Finite Group Databasebeta

← C13×#9867 #15696206

Subgroups — C13×#9867 #15696206

Order 3328.

460 conjugacy classes of subgroups.

The subgroup lattice has 326 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C13×#125C211yesmaximal, characteristic
2C13×#1767C211yesmaximal, characteristic
3C4×C13×C4⋊C8C211yesmaximal, characteristic
4C13×#1279C212yesmaximal
5C13×#1279C212yesmaximal
6C2×C13×#125C411yescharacteristic
7C2×C13×C4⋊C8—21no—
8C2×C13×C4⋊C8C2212yes—
9C2×C13×#97—21no—
10C2×C4×C8×C13C2212yes—
11C13×#389C411yescharacteristic
12C13×#389C411yescharacteristic
13C13×#387—21no—
14C13×#387—21no—
15C13×#382C411yescharacteristic
16C4×C13×C4⋊C4—21no—
17C4×C13×C4⋊C4—21no—
18C4×C13×C4⋊C4C2211yescharacteristic
19C4×C13×C4⋊C4C2211yescharacteristic
20C43×C13C2211yescharacteristic
21C13×#336—21no—
22C13×#336—21no—
23C22×C8×C13—22no—
24C22×C8×C13—22no—
25C13×#125—22no—
26C13×#125—22no—
27C2×C13×C4⋊C4—21no—
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×C4⋊C4C2×C411yescharacteristic
35C2×C42×C13—21no—
36C2×C42×C13—21no—
37C2×C42×C13C2×C411yescharacteristic
38C2×C42×C13C2×C411yescharacteristic
39C2×C42×C13D411yescharacteristic
40C2×C42×C13D411yescharacteristic
41C2×C42×C13D411yescharacteristic
42C2×C42×C13D411yescharacteristic
43C2×C42×C13C2311yescharacteristic
44C13×C4⋊C8—24no—
45C13×C4⋊C8—22no—
46C13×C4⋊C8Q814yes—
47C13×#97—42no—
48C4×C8×C13—24no—
49C13×#95—21no—
50C13×#95—21no—
51C13×#95—21no—
52C13×#95—21no—
53C13×#95—21no—
54C13×#95—21no—
55#9867C1311yesmaximal, characteristic, direct product factor, Sylow
56C22×C4×C13—21no—
57C22×C4×C13—21no—
58C22×C4×C13—21no—
59C22×C4×C13—21no—
60C22×C4×C13C22⋊C411yescharacteristic
61C22×C4×C13C22⋊C411yescharacteristic
62C22×C4×C13C22⋊C411yescharacteristic
63C22×C4×C13C22⋊C411yescharacteristic
64C22×C4×C13C22×C411yescharacteristic
65C22×C4×C13C2×D411yescharacteristic
66C22×C4×C13C2×D411yescharacteristic
67C2×C8×C13—24no—
68C2×C8×C13—24no—
69C2×C8×C13—42no—
70C2×C8×C13—42no—
71C2×C8×C13—42no—
72C2×C8×C13—42no—
73C13×C4⋊C4—24no—
74C13×C4⋊C4—24no—
75C13×C4⋊C4—21no—
76C13×C4⋊C4—21no—
77C13×C4⋊C4—22no—
78C13×C4⋊C4—22no—
79C13×C4⋊C4—42no—
80C13×C4⋊C4—42no—
81C13×C4⋊C4M1612yes—
82C13×C4⋊C4M1612yes—
83C42×C13—22no—
84C42×C13—21no—
85C42×C13—21no—
86C42×C13—22no—
87C42×C13—22no—
88C42×C13—21no—
89C42×C13—21no—
90C42×C13—41no—
91C42×C13—42no—
92C42×C13—41no—
93C42×C13—41no—
94C42×C13C2×Q812yes—
95C42×C13#4112yes—
96C4×#125C2×C1311yescharacteristic
97#1767C2×C1311yescharacteristic
98C4×C4⋊C8C2×C1311yescharacteristic
99#1279C2×C1312yes—
100#1279C2×C1312yes—
101C23×C13C2×C22⋊C411yescharacteristic
102C2×C4×C13—21no—
103C2×C4×C13—21no—
104C2×C4×C13—21no—
105C2×C4×C13—21no—
106C2×C4×C13—21no—
107C2×C4×C13—21no—
108C2×C4×C13—22no—
109C2×C4×C13—22no—
110C2×C4×C13—21no—
111C2×C4×C13—21no—
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—41no—
118C2×C4×C13—41no—
119C2×C4×C13—41no—
120C2×C4×C13—41no—
121C2×C4×C13—41no—
122C2×C4×C13—41no—
123C2×C4×C13—41no—
124C2×C4×C13—41no—
125C2×C4×C13—41no—
126C2×C4×C13—41no—
127C2×C4×C13#10412yes—
128C2×C4×C13C4×Q812yes—
129C2×C4×C13C22⋊Q812yes—
130C2×C4×C13#12411yescharacteristic
131C2×C4×C13C4⋊Q811yescharacteristic
132C2×C4×C13C2×M1611yescharacteristic
133C2×C4×C13C2×M1611yescharacteristic
134C2×C4×C13#13112yes—
135C2×C4×C13#13512yes—
136C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
137C2×C4×C13#13711yescharacteristic
138C8×C13—44no—
139C8×C13—44no—
140C2×#125C4×C1311yescharacteristic
141C2×C4⋊C8—21no—
142C2×C4⋊C8C22×C1312yes—
143C2×#97—21no—
144C2×C4×C8C22×C1312yes—
145#389C4×C1311yescharacteristic
146#389C4×C1311yescharacteristic
147#387—21no—
148#387—21no—
149#382C4×C1311yescharacteristic
150C4×C4⋊C4—21no—
151C4×C4⋊C4—21no—
152C4×C4⋊C4C22×C1311yescharacteristic
153C4×C4⋊C4C22×C1311yescharacteristic
154C43C22×C1311yescharacteristic
155#336—21no—
156#336—21no—
157C22×C13#39111yescharacteristic
158C22×C13#40711yescharacteristic
159C22×C13#40811yescharacteristic
160C22×C13#41611yescharacteristic
161C22×C13#41711yescharacteristic
162C22×C13C2×#10411yescharacteristic
163C22×C13#42111yescharacteristic
164C4×C13—21no—
165C4×C13—21no—
166C4×C13—22no—
167C4×C13—41no—
168C4×C13—42no—
169C4×C13—41no—
170C4×C13—42no—
171C4×C13—41no—
172C4×C13—81no—
173C4×C13—81no—
174C4×C13#44612yes—
175C4×C13#44612yes—
176C4×C13#47812yes—
177C4×C13#47912yes—
178C22×C8—22no—
179C22×C8—22no—
180#125—22no—
181#125—22no—
182C2×C4⋊C4—21no—
183C2×C4⋊C4—21no—
184C2×C4⋊C4—21no—
185C2×C4⋊C4—21no—
186C2×C4⋊C4C2×C4×C1311yescharacteristic
187C2×C4⋊C4C2×C4×C1311yescharacteristic
188C2×C4⋊C4C2×C4×C1311yescharacteristic
189C2×C4⋊C4C2×C4×C1311yescharacteristic
190C2×C42—21no—
191C2×C42—21no—
192C2×C42C2×C4×C1311yescharacteristic
193C2×C42C2×C4×C1311yescharacteristic
194C2×C42D4×C1311yescharacteristic
195C2×C42D4×C1311yescharacteristic
196C2×C42D4×C1311yescharacteristic
197C2×C42D4×C1311yescharacteristic
198C2×C42C23×C1311yescharacteristic
199C4⋊C8—24no—
200C4⋊C8—22no—
201C4⋊C8Q8×C1314yes—
202#97—42no—
203C4×C8—24no—
204#95—21no—
205#95—21no—
206#95—21no—
207#95—21no—
208#95—21no—
209#95—21no—
210C2×C13#148811yescharacteristic
211C2×C13#148911yescharacteristic
212C2×C13#149411yescharacteristic
213C2×C13#149511yescharacteristic
214C2×C13#198511yescharacteristic
215C2×C13#198611yescharacteristic
216C2×C13#198911yescharacteristic
217C22×C4—21no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4C13×C22⋊C411yescharacteristic
222C22×C4C13×C22⋊C411yescharacteristic
223C22×C4C13×C22⋊C411yescharacteristic
224C22×C4C13×C22⋊C411yescharacteristic
225C22×C4C22×C4×C1311yescharacteristic
226C22×C4C2×D4×C1311yescharacteristic
227C22×C4C2×D4×C1311yescharacteristic
228C2×C8—24no—
229C2×C8—24no—
230C2×C8—42no—
231C2×C8—42no—
232C2×C8—42no—
233C2×C8—42no—
234C4⋊C4—24no—
235C4⋊C4—24no—
236C4⋊C4—21no—
237C4⋊C4—21no—
238C4⋊C4—22no—
239C4⋊C4—22no—
240C4⋊C4—42no—
241C4⋊C4—42no—
242C4⋊C4C13×M1612yes—
243C4⋊C4C13×M1612yes—
244C42—22no—
245C42—21no—
246C42—21no—
247C42—22no—
248C42—22no—
249C42—21no—
250C42—21no—
251C42—41no—
252C42—42no—
253C42—41no—
254C42—41no—
255C42C2×Q8×C1312yes—
256C42C13×#4112yes—
257C13#986711yescharacteristic, direct product factor, Sylow
258C23C2×C13×C22⋊C411yescharacteristic
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—22no—
266C2×C4—22no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4C13×#10412yes—
285C2×C4C4×Q8×C1312yes—
286C2×C4C13×C22⋊Q812yes—
287C2×C4C13×#12411yescharacteristic
288C2×C4C13×C4⋊Q811yescharacteristic
289C2×C4C2×C13×M1611yescharacteristic
290C2×C4C2×C13×M1611yescharacteristic
291C2×C4C13×#13112yes—
292C2×C4C13×#13512yes—
293C2×C4C13×AGL(1,ℤ/8)11yescharacteristic
294C2×C4C13×#13711yescharacteristic
295C8—44no—
296C8—44no—
297C22C13×#39111yescharacteristic
298C22C13×#40711yescharacteristic
299C22C13×#40811yescharacteristic
300C22C13×#41611yescharacteristic
301C22C13×#41711yescharacteristic
302C22C2×C13×#10411yescharacteristic
303C22C13×#42111yescharacteristic
304C4—21no—
305C4—21no—
306C4—22no—
307C4—41no—
308C4—42no—
309C4—41no—
310C4—42no—
311C4—41no—
312C4—81no—
313C4—81no—
314C4C13×#44612yes—
315C4C13×#44612yes—
316C4C13×#47812yes—
317C4C13×#47912yes—
318C2C13×#148811yescharacteristic
319C2C13×#148911yescharacteristic
320C2C13×#149411yescharacteristic
321C2C13×#149511yescharacteristic
322C2C13×#198511yescharacteristic
323C2C13×#198611yescharacteristic
324C2C13×#198911yescharacteristic
subgroupG/H
centerC22×C4×C13C2×D4
commutatorC22×C4C22×C4×C13
Frattini, cosocleC2×C42C23×C13
socle, prime radicalC23×C13C2×C22⋊C4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4×C13 ◁ C43×C13 ◁ G

Complements

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

NH ≅ G/Ntype
55. #9867C13direct (N × H)
257. C13#9867direct (N × H)

Maximal subgroups

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

subgroupindex
C4×C13×#1252
C13×#17672
C4×C13×C4⋊C82
C13×#12792
#986713