factor, Sylow
311C23—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—21no—
316C23—21no—
317C23—41no—
318C23—41no—
319C23—41no—
320C23—41no—
321C23—41no—
322C23—41no—
323C23—41no—
324C23C13×#10212yes—
325C23C2×C13×C22⋊C411yescharacteristic
326D4—82no—
327D4—84no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—42no—
342C2×C4—42no—
343C2×C4—44no—
344C2×C4—42no—
345C2×C4—42no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4C13×#9912yes—
356C2×C4C13×#10212yes—
357C2×C4C13×#13112yes—
358C2×C4C2×C13×D811yescharacteristic
359C2×C4C2×C13×SD1611yescharacteristic
360C2×C4C13×AGL(1,ℤ/8)11yescharacteristic
361C2×C4C13×#13711yescharacteristic
362C8—82no—
363C8—82no—
364C22—22no—
365C22—22no—
366C22—22no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—81no—
372C22—81no—
373C22—81no—
374C22—81no—
375C22—81no—
376C22—81no—
377C22—81no—
378C22C13×#40811yescharacteristic
379C22C2×C13×#9911yescharacteristic
380C22C13×#41311yescharacteristic
381C22C2×C13×#10211yescharacteristic
382C22C13×#41711yescharacteristic
383C22C13×#42111yescharacteristic
384C22C13×#42111yescharacteristic
385C4—21no—
386C4—21no—
387C4—21no—
388C4—22no—
389C4—21no—
390C4—22no—
391C4—22no—
392C4—41no—
393C4—81no—
394C4—81no—
395C4—81no—
396C2—42no—
397C2—161no—
398C2C13×#146811yescharacteristic
399C2C13×#148011yescharacteristic
400C2C13×#149511yescharacteristic
401C2C13×#151311yescharacteristic
402C2C13×#151911yescharacteristic
403C2C13×#153511yescharacteristic
404C2C13×#154711yescharacteristic
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×#1797C2semidirect
4. C13×#1271C2semidirect
5. C13×#1270C2semidirect
56. #7714C13direct (N × H)
110. #1797C2×C13semidirect
111. #1797C2×C13semidirect
112. #1271C2×C13semidirect
113. #1270C2×C13semidirect
310. C13#7714direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#28542
C13×#17972
C13×#12712
C13×#12702
#771413