Finite Group Databasebeta

← C13×#7686 #15694025

Subgroups — C13×#7686 #15694025

Order 3328.

464 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#2860C211yesmaximal, characteristic
2C13×#1767C211yesmaximal, characteristic, complemented
3C4×C13×C4⋊C8C211yesmaximal, characteristic, complemented
4C13×#1271C212yesmaximal, complemented
5C13×#1270C212yesmaximal
6C2×C13×#126—21no—
7C2×C13×C4⋊C8—21no—
8C2×C13×C4⋊C8—21no—
9C2×C13×#97—21no—
10C2×C4×C8×C13—21no—
11C13×#390C411yescharacteristic
12C13×#390C411yescharacteristic
13C13×#390C2211yescharacteristic
14C13×#389C411yescharacteristic
15C13×#389C411yescharacteristic
16C13×#389C2211yescharacteristic
17C13×#388—21no—
18C13×#388—21no—
19C13×#388—21no—
20C43×C13C2211yescharacteristic
21C13×#336C2212yes—
22C13×#336C2212yes—
23C22×D4×C13C2×C411yescharacteristic
24C22×C8×C13—22no—
25C22×C8×C13—22no—
26C13×#126—42no—
27C13×#126—42no—
28C2×C13×C4⋊C4—21no—
29C2×C13×C4⋊C4—21no—
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4C2×C411yescharacteristic
32C2×C13×C4⋊C4C2×C411yescharacteristic
33C2×C13×C4⋊C4C2×C411yescharacteristic
34C2×C13×C22⋊C4—21no—
35C2×C13×C22⋊C4—21no—
36C2×C13×C22⋊C4—21no—
37C2×C13×C22⋊C4—21no—
38C2×C13×C22⋊C4—21no—
39C2×C13×C22⋊C4—21no—
40C2×C42×C13C2×C411yescharacteristic
41C2×C42×C13C2×C411yescharacteristic
42C2×C42×C13D411yescharacteristic
43C2×C42×C13D411yescharacteristic
44C2×C42×C13D411yescharacteristic
45C2×C42×C13D411yescharacteristic
46C2×C42×C13C2311yescharacteristic
47C13×C4⋊C8—24no—
48C13×C4⋊C8—24no—
49C13×#97—42no—
50C4×C8×C13—42no—
51C13×#95—21no—
52C13×#95—21no—
53C13×#95—21no—
54#7686C1311yesmaximal, characteristic, direct product factor, Sylow
55C24×C13—21no—
56C2×D4×C13—22no—
57C2×D4×C13—41no—
58C2×D4×C13—41no—
59C22×C4×C13—21no—
60C22×C4×C13—21no—
61C22×C4×C13—21no—
62C22×C4×C13C22⋊C411yescharacteristic
63C22×C4×C13C22⋊C411yescharacteristic
64C22×C4×C13C22⋊C411yescharacteristic
65C22×C4×C13C22⋊C411yescharacteristic
66C22×C4×C13C22×C411yescharacteristic
67C22×C4×C13C2×D411yescharacteristic
68C22×C4×C13C2×D411yescharacteristic
69C2×C8×C13—24no—
70C2×C8×C13—24no—
71C2×C8×C13—42no—
72C2×C8×C13—42no—
73C2×C8×C13—42no—
74C2×C8×C13—42no—
75C13×C4⋊C4—22no—
76C13×C4⋊C4—41no—
77C13×C4⋊C4—41no—
78C13×C4⋊C4—42no—
79C13×C4⋊C4—42no—
80C13×C4⋊C4—41no—
81C13×C4⋊C4—41no—
82C13×C22⋊C4—42no—
83C13×C22⋊C4—42no—
84C13×C22⋊C4—42no—
85C13×C22⋊C4—42no—
86C13×C22⋊C4—41no—
87C13×C22⋊C4—41no—
88C13×C22⋊C4—41no—
89C13×C22⋊C4—41no—
90C42×C13—22no—
91C42×C13—22no—
92C42×C13—22no—
93C42×C13—21no—
94C42×C13—21no—
95C42×C13—41no—
96C42×C13—41no—
97C42×C13D812yes—
98C42×C13SD1612yes—
99#2860C2×C1311yescharacteristic
100#1767C2×C1311yescharacteristic, complemented
101C4×C4⋊C8C2×C1311yescharacteristic, complemented
102#1271C2×C1312yescomplemented
103#1270C2×C1312yes—
104C23×C13—41no—
105C23×C13—41no—
106C23×C13—41no—
107C23×C13—41no—
108C23×C13—41no—
109C23×C13—41no—
110C23×C13—41no—
111C23×C13C2×C22⋊C411yescharacteristic
112D4×C13—82no—
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13—21no—
124C2×C4×C13—21no—
125C2×C4×C13—21no—
126C2×C4×C13—21no—
127C2×C4×C13—41no—
128C2×C4×C13—41no—
129C2×C4×C13—41no—
130C2×C4×C13—41no—
131C2×C4×C13—41no—
132C2×C4×C13—41no—
133C2×C4×C13—41no—
134C2×C4×C13—41no—
135C2×C4×C13—41no—
136C2×C4×C13#10212yes—
137C2×C4×C13#10212yes—
138C2×C4×C13#10412yes—
139C2×C4×C13#10412yes—
140C2×C4×C13#13112yes—
141C2×C4×C13C2×D811yescharacteristic
142C2×C4×C13C2×SD1611yescharacteristic
143C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
144C2×C4×C13#13711yescharacteristic
145C8×C13—44no—
146C8×C13—44no—
147C2×#126—21no—
148C2×C4⋊C8—21no—
149C2×C4⋊C8—21no—
150C2×#97—21no—
151C2×C4×C8—21no—
152#390C4×C1311yescharacteristic
153#390C4×C1311yescharacteristic
154#390C22×C1311yescharacteristic
155#389C4×C1311yescharacteristic
156#389C4×C1311yescharacteristic
157#389C22×C1311yescharacteristic
158#388—21no—
159#388—21no—
160#388—21no—
161C43C22×C1311yescharacteristic
162#336C22×C1312yes—
163#336C22×C1312yes—
164C22×C13—81no—
165C22×C13—81no—
166C22×C13—81no—
167C22×C13—81no—
168C22×C13—81no—
169C22×C13—81no—
170C22×C13—81no—
171C22×C13#40811yescharacteristic
172C22×C13#41011yescharacteristic
173C22×C13#41311yescharacteristic
174C22×C13C2×#10211yescharacteristic
175C22×C13#41711yescharacteristic
176C22×C13C2×#10411yescharacteristic
177C22×C13C2×#10411yescharacteristic
178C4×C13—22no—
179C4×C13—22no—
180C4×C13—22no—
181C4×C13—22no—
182C4×C13—21no—
183C4×C13—21no—
184C4×C13—21no—
185C4×C13—21no—
186C4×C13—22no—
187C4×C13—81no—
188C4×C13—81no—
189C4×C13—81no—
190C22×D4C2×C4×C1311yescharacteristic
191C22×C8—22no—
192C22×C8—22no—
193#126—42no—
194#126—42no—
195C2×C4⋊C4—21no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4C2×C4×C1311yescharacteristic
199C2×C4⋊C4C2×C4×C1311yescharacteristic
200C2×C4⋊C4C2×C4×C1311yescharacteristic
201C2×C22⋊C4—21no—
202C2×C22⋊C4—21no—
203C2×C22⋊C4—21no—
204C2×C22⋊C4—21no—
205C2×C22⋊C4—21no—
206C2×C22⋊C4—21no—
207C2×C42C2×C4×C1311yescharacteristic
208C2×C42C2×C4×C1311yescharacteristic
209C2×C42D4×C1311yescharacteristic
210C2×C42D4×C1311yescharacteristic
211C2×C42D4×C1311yescharacteristic
212C2×C42D4×C1311yescharacteristic
213C2×C42C23×C1311yescharacteristic
214C4⋊C8—24no—
215C4⋊C8—24no—
216#97—42no—
217C4×C8—42no—
218#95—21no—
219#95—21no—
220#95—21no—
221C2×C13—161no—
222C2×C13#147311yescharacteristic
223C2×C13#148311yescharacteristic
224C2×C13#149211yescharacteristic
225C2×C13#150211yescharacteristic
226C2×C13#150911yescharacteristic
227C2×C13#152411yescharacteristic
228C2×C13#154711yescharacteristic
229C24—21no—
230C2×D4—22no—
231C2×D4—41no—
232C2×D4—41no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4C13×C22⋊C411yescharacteristic
237C22×C4C13×C22⋊C411yescharacteristic
238C22×C4C13×C22⋊C411yescharacteristic
239C22×C4C13×C22⋊C411yescharacteristic
240C22×C4C22×C4×C1311yescharacteristic
241C22×C4C2×D4×C1311yescharacteristic
242C22×C4C2×D4×C1311yescharacteristic
243C2×C8—24no—
244C2×C8—24no—
245C2×C8—42no—
246C2×C8—42no—
247C2×C8—42no—
248C2×C8—42no—
249C4⋊C4—22no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—42no—
253C4⋊C4—42no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C22⋊C4—42no—
257C22⋊C4—42no—
258C22⋊C4—42no—
259C22⋊C4—42no—
260C22⋊C4—41no—
261C22⋊C4—41no—
262C22⋊C4—41no—
263C22⋊C4—41no—
264C42—22no—
265C42—22no—
266C42—22no—
267C42—21no—
268C42—21no—
269C42—41no—
270C42—41no—
271C42C13×D812yes—
272C42C13×SD1612yes—
273C13#768611yescharacteristic, direct product factor, Sylow
274C23—41no—
275C23—41no—
276C23—41no—
277C23—41no—
278C23—41no—
279C23—41no—
280C23—41no—
281C23C2×C13×C22⋊C411yescharacteristic
282D4—82no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4C13×#10212yes—
307C2×C4C13×#10212yes—
308C2×C4C13×#10412yes—
309C2×C4C13×#10412yes—
310C2×C4C13×#13112yes—
311C2×C4C2×C13×D811yescharacteristic
312C2×C4C2×C13×SD1611yescharacteristic
313C2×C4C13×AGL(1,ℤ/8)11yescharacteristic
314C2×C4C13×#13711yescharacteristic
315C8—44no—
316C8—44no—
317C22—81no—
318C22—81no—
319C22—81no—
320C22—81no—
321C22—81no—
322C22—81no—
323C22—81no—
324C22C13×#40811yescharacteristic
325C22C13×#41011yescharacteristic
326C22C13×#41311yescharacteristic
327C22C2×C13×#10211yescharacteristic
328C22C13×#41711yescharacteristic
329C22C2×C13×#10411yescharacteristic
330C22C2×C13×#10411yescharacteristic
331C4—22no—
332C4—22no—
333C4—22no—
334C4—21no—
335C4—21no—
336C4—21no—
337C4—21no—
338C4—22no—
339C4—22no—
340C4—81no—
341C4—81no—
342C4—81no—
343C2—161no—
344C2C13×#147311yescharacteristic
345C2C13×#148311yescharacteristic
346C2C13×#149211yescharacteristic
347C2C13×#150211yescharacteristic
348C2C13×#150911yescharacteristic
349C2C13×#152411yescharacteristic
350C2C13×#154711yescharacteristic
subgroupG/H
center, socleC23×C13C2×C22⋊C4
commutatorC22×C4C22×C4×C13
Frattini, cosocleC2×C42C23×C13
prime radicalC22×D4×C13C2×C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C13 ◁ C43×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C13×#1767C2semidirect
3. C4×C13×C4⋊C8C2semidirect
4. C13×#1271C2semidirect
54. #7686C13direct (N × H)
100. #1767C2×C13semidirect
101. C4×C4⋊C8C2×C13semidirect
102. #1271C2×C13semidirect
273. C13#7686direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#28602
C13×#17672
C4×C13×C4⋊C82
C13×#12712
C13×#12702
#768613