Finite Group Databasebeta

← C13×#9529 #15695868

Subgroups — C13×#9529 #15695868

Order 3328.

468 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3109C211yesmaximal, characteristic
2C13×#2981C211yesmaximal, characteristic, complemented
3C13×#1557C211yesmaximal, characteristic, complemented
4C13×#1486C211yesmaximal, characteristic, complemented
5C13×#1466C211yesmaximal, characteristic, complemented
6C13×#1307C211yesmaximal, characteristic, complemented
7C13×#1287C211yesmaximal, characteristic, complemented
8C13×#532C2211yescharacteristic
9C2×C4×D4×C13C2211yescharacteristic
10C13×#481C412yes—
11C13×#476—21no—
12C13×#459—21no—
13C13×#447C412yes—
14C13×#442—22no—
15C13×#436—21no—
16C13×#435—22no—
17C8×D4×C13—21no—
18C13×#432C2211yescharacteristic
19C13×#432C2211yescharacteristic
20C13×#432C2211yescharacteristic
21C13×#431C2211yescharacteristic
22C13×#423C2211yescharacteristic
23C13×#408—22no—
24C13×#332—21no—
25C13×#331—21no—
26C13×D4⋊C8—21no—
27C13×D4⋊C8—21no—
28C13×#323—22no—
29C2×C13×#41—21no—
30C22×D4×C13C2×C411yescharacteristic
31C23×C4×C13—21no—
32C2×C13×D8—22no—
33C2×C13×M16—22no—
34C2×C13×M16—21no—
35C22×C8×C13—22no—
36C13×C4⋊Q8D411yescharacteristic
37C13×#127D411yescharacteristic
38C13×#124—21no—
39C13×#121—21no—
40C13×#121C2×C412yes—
41C4×D4×C13—21no—
42C4×D4×C13—21no—
43C4×D4×C13—21no—
44C4×D4×C13—21no—
45C4×D4×C13—21no—
46C4×D4×C13D412yes—
47C2×C13×C4⋊C4C2×C411yescharacteristic
48C2×C13×C22⋊C4—21no—
49C2×C42×C13C2311yescharacteristic
50C13×#106—22no—
51C13×C4⋊C8—21no—
52C13×C4⋊C8—21no—
53C13×C4⋊C8—21no—
54C13×C4⋊C8—21no—
55C13×C4⋊C8—21no—
56C13×C4⋊C8—21no—
57C13×#102—22no—
58C13×#102—22no—
59C13×C22⋊C8—22no—
60C13×C22⋊C8—22no—
61C13×C22⋊C8—21no—
62C13×C22⋊C8—21no—
63C13×C22⋊C8C2×C412yes—
64C13×C22⋊C8D412yes—
65C13×#97—21no—
66C13×#97—21no—
67C13×#97—21no—
68C4×C8×C13D411yescharacteristic
69C4×C8×C13D411yescharacteristic
70#9529C1311yesmaximal, characteristic, direct product factor, Sylow
71C24×C13—21no—
72C13×#41—82no—
73C2×Q8×C13—21no—
74C2×D4×C13—22no—
75C2×D4×C13—21no—
76C2×D4×C13—21no—
77C2×D4×C13—21no—
78C2×D4×C13—21no—
79C2×D4×C13—42no—
80C2×D4×C13C22⋊C412yes—
81C22×C4×C13—22no—
82C22×C4×C13—21no—
83C22×C4×C13—41no—
84C22×C4×C13—41no—
85C22×C4×C13—81no—
86C22×C4×C13—81no—
87C22×C4×C13C22×C411yescharacteristic
88C22×C4×C13C2×D411yescharacteristic
89C22×C4×C13#4111yescharacteristic
90C13×D8—44no—
91C13×M16—82no—
92C13×M16—81no—
93C2×C8×C13—22no—
94C2×C8×C13—21no—
95C2×C8×C13—21no—
96C2×C8×C13—22no—
97C2×C8×C13—41no—
98C2×C8×C13—41no—
99C2×C8×C13—82no—
100C13×C4⋊C4—21no—
101C13×C4⋊C4—21no—
102C13×C4⋊C4—21no—
103C13×C4⋊C4C22⋊C412yes—
104C13×C22⋊C4—22no—
105C13×C22⋊C4—22no—
106C13×C22⋊C4—41no—
107C13×C22⋊C4—41no—
108C42×C13C2×D411yescharacteristic
109C42×C13C2×D411yescharacteristic
110C42×C13C2×D411yescharacteristic
111C42×C13#4111yescharacteristic
112#3109C2×C1311yescharacteristic
113#2981C2×C1311yescharacteristic, complemented
114#1557C2×C1311yescharacteristic, complemented
115#1486C2×C1311yescharacteristic, complemented
116#1466C2×C1311yescharacteristic, complemented
117#1307C2×C1311yescharacteristic, complemented
118#1287C2×C1311yescharacteristic, complemented
119C23×C13—22no—
120C23×C13—22no—
121C23×C13—41no—
122C23×C13—41no—
123C23×C13—81no—
124C23×C13—81no—
125C23×C13C4×D411yescharacteristic
126Q8×C13—81no—
127D4×C13—22no—
128D4×C13—22no—
129D4×C13—41no—
130D4×C13—41no—
131D4×C13—42no—
132D4×C13—41no—
133D4×C13—41no—
134D4×C13—81no—
135D4×C13—82no—
136C2×C4×C13—21no—
137C2×C4×C13—21no—
138C2×C4×C13—22no—
139C2×C4×C13—41no—
140C2×C4×C13—41no—
141C2×C4×C13—42no—
142C2×C4×C13—42no—
143C2×C4×C13—41no—
144C2×C4×C13—82no—
145C2×C4×C13—81no—
146C2×C4×C13—81no—
147C2×C4×C13—81no—
148C2×C4×C13C2×C22⋊C411yescharacteristic
149C2×C4×C13C4×D411yescharacteristic
150C2×C4×C13#12011yescharacteristic
151C2×C4×C13#12111yescharacteristic
152C2×C4×C13#12111yescharacteristic
153C2×C4×C13#12311yescharacteristic
154C8×C13—41no—
155C8×C13—42no—
156C8×C13—41no—
157C8×C13—42no—
158C8×C13—81no—
159C8×C13—81no—
160#532C22×C1311yescharacteristic
161C2×C4×D4C22×C1311yescharacteristic
162#481C4×C1312yes—
163#476—21no—
164#459—21no—
165#447C4×C1312yes—
166#442—22no—
167#436—21no—
168#435—22no—
169C8×D4—21no—
170#432C22×C1311yescharacteristic
171#432C22×C1311yescharacteristic
172#432C22×C1311yescharacteristic
173#431C22×C1311yescharacteristic
174#423C22×C1311yescharacteristic
175#408—22no—
176#332—21no—
177#331—21no—
178D4⋊C8—21no—
179D4⋊C8—21no—
180#323—22no—
181C22×C13—21no—
182C22×C13—21no—
183C22×C13—21no—
184C22×C13—42no—
185C22×C13—42no—
186C22×C13—42no—
187C22×C13—42no—
188C22×C13—82no—
189C22×C13—82no—
190C22×C13—81no—
191C22×C13—81no—
192C22×C13#38611yescharacteristic
193C4×C13—21no—
194C4×C13—21no—
195C4×C13—21no—
196C4×C13—21no—
197C4×C13—21no—
198C4×C13—42no—
199C4×C13—81no—
200C4×C13#47111yescharacteristic
201C4×C13#47211yescharacteristic
202C2×#41—21no—
203C22×D4C2×C4×C1311yescharacteristic
204C23×C4—21no—
205C2×D8—22no—
206C2×M16—22no—
207C2×M16—21no—
208C22×C8—22no—
209C4⋊Q8D4×C1311yescharacteristic
210#127D4×C1311yescharacteristic
211#124—21no—
212#121—21no—
213#121C2×C4×C1312yes—
214C4×D4—21no—
215C4×D4—21no—
216C4×D4—21no—
217C4×D4—21no—
218C4×D4—21no—
219C4×D4D4×C1312yes—
220C2×C4⋊C4C2×C4×C1311yescharacteristic
221C2×C22⋊C4—21no—
222C2×C42C23×C1311yescharacteristic
223#106—22no—
224C4⋊C8—21no—
225C4⋊C8—21no—
226C4⋊C8—21no—
227C4⋊C8—21no—
228C4⋊C8—21no—
229C4⋊C8—21no—
230#102—22no—
231#102—22no—
232C22⋊C8—22no—
233C22⋊C8—22no—
234C22⋊C8—21no—
235C22⋊C8—21no—
236C22⋊C8C2×C4×C1312yes—
237C22⋊C8D4×C1312yes—
238#97—21no—
239#97—21no—
240#97—21no—
241C4×C8D4×C1311yescharacteristic
242C4×C8D4×C1311yescharacteristic
243C2×C13—41no—
244C2×C13—82no—
245C2×C13—82no—
246C2×C13#189111yescharacteristic
247C2×C13#190411yescharacteristic
248C2×C13#190711yescharacteristic
249C24—21no—
250#41—82no—
251C2×Q8—21no—
252C2×D4—22no—
253C2×D4—21no—
254C2×D4—21no—
255C2×D4—21no—
256C2×D4—21no—
257C2×D4—42no—
258C2×D4C13×C22⋊C412yes—
259C22×C4—22no—
260C22×C4—21no—
261C22×C4—41no—
262C22×C4—41no—
263C22×C4—81no—
264C22×C4—81no—
265C22×C4C22×C4×C1311yescharacteristic
266C22×C4C2×D4×C1311yescharacteristic
267C22×C4C13×#4111yescharacteristic
268D8—44no—
269M16—82no—
270M16—81no—
271C2×C8—22no—
272C2×C8—21no—
273C2×C8—21no—
274C2×C8—22no—
275C2×C8—41no—
276C2×C8—41no—
277C2×C8—82no—
278C4⋊C4—21no—
279C4⋊C4—21no—
280C4⋊C4—21no—
281C4⋊C4C13×C22⋊C412yes—
282C22⋊C4—22no—
283C22⋊C4—22no—
284C22⋊C4—41no—
285C22⋊C4—41no—
286C42C2×D4×C1311yescharacteristic
287C42C2×D4×C1311yescharacteristic
288C42C2×D4×C1311yescharacteristic
289C42C13×#4111yescharacteristic
290C13#952911yescharacteristic, direct product factor, Sylow
291C23—22no—
292C23—22no—
293C23—41no—
294C23—41no—
295C23—81no—
296C23—81no—
297C23C4×D4×C1311yescharacteristic
298Q8—81no—
299D4—22no—
300D4—22no—
301D4—42no—
302D4—41no—
303D4—41no—
304D4—41no—
305D4—41no—
306D4—81no—
307D4—82no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—22no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—41no—
316C2×C4—82no—
317C2×C4—81no—
318C2×C4—81no—
319C2×C4—81no—
320C2×C4C2×C13×C22⋊C411yescharacteristic
321C2×C4C4×D4×C1311yescharacteristic
322C2×C4C13×#12011yescharacteristic
323C2×C4C13×#12111yescharacteristic
324C2×C4C13×#12111yescharacteristic
325C2×C4C13×#12311yescharacteristic
326C8—41no—
327C8—42no—
328C8—41no—
329C8—42no—
330C8—81no—
331C8—81no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—42no—
336C22—42no—
337C22—42no—
338C22—42no—
339C22—82no—
340C22—82no—
341C22—81no—
342C22—81no—
343C22C13×#38611yescharacteristic
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—21no—
349C4—42no—
350C4—81no—
351C4C13×#47111yescharacteristic
352C4C13×#47211yescharacteristic
353C2—41no—
354C2—82no—
355C2—82no—
356C2C13×#189111yescharacteristic
357C2C13×#190411yescharacteristic
358C2C13×#190711yescharacteristic
subgroupG/H
center, socleC22×C13#386
commutatorC22×C4C22×C4×C13
Frattini, cosocleC2×C42C23×C13
prime radicalC13×#3109C2
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
2. C13×#2981C2semidirect
3. C13×#1557C2semidirect
4. C13×#1486C2semidirect
5. C13×#1466C2semidirect
6. C13×#1307C2semidirect
7. C13×#1287C2semidirect
70. #9529C13direct (N × H)
113. #2981C2×C13semidirect
114. #1557C2×C13semidirect
115. #1486C2×C13semidirect
116. #1466C2×C13semidirect
117. #1307C2×C13semidirect
118. #1287C2×C13semidirect
290. C13#9529direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#31092
C13×#29812
C13×#15572
C13×#14862
C13×#14662
C13×#13072
C13×#12872
#952913